Day 123 – Practicing Math Live – Ch. 1 Numbers

Hey, what's going on YouTube? Uh, another day practicing basic mathematics. This book by Sarah Lang. I'm freaking stoked for this.

Um, so it's been a couple of days since we posted that uh introduction to introduction to the series video. Uh, and it's it's been freaking blowing up, man. It's absolutely crazy. Uh, I've never seen anything like this before in five years or so of six years of being on YouTube. It's, uh, you know, I'm just so absolutely grateful for everybody who's joined. Um, people who have joined in the chat, in the Discord, all the comments. Um, I tried catching up on some of the comments last night, but holy crap, there's a lot of comments.

So, you'll notice that I um first off, like I I think just default policy. I just I'm going to like and heart every single comment. Like, who cares, dude? Um part of the reason for that though, if your comment hasn't been hearted, it's a funny thing that I want to just tell you a story about.

Um uh I'll I'll put this up so that people know that we will actually do math. I promise. Um, we're not going to do multiplication today. Um, I changed my mind. I want to stay. Let's do another video on addition. I think uh although I don't know, maybe more more maybe. We'll see. We'll see what happens.

Um, I'm very frazzled. I did not sleep well last night. Luna woke me up in the middle of the night and I couldn't go back to bed. She woke me up in the middle of the night and then I checked my phone and I, you know, just dude like phone hygiene is such a thing. [music] I need to get one of those like lock boxes that you can put in another room and like you have to, you know, do some math problems or something. [laughter]

Uh, hey Eluki, good to see you, bro. Good to see you. We got some some of the homies in the chat right now. What's up, dude? You low-key want to study some physics? Somebody left a really nice comment in the video that was like, "Bro, like I really hope that after you're done with this book, like do all of physics." I'm like, "Yeah, I would love to. I would absolutely love to if I had infinite time. I I would be stoked um to study physics again. I miss physics, but uh no, probably not at all." like, you know, numbers. I'm I'm going to be busy with numbers for a while. Just like simple numbers. Like I love the purity of math. Uh so this is legit a pure math book. There's a few physics problems in here, but not very many. Um so this is pure math book.

Um Oh gosh. Okay. So yeah, I was um I didn't sleep well last night, so I'm a little frazzled. We may not do the whole 3-hour live stream today, but that's okay. Um, there was something else I was about to go on a rant about. If somebody wants to remind me in the chat some of the things I was just saying.

The most important thing for me to say right now though, this is more important than whatever that was. Most important thing is what is the stream structure? What's happening? What is this compared to those other videos? Um, this is a totally different video. Okay? like the these daily streams are completely different. Um these are hangout sessions. It's kind of like an office hours. It's kind of like a hangout spot. Um sometimes I am just locked in and studying. Like some most of the time I have the iPad up and I'm taking notes and you can read my notebook as I um as I'm studying. Most of the time we're working problems actually. Uh sometimes I'm just taking notes though and sometimes I need to solve a problem and I'll just put Hawaii up or something or just like a camera on me like sometimes I need to be purely looking at the iPad on my own without you know chat and everything.

Um so this is not a lecture. Um you don't have to watch these. A lot of people have asked if they need to um if they if I recommend that they go and watch the the live stream VODs. No, no, no. I mean, if you want to just for fun, for some inspiration, maybe it's a different energy, obviously. Um but no. Uh if you're interested in joining the course on Serge Lang's basic mathematics, um you just need to wait for those blue videos. My face isn't in it. There's no, you know, there's no um no cats. Like I think the thumbnail for today has Luna in it. Does she show up on camera right now? Oh no, she's just barely off camera. Barely. Okay. Well, um yeah. So, I I think it'll be obvious as we do a couple more videos what those videos are like and how different they are versus these.

Um, I was thinking maybe the beginning of these videos are just kind of like little daily vlog 5 minutes or so talking, giving any kind of like housekeeping updates. Um, [music] you know, any sort of logistics like a lot of people have been emailing and asking about uh the paid course, which is amazing to me. Um, so I'm looking to create a little cohort of 10 people. [music] Uh, and we've definitely gotten more than 10 emails so far. Uh, three of the seats are are already taken. Um, so if you want to join the the cohort for weekend group, small groupoup study sessions, email me uh jc practices atgmail.com and uh I'd be happy to try to describe the vision [music] that I have. Uh, we might book a call so because it's just going to be easier for me to just say it, you know, and maybe record one of them and then just link that to future people. I don't know. I don't freaking know, dude.

Um, so, uh, that's the most important thing to say. If you want to follow this book, don't no, don't don't, um, don't only rely on my videos. If if you're serious about learning this book, definitely watch all of the blue videos, but you have to get the book, too, dude. You have to actually get the book. You can get it for free uh by renting it from your library. Um or you could [music] get it, you know, in paper for it if you know if you're in the position where you can.

One of my favorite things about paper books, dude, is like here. This first exercise, I haven't done it yet. Um where's my pen? Like this is crazy. I know this is like really wild to a lot of people, dude. I just cross out the problems. Every time I solve a problem, I just cross it out. Yoink. Right there. Um, and then that creates a nice little checklist. I don't take too many notes in the book. Some people scribble in the margins. I wish I was that kind of person, but I, you know, I cross off every exercise that I that I do, and it's just like it's delightful for me. Um, I have some other ideas about paper books, but like my point here about why I recommend it to you is [music] that paper is the most effective method, dude. Like there's no notifications. You know, Tik Tok is not just a swipe away. Like, dude, like paper books and the feeling of writing on paper with like literally pen or pencil. Um, it's going to help you connect with the math better. Like flipping pages back and forth quickly and being like, "Oh, you know, I I think it was over here in this part of the book was da da da." And like flipping and oh yeah, it's right here. This other part, let me jump back. Like, dude, this stuff goated. All right, paper books are goated. I mean, PDFs are amazing, too, and they have their benefits. And someday I'll argue why you should use PDFs instead. But um for this course, I recommend getting this book, you know, PDF form, freaking library loan form. You can get it from your library. You could buy it from Amazon. Whatever method you can um

Would I rather fight 200 duck-sized horses or one horses-sized duck? Let me think about that for a second. I've never actually given this one thought. Oh god. I would say one horsesized duck, I think. Yeah, for sure. Um, one horsesized duck. Dude, I feel like I could run faster than a horse-sized duck. I don't feel like ducks are fast. I don't feel like I've never thought of ducks being a fast, nimble animal. And I could just run away and then if I have to fight it, then I can like attack it from a distance, you know? I could like craft a bow and arrow and then just attack it from a distance if I have to attack it. Like if that's part of the of the game and I have to uh fight, I'd fight from a distance. One horse-sized duck for sure.

Um, hey, what's up, Arod? How's it going, dude? Uh, nice to hear how well it's going. Yeah, it's it's wild. Um, I'm a little frazzled today because I looked at my phone all night. Um, [laughter] accidentally. Accidentally. But it's Luna's fault. I wouldn't have done that, but Luna woke me up in the middle of the night and I just Luna, it's all your fault. It's all your fault. You're so cute.

Uh, tomorrow's your calculus exam. Let's go, Zakir. I'm happy for you. How do you feel about it? What topics? What topics are coming up on it? Are [music] you in derivatives or integration or series? Sequences and series. Speaking of sequences, um I consider myself an adventurer and my scribbling the mark of exploring new ground. Scribbling forever. That is so wholesome. I love it. Yeah, dude. Like, if we could get a bunch of people scribbling in paper math books in this chat, like, dude, that's like so painfully wholesome to me. That would be awesome. [laughter]

Um, heck yeah, dude. Nice to meet you, I think. Let me reread. Um, Atomic Baby, this is your first time here, right? I like your name. Uh, insert great username here. That's an awesome name. I like that one. You're so right about writing on paper. When I feel like nothing's sticking, I resort to good old writing for real. Dude, I keep telling the students, by the way, this is lore that I need to drop here cuz I've gotten a couple of random comments. Um, I do need to drop the lore that I do teach and I have been teaching. I've taught math for six years in total, six and a half. um four years uh as a tutor um running [music] the two years running the tutoring department in college um and tutoring all undergrad subjects that we taught. Um, and then now I've been tutoring for 2 and 1/2 years uh at a tutoring [music] center and dude I just love teaching a lot obviously otherwise I wouldn't be here. I like working with people in person, [music] you know, and like scribbling on paper with those people like together and being like, "Look, numbers. Yay." And and they get so excited and everything. So, um, when I say that I think some of these topics could work for for an honors algebra 1 course, what I really mean specifically is that an entire lesson plan, an entire structured course could be made out of this material. [music] I know for a fact that I can get individual students, multiple individual students interested in this stuff. Um, but I don't know if somebody could teach it instead of the regular stuff. [music] Like I do way fewer word problems. Like almost no word problems. I would like ban word problems almost in my classroom. And you know, not really. Not really. They are very valuable, but we just need to know their time and place for why we do word problems like and [music] understand it. Um, it's word problems are not math itself. Word problems are applying math. They're like applied math, but they're not even applied math. They're applying math to the real world, which is great. They're engineering. That's how you make money. You don't make money from art. You don't make money from from pure math.

Sup, geometry. How's it going, dude? Ducks walk clunky, so yes, you can be faster. Yeah, to me that's a no-brainer. I've never actually thought about it, but I think four for sure one horse-sized duck. Yeah. Um, what's up, geometry? Imagine 200 duck-sized horses biting your ankles. Yeah, that sounds awful. [music] Like small duck-sized horses. Like they sound fat. Horses are fast animals to begin with. Horses run so fast. just like a regular horse. So like I'm just imagining a small one that's like even more nimble. Like they would be like zooming around and like you know just like tackling you just like covering you and all like like biting at your ankles until you fall and then they like you know collectively take you down. That sounds horrible, dude. Um I can't even believe that that this is a real question [laughter] to me. like I've never given this real thought, but yeah, one duck sized horse, no doubt.

Um, hey, can you create a proper playlist or something for these lives? Yes, that's the other thing. I apologize, Uveh. I do have a playlist called fundamentals [music] and they've um Yeah, so the live I have lots of playlists and they're all organized to primarily um calculus, linear algebra, and representation theory. Um, [music] but right now we're starting this brand new series on fundamentals and there's live streams versus lecture videos. So, let's get back to that main thing. Let me write it down on the on the blackboard cuz this is important.

Dude, I have two different types of videos and they're very different. This is a live stream that we're in right now. Um, okay. So, we're in a live stream today and we also have lecture videos. Okay. So, we do both. We do live streams and we do lectures. Um, I think that episode 2 is dropping on Saturday. No, Sunday. Episode two. Um, so if you want to follow the lecture videos only, please feel free. Please be my guest. Um, I would tune into these every now and then, but like I would mostly personally be watching the lecture series. [music] Like if you want to really truly do math, like it just depends. If you want to vibe and just hang out and you don't care about math, but you just like the community and the chat and you just want to feel inspired to study your physics, that's awesome. Hang out here in the live stream. This is a nice little community of people who are studying, right? Oh, I forgot to go live on Twitch, too. My bad. Um, yeah, Twitch is kind of a second Yeah, second secondary priority.

Um, so, um, feel free to watch whatever you want to watch, dude. Like, I don't know. Someday maybe we'll do separate channels, but I'm not even monetized on this one, so, you know, someday maybe. [music] Um, too much work. Too much work.

Um, no way. You just bought a fresh box of pencils. Nice, dude. Nice. I will say I love pen. Okay. Okay, it's kind of hardcore mode, but like hear me out, okay? I do math in pen only. Like, I love writing math and pen. Hear me out. Um, first, I just I don't mind if I have to scribble stuff out. If I make a mistake and I have to scribble stuff and start on a new sheet and start over, I don't mind. So, like, dude, I don't know. Paper is recycled. I buy the recycled paper notebooks. I think all of them are now. So, it's not like paper is like in short supply, right? Paper is not in short supply. I don't mind tearing out a page and throwing it away. Um, [music] metaphorically, uh, and when you're writing and you're doing math in pen, it forces you to slow down and think about every single step like a little bit more carefully, like, wait a minute, is this true? you know, and it's like, yeah, I think that that's true. And then you write it down. Um, that skill and that that benefit is just a little bit more important once you [music] get to proof- based math like this stuff. If you're just doing calculations, I don't know. Somehow I would rather do it in pencil, maybe. I don't know. I don't know. But ever since I went to college and started learning uh real math, uh I started doing everything in pen and I like it. Maybe it's also I'm left-handed, so uh pencils smudge with my hand, but

All right. All right, let me read. First stream. What do we usually do here? What's up? Hey, are you a guitarist, by the way, dude? This is my second channel, bro. What's up, dude? Um y'all, I hope you uh give this a shot sometime. I'm also a classical guitarist and my primary channel that I've been running since um 2020 is uh dedicated to deliberate practice of classical guitar. [music] Um and I thought I was going to stream later today, but I don't think we will. So, this channel is JC Practices Math. The other one is just called JC Practices. Um, or now the display name now says JC practices guitar, but I just want to keep the short handle. You know what I mean?

Um, D. So, we study mathematics. To answer your question, to answer your question, we this is a hangout, office hours, chill study sesh. In a moment I'm going to lock in and try to study addition of positive numbers [music] um from this fantastic wonderful beautiful book. Um, so if you are super confused about what's happening, if that just conf gave you like five more questions, [music] um, dude, I'm going to call my mom later and tell her like, "Mama, I made it." Okay. So, uh, like, um, I've never seriously with a straight face said that I've made a viral video before in 6 years. Oh, shoot. My bad. My bad. Where is the My neck hurts, dude. Um, this is part of it. Like my Dang it. Where is it? This one? Is it that one [music] or is it this one? No, definitely the other one. There it is. Um, there uh small time viral, you know, I mean, we'll see where it goes. Viral question mark. Um, it's called uh you can find it on on my channel. Like YouTube will recommend it to you after this um stream. Um, it's called something like uh math can be a hobby and it's just blowing up. It's crazy. Like this over the last 3 days, we went from 1.7 uh subscribers to where are we now? I'm going to check I'm going to I'm trying not to check the damn numbers, but 7.7. We went from 1.7 to 7.7. Dude, that's amazing. [laughter] So, um, go check out this video. This is a new series. Um, and this is like lecture zero or episode zero. Episode one is also out on edition. Um, episode two soon uh on addition. So keep an eye out for that.

Um, so today I want to practice a little bit so I know just I need to figure out exactly the structure because I'm I improvise all of this, dude. Like I don't know what I'm doing. I'm making it up as we go. Um, like this weekend I want to film episode 2 and I think I have the general structure in mind, but these are meant to be like 30 minute episodes that are lectures. It's just a 30-inut lecture. Um whereas these are three-hour lectures or well three-hour hangouts, three-hour um math and vibe or something. Three 3 hours math and chill or something. I don't know, dude. 3 hours 30 minutes. This two different streams of content. So watch whatever you want to watch. I don't care, dude. I'm here. I want to I want to practice. Um I hope you join us. Uh here's our chance here. Here's your chance or here's my chance. I'm trying to say join the Discord, dude. Um join the Discord if you want to, if you feel like it. Uh you I think all the notifications are off by default cuz I don't like notifications. Um but you can opt into them to get going live notifications. Uh and more importantly what I just wanted to say is we have a new channel um which is called uh #lang basic math. So um we're forming a study group and we're working through this entire book. Uh so far we've only talked about addition but we will get to everything from addition to pre-calculus everything before calculus and a little bit of linear algebra like a little bit of matrices and also proofs like intro to proofs well proofs are throughout but like a little bit of um um what am I looking for set theory and propositional logic uh that type of content as well like proof by induction ction, um, complex numbers, induction, determinance, trigonometry, um, cartisian geometry, uh, uklidian geometry. Dude, there's some good stuff in this book. Um, it's like it's just all of middle school and high school math in one book. It's hardcore, but it's it's going to be fun. I think it's going to be fun if you like math.

Um, okay. So, my neck hurts, dude. I have like such tech neck, dude. Like, I have such tech neck. Like, if you're like hunched over and um typing on a computer all day or something or like looking at an iPad all day or looking at your phone all day, like your head is the weight of a bowling ball. Do you realize that everybody? So, like take it seriously, you know? get try to do a standing desk or like a a laptop stand, things like that. Don't be me. Don't be me. Do what I say, not what I do.

Um, all right. Uh, any more comments to check out before we start practicing addition? Um, yeah, with pen I just scribble out a mistake and start over. Yep. Yeah, you've been scared. Try it, bro. Like, this is like uh pure pressure. I'm like, "Come on, just try it once. Try a pen once, dude." Uh, it'll it'll be fun, man. Like, it's like it I know it seems like heretical, but I write in pen in the book now cuz like it's it's just fun. I don't know. Like, I just scribble it out like kind of angry. I'm like, scribble that out and then, you know, just start over. Just start over. Like, seriously, that's a very good tip. No matter what, like if you get stuck on a problem, sometimes it's best to just throw away that sheet, start with a new fresh sheet of paper and just start totally fresh. Um, forget everything that you tried to do a moment ago. Maybe you'll come back to the same point, but maybe not. Like, that is a really, really good practice tip, I think.

Um, I'm using Notability as the app. It's a really really great app. Um, someday I'll set up like little um soon soon I'll get uh little exclamation mark commands so people could say exclamation mark app and then it would tell you all that.

Um, all right. Practice problems from fast and easy maths. I haven't heard of that one. Let me write that down. Thank you, dude. Um, I hope y'all don't mind if I write usernames because I think it's nice. I I think it's kind of cool. Give you credit like um Bob Chanel like the fashion brand uh Chanel. Chanel 35 53. I'm a little frazzled today, so I wrote all of it. Um, I'm very curious about this one. I think I'm going to hate it cuz I don't think math should be fast or easy. Math is hard and math should take a long time. Like a good problem um should take you a week. Like dude, the problems in like this is baby Lang. This is baby Lang. Uh this is Papa Lang. Okay, this is this is Papa Lang. And the the problems in this book take you a week. No, not even joking. And it's still algebra. It's it's actually algebra. And I can't solve these problems. like they take me a week and then I give up cuz they're too hard. [laughter] Uh, which is fine. It's okay. We'll get there someday. We'll get there someday, I think.

Um, might be a hard one, but what's your favorite topic in math? Uh, dude, abstract algebra. Broadly broadly speaking abstract algebra group theory group theory and but also linear algebra it's a hard call between the two for me vector spaces like abstract theoretical linear algebra is equally as beautiful in some in for different reasons than um group theory. Yeah. and we'll do some some of that stuff um next week. So, um another one that I do want to say before I mean, you know, cuz I'm introducing myself to so many people here. Um and and it's really nice to to meet you all. I'll set up ways for this to be more efficient in the future, but I have stream weekly stream structures. We do a week of high school math, a week of college math, and then a week of graduate school math, and then we recycle. On the next week, we start over again. So, right now, we're in high school math at the moment. Um, but in grad school math, I've been doing a lot of group theory and um, uh, applying linear algebra to studying symmetry. Yeah. [snorts]

Um, Notability is amazing. You did math using markers different with pen. You just scribble out a mistake. Yep. Yep. Yep. Um, don't be scared, dude. It'll you'll survive, man. I promise you. I know that that sounds scary, but you will make it. You know, it's going to build up your confidence. You're going to toughen up by trying math with a pen just once. Um, it's not better, but like just it's worth trying, I think.

Um, oh my god, I typed my guitar. um link that long ago. Jacob, hello sir. I have very much interest in math but I'm not able to understand it. Please give some suggestions. We're starting from the very very beginning. Um Jacob, I guarantee you you're going to be able to follow along today. So you found the right place, bro. If you want to learn math the right way, uh and you want to start from the beginning, that's what this channel is all about.

Um, yo, we got another math student, another math major. What's up, shared act CCW1 undergrad pure math? Um, what do I want to talk about numbers? Um, today I want to do I just want to mostly work some exercises today from Lang. like last time. These are practice sessions uh where I'm like hanging out, vibing, working problems. It's not a lecture. Um so I think I'll I'll just be working some of these exercises. They're you know, they're not hard for me, but the first time that you see these types of problems, you know, they're not they're not obvious. Like this stuff was hard for all of us once at some point. micro niche celebrity. Hell yeah, dude. Hell yeah. Hell yeah. Um, the channel's growing incredibly fast. New Hobby Maths videos are getting mad views. Yeah, dude. I I kind of felt like it was like coming like cuz I hadn't I haven't tried a video since I restarted this channel. Like my philosophy is that I could do a live stream every single day the rest of my life, no problem. I would study math from books and share it with the world every single day forever if I could. And like the way things are moving right now, like don't get my hopes up, dude. Don't get my hopes up, you know? Um, but videos take more real effort and work and sometimes video editing. Um, so the idea for me is like get really good. get as good as you can and practice and learn, you know, all the skills in the in the live streams which are fairly low effort but really high value also. Like it's low effort but high value cuz this is so much deeper of engagement. you know, I can at least right now I can still remember your usernames and hopefully for a while, but um and I don't know, dude, just like we can geek out like a like a real community talking about math with one another, whereas you don't really get that in a comment section, you know?

Um intro to math for free. Yeah, dude. For everybody, too. Um, my goal is that this could like I use PG-13 sometimes a soft rated R language sometimes here. Um, but other than like a couple friendly fbombs, um, I will uh, mostly it's PG PG-13 kind of humor I feel. Um, I think a smart a smart middle schooler could learn math from this, you know. like a super like it's not about being smarter or not, but like uh I don't know. I think like a a younger kid might enjoy some of the stuff that we do here.

Um so we're going to practice addition. We're going to do some Fibonacci numbers actually. [music] Um intro to math for free. Thanks man. You'll probably hate it. Scary Lang. Yeah, scary Lang is scary. Hello. What's up entropy Liz? Nice to meet you. What about someone like me who hasn't worked on math for about 20 years? Where do I start? Right here. No joke.

Um, I think I lost my train of thought. I want this to be for everybody, not just gifted honors algebra students or something. Uh, not just math majors or people planning on studying math in college. Um, [music] in in some sense, my main target audience I've had in mind for a long time has always been [music] adults studying math for fun. Like like math as a hobby is such an under represented freaking niche. Like I don't think it's the majority of people. Like it's not the majority, but it is like a quiet minority. Like, but it's a sizable like I think that there's a lot of people out there who study math for fun. Like, it's not any more niche. I think that there's way more people out there studying math for fun than chess. Like, I think that there's way more people. Like, [music] 10 times as many easily.

Um, oh, my Discord link doesn't work. What? What? Are you serious, dude? Thank you so much, Math Ace. I appreciate that. Um, wait, try this. Oh, yeah. Lots of people do both. And I would love to do both someday. I I tried learning a little bit of chess in the um in the pandemic, [clears throat] but I didn't get too far. I was I wasn't very good. I'd be embarrassed. I Who cares, dude? I do not care. I I was like a 600 ELO. Like, dude, I did not get very far in chess. I know if I kept practicing I'd get better, but like I don't know. Yeah. Anyways, who cares?

Um, YouTuber Math Scribbles. Um, chess is fun though. Like I'd like to learn it and I think we could get I think we could get there. Like I I definitely think we could hit 1k someday. Um, yeah, representation theory has been so fun and it's like it's it's in large part thanks to the community here. Like you must have if you watched that video um [music] you must have seen the chat and the people I was talking with like literally um shout outs to uh to K theory. If you all like this channel, you should definitely check out K Theory as well. Um math there's just very few math streamers out there, but I think it's a such a cool little niche. Um, and he's still much bigger than me right now, but you know, I'm catching up. You know, I'm I'm catching up fast. Um, let's see. Is he live now? No, he's not live now. [music] Um, shout out to K Theory, fellow math streamer. But uh advanced graduate level research level research mathematician. I'll say chill research mathematician cuz he's a chill nice guy, you know, chill research mathematician.

Um that's a specific video. I don't need to do that. Um I'm a I'm making mistakes. Here we go. This link. This is the one that I want. Woo! Um, you missed the tutorial. Don't worry about it. You got plenty of time to catch up. You got the rest of your life. You can study math the rest of your life. It's [music] not going anywhere. It's not going anywhere. You just need to get a pencil and a piece of paper and you can just [music] start studying math for fun, dude.

Um, what do you think about math scribbles? Yeah, you're the second person to mention math scribbles. Um, let me h I'll write it right here. Why not? I'm definitely going to lose this, but check out math scribbles. Tell me more about math scribbles. Um, so some shout outs to math scribbles, K Theory. Who else streams? Leo lectures streams. Um, dude, like there's so many video game streamers out there. Why aren't there more Why aren't there more people streaming study sessions in math specifically and geeking out about math? Because there's so many people who geek out about math for fun. Um, so shout outs to these folks. If you recommend math scribbles, I'm sure you know a friend of a friend is a friend or something like that. What is that? What is that property? Um, the transitive property. Yeah, it's not real. It's not a real thing for friendship at least. Um, yeah, group theory is going to be fun, dude. Yeah, group theory is going to be is going to be dope. I have some ideas. I have ideas there.

Um, Discord link should have been fixed. Let me know if it's not. At this rate, tomorrow you'll have 15. You'll have 15 subscribers. Dude, don't even don't get my hopes up. I don't know if that's a good thing or not. Like it's hard to be a streamer with a lot of people to do the kind of live stream that I've practiced and that I I like doing. It's hard to do it with 15 with 15 people, I think.

Um, chess and math. Study math for fun, too. Lots of people do. Lots of people do. What chess piece are you? Um, dude, I would say on the knight like I'm bouncing around. I'm always changing directions. Like I'm making like good progress in one direction and then I I take a 90° turn, you know? Like I I I do some good progress one direction and then I'm like, "Ooh, shiny thing." Like, "Let's go that way instead." Right? Like I'm a knight for sure.

Um, preparing for J. Let's go, dude. Um, yeah, there's a lot of people who are. So, if you join the Discord, there's like a an #exams channel. So, if you want to talk about exam prep, I should call it exam prep. Like, that's what these channels are meant to be. Like, ask each other questions, share your problems that you're stuck on or something. Like, if you're stuck on a problem, post it. Post it there, dude. Um, yeah. Not exams. That sounds like people might be sharing their like exams or something. Exam prep. All right. So, join the Discord. Join the exam prep channel.

Um, nice, dude. Liz, if you're somebody who likes letters more than numbers, you found the right place, cuz we try not to use numbers. We try to use letters [music] instead. So, you might you might be in the right place. Yeah, chess is a time sync. For me, my time sync is classical guitar. Like, oh my god, dude. Like, I've put way too many hours into it. like [laughter] it's um it's I'm gonna say it's immoral how how much time I've put into the classical guitar. Like it's like in a good way, but like I don't recommend it to people. Like I don't recommend somebody gets that into chess or the guitar. Um you know, but it's I don't know. It's fun. It's It is fun though. like but there I'm just ref referring to that sentence that um that joke that um a chess master is a wasted life or something like that. I mean there's just like a beautiful sad tinge of sadness you know in somebody who says that it's like uh but I love it. I still love it though. You know, I can imagine math becoming popular like chess as they're similar and the big streamers like I showed Speed doing Oh, you're imagining Speed might do math live. Bro, why don't we have Speed? Like, dude, tell Speed to come hop on this channel as a guest. I'd love to teach Speed some freaking math, dude. I'll teach anybody math. Like I I think so. I think for real. Um clip this if you want. Uh or just link to this timestamp. Like dude, send this to Speed or Lwig or like freaking all these badass streamers. Like I really like the Primagen. I would love to to talk math with uh with Prime. Or who else? I I heard that Kaisenat is doing like reading streams and he's just reading a book out loud or something like that's awesome. That's the kind of that YouTube needs. I feel um yeah, we are covering I've done a lot of calculus videos actually. Reg um definitely check out my calculus playlist. Math is worth studying. Yeah, it is. You know, not too much but yeah, definitely. It's better than Tik Tok, dude. It's just better than Tik Tok.

Um, the root of a negative number is fine. Yeah, complex numbers like we can imagine it. Okay, so here I had this idea the other day cuz right now we are not just working in the integers. Where is it? Where is it? Lang starts section one with the integers. So Lang starts chapter one cuz he's like I'm hardcore. We're going to do an entire section on the integers. No, dude. No, no, no. We're going to chill for an entire week on the positive numbers. We're going to chill here for an entire week, two episodes, and probably 6 hours of live streams just talking about counting numbers, cuz there's some beautiful stuff here, too. So, I promise you if you remember how to count, uh, you can join this freaking channel. I'm I'm telling you, you can.

Um, so, uh, what was I going to say there? Um, okay. So, um I have one apple then ate two, right? Like, dude, what is an like I only have one apple and somebody told me to to eat two apples. I don't have another apple to eat, right? Like that doesn't exist. I'm sorry. I I don't I can't even imagine what what I have now. I'm the only person in the universe, okay? I'm the only person left on the planet after AI ruins everything. [music] And I found one apple. I found the last apple on Earth. Okay? And but I'm so hungry, I need to eat two apples. Uh, so I ate one apple and I want to eat another apple. You all don't know what I'm talking about because I'm frazzled. I'm talking about one minus two, right? Um, -1 is an integer. Um, so in the integers this is negative one. Okay. But, but 1 minus 2 does not exist. It doesn't even make any damn sense to eat two apples if you only have one apple, man. Um, in the natural numbers, like that just doesn't even make sense. I can't I have to borrow an apple from somebody else or find another apple or something. Um, so, uh, I don't even remember how I got on that rant, but this was a idea that I had when I filmed the other video. It was, uh, I think it's a good one. I think it's a good, um, introduction to the idea that there's different number systems that you work in, right? The answer to this equation is nonsensical. There's no answer to 1 - 2 when we're working with the positive numbers. But when we're talking about positive and negative numbers and we've invented the idea of owing somebody else an apple, like borrowing an apple from somebody else, then now there's a solution. I owe I'm going to borrow your apple or I'm going to steal your apple and now I'm in debt or you're angry at me or something and I have negative one apples.

Um, so what was the comment? How did I get on this train of thought? Uh, the root of a negative number is fine. That's exactly it. Um so in the complex numbers in the complex numbers um the square root of -1 exists right the square root of -1 is a is a complex number but the square root of -1 does not exist in the real numbers. So, a big part of math is telling people what kind of math you're studying. Like, if you're studying these numbers and you care about and you only care about um real numbers like I don't know some engineering problems, then x^2 + 1 is never zero, right? x^2 + 1 is this parabola in the real numbers and it never crosses the x-axis. Okay, so that doesn't have a solution. It never crosses the x-axis. Don't lie to me. Like I drew it. It will never cross the x-axis. Dude, don't lie to me. Right? But in the complex numbers we can imagine that it exists and then we create a new math a new world that we can imagine like let's imagine that I have a negative apple like that's an invention that is something that um doesn't exist directly in the world numbers don't exist in the world we use it as an idea for things that exist in the world but the study of math is about those ideas and those inventions that we make.

Um, yeah. Anyways, chill. Thanks for your comment. Um, the, uh, what was it? The square root of a negative is okay is what somebody said. And that's a great great commentary. And it just ties in perfectly to the fact that right now I'm being more hardcore than Lang, dude. like I am being more hardcore because we're only working with positive numbers. We're not looking at the negative numbers yet and we're going to do probably two or three hours today just talking about counting numbers and another episode.

Um, so thanks for hanging out with me during this. Uh, purple math. No, I don't know. I don't know purple math. Where's the shout outs board? Um, so check out I'm going to say to-do for myself. This is a a lovely little symbol that we write in software. It sounds like to like the name Toto or like tooro or something. Some people will say toto and it's just kind of cute, but um no, it means like todo, like a to-do list. Um and this is the only way to spell it. Like you do not ever spell it any other way. It has to be this way. Um, but uh I will check out Math Scribbles and I will check out this other person that you just mentioned. Uh, what's their name again? Purple Math. That's it. Uh, all right. We got to we got to stay on track.

Um, what's next? Preparing for J. Um, join the Discord. Uh, not related to the stream. I proved Gaus's proof. Yeah, dude. Um, sell stuff. Did you leave the comment about a geometric proof? Cuz I don't know that one. Um, I haven't responded to your comment. This was this was something I meant to say at the beginning of the damn entire video, but we got into more important things.

Anyways, um, dude, this is crazy. Okay. on YouTube. If I get a comment in YouTube Studio, if I get a comment and it's really rude or something and they, you know, say something mean about my guitar or something, uh, or about my math, uh, you can't dismiss a comment. This is cra This is the weirdest oversight in the world to me. You can't dismiss a negative comment. WTF, right? This only matters when you're a small streamer, when you're a small YouTuber. But like every time that you open YouTube Studio, you're like, "Dang, dude." Like that that, you know, shitty little comment there is still there cuz it's wimpy. I mean, I guess like somebody would say like you can delete the message. Like you can delete a message, but that's so lame, dude. Like I don't want to delete a message. like, "Thank you for your comment, but like, you know, you're you're welcome to have your opinions. Um, that's just too wimpy. Like, I'd rather just like ignore it, right? Like, I can't just hide a message." Okay, so now that's when we were a small YouTuber and now we've got a lot of comments instead. Um, I'm doing it the opposite way now. Um, Harding is like the go away button kind of. That's the uh another YouTuber I know said that he does um he uses the heart for for the hateful comments. Um so heart means go away and then empty means please stay. [laughter] Okay, which is crazy. Okay, like oh it's just so broken, dude. Like it's so broken.

Um here, look at this. Look at this. Um, this is a book all about product design. And I used to want to work at YouTube on product design. And there's just so many little gaps like this that are just, you know, they're just most people working on these systems are not creators themselves. And of course they're not. [music] Of course. Um, so I don't know if somebody said it. Oh yeah, you somebody mentioned a comment about the uh uklidian uh geometry or no not uklidian geometry, a geometric proof of the sum of n integers. I've never really bothered to learn it. Um, uh, how does it go? Let's try it. Let's see if we can figure it out. Um, I know you can do it with like How does this freaking work? Um, you can do it with squares somehow. Uh, so now we have um we have 1 + 2 + 3 is 6. I I bet you didn't expect to be watching somebody think about this. Um, I'm stuck. Okay. So, uh let's see. Last time

In a video, we saw Gauss's genius proof of this. Um, he was a little kid, and, uh, somebody, uh, told him to add a hundred numbers together, and he, uh, was a genius. So, he noticed that that was 100 * 101 / 2, which is, um, if you ask ChatGPT, that is 50/50. Uh, [snorts] so he had this argument, and it turns out that it works beautifully for any number.

So, for example, here in this example, this creates literally like a triangle. It makes like a triangle. I've never, I've never thought of this. It's really nice, actually. Um, that's that's delightful. Uh, so these are called the triangle numbers. This is the third triangle number. >> [snorts] >> And in general, the nth triangle number is n * (n + 1) / 2.

So, I'm thinking that there might be some way to Oh, yeah. Dang, dude. Okay, I think I got it. Um, okay. So, n * (n + 1). Um, this is a multiplication of two numbers. And if you have a bunch of acorns, you can line them up in rows, right? Um, so it turns out, like, if you're organized about your acorns, or your apples, or your, um, you know, why does bayonets come to mind? If you're organized about your bayonets, uh, or your apples, uh, or your iPhones, then you can line them up in a grid like this. And then we notice that we can count by fours, right? 4, 8, 12. And counting by fours is just much faster than counting every single one, like with your fingers. 1, 2, 3, 4. That takes a while to get all the way up to 12. You, you notice that you can start grouping by fours and count 4, 8, 12. And then you start memorizing these, right? Dot, dot, dot, forever.

So this means that if I have one row, then, uh, I have that many, um, acorns. If I have two rows and I organized them and I made sure that they line up really neatly, um, it turns out that you'll have eight, and you can just memorize this. It's so much faster than counting all of them one by one. Um, then on and on, right? Dot, dot, dot.

Um, so what I'm trying to get at here is that here, why don't we try to do some magic here? Um, I love, I love, I love doing that. [laughter] Um, okay. So, what I'm trying to get at here is that we have four along this side and we have three along this side. Right? So now we can just start thinking of this, actually, instead of thinking of all the space in between, we can just start thinking of the thing as a freaking rectangle. Like, as long as you, um, line up your acorns, you know, in neat little rows, like you can, you can build like a little container [music] and it can be a rectangular container of this size, and it will fit four freaking acorn, uh, four freaking acorns per row. 12 in total, right? So this is, um, the area of a rectangle is, uh, length times width. Um, and this comes from multiplication. Just freaking regular multiplication. And multiplication comes from, um, addition, right? Which is, um, also known as counting. Well, no. Addition, I would say, comes from counting because counting is one at a time. That's counting 1, 2, 3, 4, 5, 6, 7. Uh, and then eventually you can be like, oh, there's three here, four there, those add to seven, seven, like plus three more, you know, etc.

So, okay. Gosh. Um, also, Stucky on Twitch, good to see you, bro. Thank you for for joining. I hope you don't mind that I'm not engaging with Twitch as much, but I will, I will respond to all the comments at some point soon. But I'm on a train of thought here. So, I think that we want to see this, we want to see this part of the formula as literally a rectangle. N on one side, N + 1 on the other, because we have a multiplication, right? Um, but then we divide by two. So, let's freaking divide by two and only take this part of the dang thing, right? And that's it. I think that you just, you line these things up. How do I rearrange them? So, 3 - 2 minus, or wait, no, plus one, like we're going to get the pretty little freaking triangle here somehow. Um, so in this case, I want 3 * 4 / 2. Where do I get the four? Did I say that wrong? Wait. Uh, four divided by 2 is 2. 2 * 3 is 6. Um, what? Three. Why? Okay. Okay. Because these are contained along this diagonal. These are completely contained. Those are completely below that diagonal. Um, whereas these are only partially below that diagonal. Right? So they're incomplete. Because I could, um, I can see that these are mirror images of the three that are completed, right? Like this. One, two, three. Those are. That's terrible contrast right there. Let's do white. One, two, three. That looks horrible to me, too. But let's keep it for now. Um, so those are, uh, completely contained there. And I could find the matching ones over here. One, two, three. Right.

Um, dude, I feel like we're so close to this. It looks like a Rubik's cube. I have a Rubik's cube coming. I'm, I'm not very good at them, but, uh, Oh, my brain's not working. I didn't sleep well last night, but I feel like we're close. We're so close. Like, I think I got the basic idea here. We, we like move a couple of these around like a little jigsaw puzzle, um, in [music] a way that, I mean, okay, um, so I was thinking this earlier, like, if I moved, Oh, this is going to be cool. Yoink. Nope. Well, let's put it there. So, if I move that blue bit over there and then move this red bit over here, right? Then now I can, you know, the two match, the two are like corresponding. So, so now the only problem is how do I, how do I make that concrete? I think I need to see this as dots because it's not, um, a full area. So, we got acorns that are lined up like this. Oh, dude. This is actually kind of connecting to a topic I wanted to talk about soon. Oh, holy crap. This is cool, dude. This is like partitions. I think, like, like you get really nice little diagrams like this in part, additive partition theory. Um, oh, wait, no. Oops. But yeah, this is still. Dude, this is so cool. This is like some of the stuff I wanted to talk about soon. Anyways, um, I've forgotten how these things work, but, uh, how do these things work, dude? Um, this is like related to partitions of a number. If y'all are curious about what I'm thinking about right now, um, you can check out my, um, episode one video where we showed that the partitions of five are [snorts] like this. Oops. Four and one. Three and two. Three and one [music] and one. Uh, two and two and one and two and one and one and one and one and one and one and one and one. These are all the ways to share five acorns among people. Like, all the ways to distribute, um, like, all the ways that you can partition up the number five. You can have one part, or two parts, or three parts, four parts, or five parts. With two parts, one of them can be four and one of them can be one. Right? Sharing, splitting acorns between two people. One of them, one person gets four and one person gets one. One person gets three acorns, the other person gets two acorns, etc. Right? These are there are exactly five. [snorts] No, sorry. Um, there are exactly seven partitions of five. Um, and there's some very cool unsolved mysteries about this function. Um, I think at least there's some, there's some recent, uh, math development about this stuff. Uh, which is really cool, and I don't know anything beyond that. Um, but in this case, okay, okay, this is so cool. I think if I just, like, take a nap because I barely slept last night, I would be able to finish this. But, um, in this case, we found a partition of six. We found the diagram of six. Um, I'm going to try to read chat and catch up with you all, 'cause this is, Oh, dude. This is so cool. Great. I don't even remember the comment that made me start thinking about this. It's going to be really funny if it had nothing to Oh, shoot. Look at that. Um, okay. So, how does this go? How does this go? Uh, I'm finding all of the partitions of six right now. Um, so I'm thinking algorithmically and I'm thinking about the last number in each of these. Can [music] I split that? Can I partition that number? No. Okay. Can I partition this number? No. Then I have to partition this number. So we decrement that number, uh, and then pick the biggest number equal to it, or, um, or less than it. Pick the biggest number that doesn't overflow beyond [music] the number that you want. Right. Oh, we can pick 3 + 3 right there. So that's kind of like, um, algorithmic, sort of computer sciency thinking. Um, so I can't split one, but I can split two. And now I have that, uh, okay, I can't split any of those ones, but we can, uh, take from the three. Dude, I, I was hoping we were going to get some just like chill little, like ASMR. I, this feels like ASMR to me. It's just relaxing to do this. It's just fun. Okay, I'm allowed to say it. I'm an adult. This is fun. This is just fun. Uh, 1, 1, 1, 1, 1, 1. There's six of them. Okay. So, how many are there? I, I think that there's 11, if I remember correctly. Um, my head hurts. My neck hurts more specifically. I've been, Oh god, there's 42 people watching me try to solve a math problem. Um, what's up? Nice to meet you all. Join the Discord. Hit the like and subscribe. It really helps the channel so much more, you know, than you ever realize. Share it with every single person you know. Also, um, especially if they like math. Um, what, what am I doing? 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. Yeah, I got it. Heck yeah. So there are 11 partitions of six. Dude, we're making progress. Making progress here. Um, so what I drew in this here was not a partition of five, but it was a partition of six. Um, I don't know if this is actually going to get us to our solution. And I don't think that this was the, um, the proof that this person is thinking of, like a geometric proof, but this perfectly lines up with, lines up with, um, one of the topics I was thinking of talking about today, which is, um, partitions. This is some really beautiful math. Um, and I don't know if I can, well, dang. Um, I'm gonna, this is a practice run. This is long. I'm just going to do the same thing again in a 30-minute video. This is a practice run. Um, trying to think through. I'll do, let's do part of it. Um, I feel like there's some way I might be able to try to utilize this, but maybe not. But what I wanted to say is like, I'm, you might be able to just like move one of these dang things over or something and just realize which one you need to move, and then you split, you split it. Like, we just need to move those dots, or we need to move those acorns around the right way, and then we can see this as half of 4 * 3. So if I need four rows and three columns, why is that half of [snorts] I'm frazzled. I need some coffee. I, I think if I didn't have 40 people watching me right now, I would see it. It's fine. It's fine. I, it's, it's okay. Um, I think I'll see it like right after this, but I, I think we're close to something. But, um, these little diagrams are really cute. Um, these are super cute, and you can draw them for any number. Um, well, really for any partition of a number. So, uh, let's do blue. Blue. Blue looks nice. Six is six. I could give one acorn. One, two, three, four, five, six. Six. Oh, wait. No, shoot. I got this wrong. I like doing them as columns. You can. It, it works either way. One, two, three, four, five, six. So, this is the number six. This is the number five. One, two, three, four, five. So, I'm going to keep five of my acorns and I'm going to give you one acorn. Um, okay. But then you say, "No, dude. I want two acorns." Like, I want more than that. Don't be so greedy about your acorns. Um, so, okay, fine. I'll keep four and give you two of them. Um, this may not seem like it, but this can be used to prove, um, a really nice little result. Uh, four, one, and one. So, in this case, there's three people. The first person is greedy and they get four acorns. Player two gets one. Player three gets one, right? In this one, player one gets three, player two gets three. Life is, is nice, and, um, you know, we have equality. Uh, in this one, this is the triangle number that we're thinking of. H. So I could double it. I could double one of these other ones. I think, um, like in this case. Yeah, dude. We may have gotten it. Yeah. Yeah. How do I want to present this? Um, so let's double these. But these are all like new, new versions of them. These are duplicated. It's like a virtual new copy of the original collection. And now we have 3 * 4, but we have to remember that we imagined the right-hand side. So we get 3 * 4 / 2. Yeah, dude. I feel like that's like a mic drop moment. I feel good about that, dude. Uh, I, I think that you just need to kind of, um, formalize that a little bit from there, and, and you get it. So this is a rearrangement of this type of partition. And you might be able to do this in general and show why you can move a dot to the right, other dot, the right other spot of the, of the thing. Um, we showed it for an even number. I guess we would need to show it for an odd number, too. Uh, but then that's an exercise for the reader. Just give it a shot. I think you can see how it still matches up. Um, one, two, three. One, two, three. So, in this world, um, I'm going to keep three acorns. Player two gets one, player three gets one, player four gets one. In this one, it's a nice world of equality. Uh, in this one, we get two, two, one, and one. Just a little bit of inequality. And then in this one, we get two, one, one, one, uh, one. This one is even more, you know, even more like closer to equality for all. One, two, three, four, five, six. Now, this one, everybody, everybody gets one acorn. And, um, beautiful. So, this, what are these called? Um, [snorts] it's in this book. I learned it from this book. Graphical representation. Euler's partition theorem coming soon. You, you use some of these ideas to prove one of the most incredible facts that I know, one of the most beautiful things. Um, yeah, we got these graphical representations are, I feel like there's a name, a specific. Okay, so we will see conjugation in, um, in complex numbers, and you can define conjugation on these things similarly to like a conjugate of a matrix, uh, or the transpose of a matrix. You write rows as columns instead of, you know, you swap rows and columns. Uh, and you can prove some really nice little facts if you do that. Um, so that's why it's a whole section, like a graphical representation. I think that there's a name for these, but I, this book doesn't say what they are called. Um, I have to pee. So, I'm going to just skim through chat real quick. I feel really good about that. I think I think that this was the idea of a graphical proof of the, uh, triangle numbers of the, uh, sum of the first n integers. Um, I don't know if it's the graphical proof that somebody mentioned in a comment. Um, but the reason I didn't respond to your comment yet is 'cause I wanted to save it and make sure that I responded to it and like looked that up. And so if you all don't get a response or a heart on your comment, um, you know, it doesn't mean that I don't love you, okay? Like, it just means like I want to take some time. I, I don't want to forget about that comment, and I'll come back to it later and, um, and then, you know, handle it appropriately in whatever way. Um, sick, who said it? Who was it? Somebody said started with S. Could share in the Discord that. Yeah, please share the the proof that you're talking about. It was you, right? Safe stuff. Is that right? Oh, yeah. Yeah, yeah, yeah. It's right here. I see it. Would you be interested in some other proofs of the identity besides induction? Yeah. I'm interested. Many proofs. Like, the part of the idea of this channel is like, let's see multiple arguments. Let's find multiple solutions for this problem, and let's, let's get vague and philosophical, and, you know, let's talk about which one do you like more? Like, let's run a poll, you know? Do you like Gauss's proof more, or this proof? For those who saw Gauss's proof, I could actually run that. Um, it's nice that today is actually day 123, too. What a, what a nice little freaking coincidence. Did I remember to update the day correctly? Um, dude, today is day 123, and we split up. That's nice. On day 123, we did, we tried to understand 1 + 2 + 3. That's cool. Um, I hope that the iPad is still updating correctly. I think I fixed it so it doesn't get stuck. Yeah, we still got the iPad. Um, that would be a shame if the iPad was not, was frozen this whole time. Uh, okay. Okay, okay, okay. I have to skim chat really quick. I will come back and read chat, but dude, this was fun, man. We got a lot of chat. Take care, Levi. I think I missed you. Um, take care. Imagine Speed and Kai working together on a proof. Dude, I can imagine that. Like, I could teach both of them at the same time and have them like quietly working and making some progress, and then I like, you know, you know, kindly review their solutions and compare and and decide whose solution was better. >> [laughter] >> Dude, that, that would be hilarious. Uh, when is the next live? Um, probably tomorrow, I think, at this time. Yeah. Um, okay. I have to pee. I really have to pee. So, I will be back and I will read chat. Um, here's some classical guitar for you all. I'm a, I'm a classical guitarist. So, if you enjoy this and you want to help support me as an artist holistically, broadly, um, I have two YouTube channels and I have one Twitch channel, and you are welcome to watch wherever you prefer. But on YouTube, uh, this is, uh, my guitar channel, 'cause on YouTube, you really need to separate, you know, for the algorithm, you know, people subscribed for this thing, not this thing. Whereas Twitch is kind of weird. Like on Twitch, people will do a lot more variety stream kind of stuff. It's really fascinating, like how, like the design decisions that these platforms have made that result in different outcomes >> [music] >> um, in terms of creativity and what people can do on the platform. Um, yeah, I just, I geek out about this. I geek out so much about this. Um, all right, be right back. I got to pee. Here's, uh, some, some guitar music. >> [music] [music] [music] [music] [music] [music] [music] [music] [music] [music] >> Heat. Heat. [music] >> [music] [music] [music] [music] [music] [music] [music] [music] [music] [music] [music] >> Hey. Hey. [music] >> [music] [music] [music] [music] [music] [music] [music] [music] [music] [music] [music] [music] [music] [music] [music] [music] [music] [music] >> Okay. Dude, I am, Oh, wrong one. Wrong one. This, uh, dude, I am so annoyed right now. My mouse is is stuck on the, Oh, shoot. Shoot. Not linear algebra. We're in basic math. We are in this one. Um, I can't get my mouse to continuity back to my computer. It's so annoying. Um, so I was reading chat, but then I got stuck. Uh, so I'll continue reading chat once I figure out how I can get my freaking mouse over to my computer again. Um, but anyways, what's up, y'all? The main question I was just reading chat, um, and trying to catch up. Uh, the main one I wanted to respond to is, uh, how is the interview? It, uh, they canceled. They canceled it. It's really weird. Um, yeah, they, they told me that the interview would be Thursday or Friday, and then they told me that on Tuesday. Um, I've been interviewing to become a middle school math teacher, just 'cause I, I freaking love math, and I want to teach little kids math. But, you know, I've got a lot of learning to do. I've never worked with like a classroom of 20 or 30, like, you know, kids going through puberty or whatever. Prepubescent, mid-pubescent, that's what I was trying to like, pubescent. Do you just say pubescent kids? Like, they don't give a, like, whether or not I worked at Google or whatever. Um, I don't know. That would be hard, but I think I could learn it. I've learned a lot of hard things before, so I'm, I'm confident I could freaking learn how to manage a, a classroom of kids. But anyway, so, uh, interview was lined up for Thursday or Friday. Um, and then I didn't hear anything. So I pinged them yesterday, and I was like, "Hey, what's going on?" And they're like, "Oh, sorry. The school decided to go a different direction." And I emailed back and I was like, "Okay, yeah, no, no hard feelings. I totally get it. Uh, but then like, just [clears throat] five minutes later, I got another email from the head principal. Um, and they were like, "Oh, we can't do the afternoon, but what about Tuesday morning at 9:00 a.m.?" And so I was like, "Yeah, oh, sure, of course." But this other person just told me that you canceled. So like, obviously I'm not their, their top choice right now. So, I, I don't know. Um, yeah, we'll see. The longer they wait, the harder it's going to be to say no. That's how I see it right now. Um, so that's, yeah, it's, uh, we'll see how it goes. I'm, I'm kind of cramming. Like yesterday, I, I left my phone at home and I went to a cafe and just tried to read a, a textbook about, um, behavior management stuff, and just, I've been preparing for this interview. I'm excited about it. Like, yeah, I just [music] want to teach kids. I want to teach the little kids that it's okay to like math. It's like, it's just fun. Like, it's just fun. I could make more money if I went back to tech. Um, but, uh, I just, I think math is super fun, and there are some people out there who just really like math, man. Like, it's an art form. Like, not everybody likes Romeo and Juliet, but like, at least we recognize that Romeo and Juliet is an art form. And like, maybe you don't get it. I don't feel like I totally got it. Like, I kind of got it, but not completely. Math is an art form, too, and it also happens to be useful, but let's let the engineers teach you that stuff. That's my opinion. So, I'm reading chat and I finally got my u my mouse back on screen. So, um, this was fun, dude. Uh, I think that this is more of the combinatorial proof, right? Um, I'm, I'm glad I, I think I got it. Essentially, you got to move one extra dot in the, in the odd case, but, um, or something like that. I don't know what you all are arguing about or something. I don't know what was going on there. But you're studying group theory. Yeah, dude. Group theory is beautiful. Super beautiful. Did the mods handle something or like what's going on? Who's, I don't, dude, I did not sleep well enough for this right now. Yeah, I'm trying to show, um, the sum of the sum of the numbers. [music] Yeah, it's, it's, I mean, it's not a badly paid profession. Like, dude, I've been, I've been practicing classical guitar as a YouTuber. Like, I've been, I've been a YouTuber for two years now. Like, if you want to talk about like a badly paying job, it's YouTube. And there's a lot of people who want to do YouTube. So, I mean, like, to me, I'm going to be rolling in it, dude. If I get, uh, like, just any, any math teacher job, I'm looking forward to that 'cause I'm, I'm burning through some savings, [laughter] which is fine. Like, it's worth it to me. Like, I, I saved up so that I could take a risk and try to build something for myself, and, um, you know, I'm, I'm happy with how things are turning out. So, um, yeah. Yeah. Anyways, like, but still, all, I still consider all this a side hustle. I'd love to do this on the weekends, man, and just still teach. Like, I just really enjoyed teaching and like sharing my love of math with other people and like seeing people's faces kind of light up, you know? So if we got like Kai and Speed on stream and and we're on Zoom and I could see them be like, "Oh, that's cool." or something like, there's so many math facts like this, uh, that I would love to, uh, to share with, um, with the world, with other people. Like, I mean, that's, that's crazy talk, but, you know, who knows? Anybody who wants to be a guest on stream [music] um, let me know. Hit me up, jpractices@gmail.com. I really enjoy teaching people, and it's, it's nice to see and be able to have a two-way quick conversation and things like that. Uh, all right. Yeah, teaching is fine, though. Teaching is like, it's a super solid wage versus others, but it's really underpaid. Like, I shouldn't say that it's super, like, dude, teaching is underpaid. It is so underpaid. Especially some places. Like, I moved from California in, like, Silicon Valley, and I worked as a tech worker there, uh, and I made a lot of money. Um, but I know that the teachers there were not being paid that much more than anywhere else. And like, dude, I don't understand how, like, say that it's two teachers. Like, if it's like two teachers who are married, um, dude, like, how would two teachers afford to live in the Bay Area? It's insane. Like, yeah, teaching, uh, is very underrated, but, um, you know, the funny thing about that is that AI is now going to make teaching one of the most valuable jobs. I think, like, teaching is like one of the last remaining human performance arts. I think it's going to like, yeah, knowledge is out there, but a, a good teacher is a motivational coach, like getting a kid to care in the first place. ChatGPT is not going to motivate an unmotivated kid who has, you know, behavioral issues and and social issues and and difficulties at home and everything. Like, ChatGPT is not going to get somebody, you know, off of TikTok. Uh, sorry, I keep railing on TikTok. I replace your favorite social media platform in all of those sentences. Um, I use, I use TikTok sometimes. It's not, I'm not diametrically opposed to it. Uh, I think if your class is chill, being a math teacher would be super chill, even if you don't get paid. Well, yeah, like in a dream world, I have a captive audience of little kids who love learning math. That is exactly what it's like, right? Like, teaching, teaching a classroom of kids, it's, of course, they're, they're hanging on to every single word and they can't wait to learn, you know, something new. Like, what are we going to learn today, Mr. Crossley? What are we going to learn today? Nope, I don't, I don't think that's how it works. Um, so yeah, you don't work in businesses and you're doing meaningful work. Someone once said coaching teachers are well paid. What is chaching? Is that like exam prep or something? Oh my god, my neck. Um, my neck, dude. My my neck. H my back. Like, dude, I'm just doing so much classical guitar recently and math, and they're both just hitting my neck and back all the time. Like, I need some freaking acupuncture again. I haven't been in a long time. Uh, dude, dual degree comp sci math. I think it's, I wouldn't do comp sci. I wouldn't do, I would just do math. Between those two, I think math is one of the most valuable degrees you can get now in the age of AI. I think math is one of the most valuable. Um, arguably, like a math philosophy combo. Like, hear me out. I'm not going to make the argument today, but just try to imagine why I think math and philosophy, dual degree math, philosophy would be an excellent, excellent, um, career decision. Um, I did math as my major, and I did philosophy as a minor, and then, uh, at the last minute, I did computer science as another minor. Um, when I realized like, oh shoot, I, I'm not cut out for pure math. Like, I, I should, I should go work in industry. Coding looks fun. Coding looks like, like it seems like doing pure math. Like, it seems like abstraction and puzzles and problem solving, and, um, it tickles the same part of your brain as, as pure math, I think for some people. Um, so I really like coding in Vim, by the way. Uh, problem, interested theoretical computer science, logic. You don't like programming, but you like theoretical computer science? Well, then I changed my, I, I changed my tune. Yeah, you might. That, that would be a useful degree. Go study theoretical computer science. Um, actually, that is probably super useful. That's probably the single best degree you [music] could study, I feel. Um, I'm a little tired, so I'm making like extreme hyperbolic claims right now. But, uh, I didn't even think of that. Like, I do think theoretical CS is, um, I think that that is going to be around. Um, and if not, dude, it trains your brain to think, and [music] it's, it's very, very similar to math. It kind of is a subd discipline of math, like theoretical CS. Um, [music] so if you, if you can't make it, you know, then like, it's still trained your brain in problem solving, and every single industry needs problem solving. Like, that's what you get paid for at the end of the day. Like, as engineers, we always say, like, we don't get paid to code. Like, code is not what we get paid for. We get paid to pro, to solve problems. And I mean that's true. Like, sometimes the right solution to the problem is to not write any code, or to delete some damn code. Like, delete the code. Um, that's the best solution. Like, don't, don't write any more code. Delete the right lines. [music] Delete the code. Delete it all and start over sometimes. Um, um, I think I'm almost caught up, right? More. Oh, yeah, I'm so, I'm so close to caught up. Uh, wait, why are we doing addition gang? I'm new. Hey, what's up, Vampy? How's it going, bro? Um, Vampy, I hope you're still there. Let me know if you are, 'cause this is a great question. We're starting over. Uh, and we're gonna learn math. Um, Vamp, Vampy says, "What addition here?" More specifically, 1 + 2. Vamp is confused about 1 + 2 + 3. Um, which is very understandable, I think. Um, yeah, we, we are, uh, we're restarting, and we're going to learn math from the beginning, from the very beginning. And we're going to do it better this time around. We're going to learn math better than the first time that we all learned it. The first time that I learned, um, how to add, I didn't know about these really cool facts. Like, um, check this out, bro. Um, Vampy, since you're new, um, if you want to see a whole video about this, check out, uh, my brand new series, Math as a Hobby. Math as a Hobby, episode 1. I do a longer thing on this, but if, let's just do the spoilers. Let's do the rapid fire version right now. Um, okay. There's a story that there was a, a classroom of kids, and they were being very noisy and very rowdy and acting up, and the teacher told them to add all of the numbers 1 + 2 all the way up to 100. Okay, so what does that mean? That means like, uh, 1 + 1. Oh, wait. No, 1 + 2 is three. Uh, 3 + 2. Well, 1 + 2 is 3. 3 + 3 is 6. 6 + 4, um, 10 + 5, uh, 15 + 6, 21 + 7, 28 + 8, uh, 36 + 9, 45 + 10. Nope. 45 + 10. 55 + 11. My battery, my my iPad's almost out of batteries. And I think that's a great sign that we should maybe call it soon. Uh, 55, 66, uh, + 12 is 78, + 13, + 14, um, + 15. So that's good enough for now. Um, we got to, it's fun, dude. It's just, I don't care how old you are. This is fun, dude. [music] This is plus 15 here. Um, and you just keep doing that until you get to plus 100. Okay, this kid, this little whiz kid, this little genius took two seconds, looked at this problem, and and knew. He said it's 50/50. So, they thought that this kid was a crazy genius. And they asked, "How the hell did you, how do you know that? Why do, what, how did you solve that in two seconds?" And he said, "Well, obviously, it's just easy grouping. It's just, or like, you, you add the easy numbers. Um, 1 + dot, dot, dot, n is the same as n + dot, dot, dot, 1. Um, whatever the answer is, there's, we can find double the, the answer by adding this number to itself. This is going to be n + 1, plus dot, dot, dot, n + 1. Shoot. Okay. Um, and how many, and so every single column, I didn't emphasize that enough, I feel. Every single column in this addition of two lines is n + 1. Like, this is so clever of a, of an argument, I think. Um, I would not have come up with this. Uh, how many columns are there in this? There are n terms, n columns. Um, because, well, there were n numbers in the beginning, right? So, there's n columns. So, then the answer is going to be n * (n + 1). There's n of them, right? n * (n + 1) = 2n. So, then therefore, using algebra, divide both sides by two, and we get this beautiful, beautiful formula, beautiful math fact. Um, yep. So that's why we're doing addition. Uh, we are learning proofs. This is your very first proof. Um, and it's just a beautiful argument. Uh, a proof is a math argument. But the really beautiful thing, and why we say proof instead of argument, is that if your proof is correct, we can tell if it's correct. We just have to like, read it carefully. And then if it's correct, there's no arguing back. Like, the other person can't argue back. We know forever this will always be true. In any possible universe, any possible alien species would come up with this exact same formula if they're smart. Um, which is crazy. Like, isn't that, isn't that crazy? Like, this is never going to break. Like, AI is not going to make this equation false, [laughter] right? Like, AI is not going to break this math, which is amazing. Like, it's, it's a fact forever for any number. Um, for anybody who might be a little lost, I understand. Um, more concretely, we're talking about these additions. Um, and 1 is the same as 1 * 2 / 2. 1 * 2 is 2. 2 / 2 is 1. Uh, 2 * 3 / 2 is 6 / 2. That's the same as, as that side. Um, 3 * 4 / 2, 4 * 5 / 2. All of those, uh, yeah, this pattern will always work. So, something that used to take, uh, technically, well, actually 99 operations, 99 flops in a computer, like 99 steps in this problem, or n, like a billion, like, dude, computers add a billion terms all the time, like very frequently. I think I don't know, that's approximately true, right? Like, computers will do a billion additions all the time. Um, so this would take a long time, but this just takes a split second because it's just one multiplication and one division. So we took something that was, uh, in fancy language, O(n). It depends on how many terms there are. Like, adding one through 100 is hard. Um, but Gauss was a little freaking genius. So he converted that. It's the same thing as just adding 1 + 2. Like, it's just as easy as adding 1 + 2. Like, it's, it's amazing. Like, it's actually very, very cool. Um, so the real math, like math is this. This is math. And most people never learned math. Like, the only math you've ever learned. This is such an exaggeration. And I know some teachers are going to get mad at me 'cause they do teach this, but just, it's non-explicit, other than geometry class. Geometry is so boring, dude. Like, those, like, table proofs are so boring. So, like, who cares? Like, I mean, they're nice. Like, you can develop an appreciation for them, and they're historically very important, but, uh, for me, this is so much prettier. This is so much nicer. Um, and, but the point, the point that I'm trying to make is that proofs are real math. What we call pure math, or real math, is about the arguments why things are true. It's about the concepts behind [music] all these, like, little calculations that you do all the time. Um, so there's that. Um, thank you for asking. Uh, do you have an affiliate? No, not yet. Um, I haven't gotten around to it. I'm, I'm too lazy. If you want to wait, you can, but I don't know when I'll get it set up. Feel free to just buy the book. Um, if people are asking for ways that you can support me, [music] um, shoot me an email. I'm available as a private tutor. That's one way that you can support me. Um, thank you for asking, dude. Um, I'm also starting a weekend, uh, I'm also starting a weekend, uh, study group for this book specifically. Um, currently, there are seven seats available. Um, three of them have been taken by some of my friends. Uh, so, and right now, I'm trying to decide between the people who, uh, who are reaching out about, like, I just, it's not about, you know, for me, it's not about the money. Like, like for me, I want to run this little cohort. This is going to be cohort one. Um, and it's going to be practice because I want to learn how to teach a group of 10 people at once, you know. Um, so where was I? There was another point I wanted to make. Um, I'm blinking. I'm, I'm tired. My iPad is literally going to die in like a second. Um, so right now, um, if you want to join the group tutoring on this book in particular, uh, reach out there. Also, feel free to just freaking watch the free, free videos. Like, I think that this stuff is super valuable. Like, dude, you don't need to be in the group tutoring unless you really want to. Um, uh, we've got lectures coming out about two per week. So, I got, I owe you all one for this week. Um, and the Discord and the iPad is dead, but there it is. That's a sign that we got to go. Thanks everybody for watching. Um, join the Discord. Let me drop a link in the chat. Uh, but you could also always find it in the video description, right? [music] Uh, discord.jcpractices.com. Very easy to pronounce. Um, I stream almost every day, uh, weekdays, usually around 9:00 a.m. Eastern time, like New York time. [snorts] [laughter] And Stucky on in Twitch, every line of code is a liability. Something too many people do not understand. It's so true, dude. It's so true. When I was working at Apple, and there was this intern, and we shared an office, and he told me that in his, at the end of his intern project, um, he told me that it turns out that he had a negative, like, he had a negative, um, contribution. Like, he deleted more lines of code than he added, and he was like nervous about that, and like, he was literally like, "Oh god, I don't know if I did anything valuable during the summer project. I deleted more lines of code than I added." I was like, "Dude, tell people that. Bring that up in your, in your, in your presentation, and you're going to get a standing ovation." Like, you don't understand. Deleting lines of code is so much better than adding lines of code. It is so much better. It's because there's so much to learn about it, you know? When's the next live? Probably tomorrow. I'll do some bonus weekend streams sometimes. Um, it's almost 2 to the 13. Good lord, dude. Uh, I'm not a teacher. I'm trying to become a, I'm trying to get a job, dude. I'm trying to get hired, but every single school I'm applying to is ignoring me. I'm like, why? Come on, man. Like, I'm telling you, it's going to be a fun conversation, even if I don't get hired. Like, it'll be a fun conversation. Like, I'm a quirky person who's like really into math, you know? Um, people on Discord say math and philosophy are both unemployable today, but in a couple of years, that's all that's going to be left. Like, there's now we're filling in the details on this argument. Um, that's all that's going to be left in a few years. Did I enjoy coding very much? Yeah, I, I enjoyed, like, especially like flying around in Vim and T-Mux and just like really quick, really quickly like copying and pasting code, which is crazy [laughter] like, like, it just sounds like, back in my day, we used to copy and paste code, and we had fun with it, and that's, uh, actually exactly what, what it was like. Like, I was just really fast at copying and pasting and deleting code like a surgeon. Like, delete from here to there in just like a split second, and then fly over to this other window and then copy that and paste it back, and then change this character to that, super fast. That, it was, it felt like playing a video game or the classical guitar for coding. Like, it just, it felt like, like playing the guitar. I was like, I don't want to be here. Oh, I wish I were playing the guitar, but at least this feels like the classical guitar. So, okay, this is pretty fun, too. Um, yeah, currently saying CS. Great. Do it. Theoretical CS. Are we at 8K? Dude, that's too many people. That's too many people. Hey, JC, isn't that too basic? What? 1 + 2 + 3? We just spent three hours. Well, two hours understanding 1 + 2 + 3. It's worth it, dude. It'll put some hair on your chest if you try to learn this stuff. Like, this book will, like, it's going to knock you on your ass. Like, you're going to restart and you think that you know 1 + 2 + 3, but this, this book is going to put some hair on your chest, dude. It's, it's a good book. Um, especially if it's with a, with a teacher who can like help you with it, because it's hard, and sometimes he makes you feel bad. Like [laughter] sometimes this dude will make you feel bad, but like, trust, trust that he knows what he's doing, and, and it's really pretty once you get it. Once you get it, like the way he writes is actually very nice. But yeah. Um, who is Veratt? I don't know what that is. Um, Leo Lectures is here. Ew. Shout outs to Leo Lectures. I gave you a shout out earlier. Um, I need to figure out how I can have like a permanent, um, you know, streamer recommendations list. If the iPad was alive, I would show it. But shout outs to Leo Lectures. He is a fellow math streamer. We need way more math streamers, and we need way fewer video game streamers. Like, let's get some video game streamers to change to math. Dude, there's so many. It's so saturated, right? Like, video game streaming, like, how do you get found, dude? Just learn math. Like, I would, I would love to watch somebody go from suck to sick, to use somebody's, uh, phrase, somebody else's phrase who I know, like, to go from suck to sick in math live because it's fun just as a hobby. Like, that sounds so fun to watch. I would watch that. Um [laughter] yeah, every, every true or false statement is has a 50% chance.

of being correct. Yeah. 50/50. Oh, the call tomorrow. Hell yeah, dude. You want to join? Um, email me, Leo. Uh, just as a reminder, um, I think it'll be all right. Math hang. Dude, I don't know about math hang. Um, 10:00 a.m. Yeah, 10:00 a.m. tomorrow Eastern. Uh, and then I think study group is at 11. Um, and you're welcome to stick around for study group if it's just you and me, Leo, and we can just nerd out about math during math hang. I think that's a pretty cool little group. But I'll try to reach out to a couple of others as well. I think folks from the from the study group will also show up as well to Math Hang. But right now, unfortunately, it's invite only. Um, yeah, MathHang is unfortunately invite only because otherwise we'd have a lot of people. Um, maybe we'll do it later, but right now I I think it needs to be a smaller thing. Um, yeah.

Dang. I can't believe I'd ever say that. Dang. Multiplication is kind of harder. That's true. What is it? Um, Schultz says math didn't really start until Grathendique. Really? Um, that's interesting. Uh, yeah, snarky comments help. Please do drop as many snarky comments as you want. Um, it's all good, dude. Leo, it would be fun to have you there. Um, yeah. Yeah, I I think it'd be great to have you there, dude. If you can make it. You have interesting videos. Well, thank you so much. Um, you're starting university to study maths. Nice. Nice. Um, Lewis, do you know what kind of math you want to focus on? Um, are you like planning on a on a pure math degree or like education or um engineering or something? Applied math. Uh, if you deleted more than added, that sounds valuable. That's extremely valuable. Yes, it's extremely valuable. Um, no. Don't start watching my Don't You're not supposed to re-watch my live streams. You can if you want to, but um that's not what they're designed for. Just jump in, hang out with us. This is a live stream is not as valuable afterward. Um, but if you feel inspired and you want to just learn a little bit of calculus or any random topic, feel free to. But the only thing that if you want to follow uh like a series, if you want to actually follow like a course, um I only have two videos. Lecture zero is uh math as a hobby. Math can be a hobby and then um episode one is uh on addition. So dude, trust trust me, you can jump in right now. It's we're not too far. Um lecture or uh episode two is dropping this weekend also on addition of positive numbers. Um, yeah, I've been reading YouTube chat. It just took me a while to catch up. Multi-hat drifting. Well, there was a brief there's one person in Twitch uh chatting at least. Now there's four people watching, but one person chatting. Um, yeah, dude. Oh, that's awesome. Yeah. Yeah. So, you're doing like um like a streamer recommendation list. Like, it's something I miss from Twitch. On Twitch, you can just have like JC Practices recommends these other streamers. And it's so important because if you're offline and somebody wants to see your type of content, who do I recommend? If I'm offline, maybe these people are online. like YouTube, dude. I hope that someday they catch up on some of those types of features. I hope someday, you know, what jobs can you get with theoretical computer science? Um, that's a complicated question. Um, yeah, dude, everybody should follow Leo. He's a he's a dope guy. He um I don't know, funny guy. And he also plays some mean jazz piano as well. Um, so ask him ask him to play you some piano. Oh yeah, and Leo is a theoretical computer scientist. I forgot about that. Hey, hey, what's up, Leroy? Dude, Leroy, are you still down for math group for study group on tomorrow 11? Dude, Leroy Leroy is one of the three people who have uh been accepted to the first cohort. Um, yeah, Leroy is a long time regular of the channel. I'm putting you on the spot hardcore right now. Uh, but yeah, man. Um, 11:00 a.m. tomorrow if you can make it. I know. Um, one person can't make it. Um, and then I don't know about the third person. TCS and logic are useless today and yesterday, but tomorrow, dude, like it might be the only thing left. Like philosophy, logic, math, like art, like these things are going to be around for a while. Um, I I'd study an art degree of some kind. A philosophy or art degree. I mean, philosophy is art. Like, everything is art at the end of the day, if you ask me. Like philosophy is people say that it's like the root of every single Wikipedia article. It's the root of everything. I don't know. Art also isn't philosophy also art. I don't know. Creativity for like a bridge like a little connection point between them. uh someone on Discord something or other. Um join the Discord and introduce yourselves, y'all. If you want to join the Discord, um it's nice to just see, you know, all the people that are joining, but if you want to introduce yourself, there's a nice little um introductions channel. Um, yeah. I can't reply to everybody or else I'll be looking at my phone all day long. And uh, no, no, no, no, no, no, no, no. I I have to study. [laughter] I have to go to the library and and read and study today. Um, like I am behind on my to-do list. Um, my my neck, dude. My neck. Um, oh, nice, dude. Leo, like that could be a product. Like, if you want to vibe code that together and sell it, like that that should be a product. I've thought I've thought of this a lot. I have a lot of ideas there. Um, that is missing and that could make a lot of money. If you want to do that together, I think that'd be pretty freaking sick. Um, just discovered me today. Let's go, dude. DevOps. MTO. Let's go. I don't know what MTO means, but uh I know DevOps. Howdy. I'm a fellow software engineer. Um my team got laid off uh from Google um a couple months after Chatubt released. Um I worked on the team of mobile specialists at Google. Uh, and then ever since January 2023, I've been trying to uh trying to chase the entrepreneurship thing. And like I'm just I'm so happy that this uh is starting to to grow cuz like math and classical guitar are two things that I could do every single day for the rest of my life and share it, share practice sessions and um it would not be work to me at all. Uh so I think that there's like kind of a little ecosystem around those two passions um that I could build. Um alternatively I could go work at a high school which is actually that has been my my focus my 90% likelihood focus for a while. But yeah, anyways, um, so I don't know. Just teaching math for fun sounds absolutely amazing to me online or in person or tutoring. Tutoring Jason practices atgmail. Um, Yeah, that's a good definition of it, MP. It's just that I would define it a little more broadly than that, even like, dude, when the traffic light is green, you go. When the traffic light is red, you stop, right? I guess when it's yellow, sometimes you slow down and sometimes you speed up. But ignoring that um ignoring that like it's an input and output. Anything uh that is a a set of rules that associates an input to one output is a function. So, um, like when you type in your email into Tik Tok, uh, and the login button is not enabled until you type in your, um, until [clears throat] you type in your email, like the the state of that fun of that button, like if it's disabled or enabled depends on whether or not what you typed was a correct email. If you just type the word uh poopy or something or banana or Luna um then it it will like freaking not become enabled or like uh a credit card input field like there's amazing little functions where um I mean now that now we're getting back to something mathy but um like check some digits um that's another example where like if the credit card number in a payment field um has a typo. There's a way that an app can detect a typo without um reading without actually reading your uh credit card number. Um, and then the button that says pay or don't pay or something, it becomes enabled or disabled or at least when you click it, it'll say something went wrong or like dude, you you made a typo, like go fix your typo. Um, those are all functions and we write functions all the time in programming. Like in some sense some programmers like myself who love functional programming we try to pretend like everything is a function like we can write all of software as functions as pure math functions. Um, it's got its pros and cons but uh, you know, I enjoy it. It's fun. It feels like pure math. Um, so functions are cool. We'll talk about functions like in a year or something at this rate, but like we're going to have fun along the way. I'll I'll be talking about functions all the time like this, but then we'll get like deep into functions someday. Me stumbling out out of the bathroom after an hour. Everything is art. That's like a Yeah, definitely a a shower thought or something like that. Where should you start? You should start with episode one or episode zero, the uh math can be a hobby video. Watch that and then watch episode one. Um, these live streams are are not meant to be rewatched unless unless you really want. But they're um but those two blue videos, the blue thumbnails, um those are the ones to watch. Thanks, dude. I think it's I think it's got a lot of potential. Yep. Aesthetics is a part of philosophy which deals with art. So, dot dot dot I've got an aesthetics book back there that I've always wanted to read. And someday, dude, someday I'm going to read that book. Um, yo, potentially famished on on Twitch. What's up? What a name. Um, nice to meet you. Nice to meet you. Um, cool. So, most of the parties on YouTube, but please feel free to watch wherever you prefer. Um, I'm multistreaming um classical guitar and mathematics to Twitch and then I have two separate YouTube channels. So, if you only care about one thing, maybe you want to watch on YouTube. But, I don't know, you know, whatever. Math is cool. Yeah, my iPad just died. So, um, but yeah, check out this freaking video, everybody. If somebody asked like where should I start, I'll tell you exact. Holy crap. We just Oh, dude. We just raced through another another doubling. We're two to the 13 now. Oh, man. That's crazy. That's crazy. [snorts] That's That's crazy. [laughter] I've like doubled three days in a row, dude. Um, man, that's wild. Uh, okay. I had I had 1.7 subscribers three days ago and then I had two subscribers the day after that and then I had four subscribers the day after that and now I have eight subscribers. Um, which is wild. Uh, so nice to meet you. Um, here is let's change that. Yeah, dude. Um, there is episode zero and then here is episode one and then episode two is dropping this weekend sometime. Hold me to it. Um, episode zero. I need to go to sleep. Episode one. [sighs and gasps] Good lord, dude. Um. It's a pretty standard math person to be like, I I suggest that you study mathematics and music. That's a good career decision. I promise you, it might not seem like it, but I I suggest that you learn classical music and mathematics. Yeah. Yeah. I I actually do. I think that those are good career decisions right now. I'm not being sarcastic. Um, definitely interested in vibe coding education stuff. Yeah, let's [snorts] talk, dude. Um, your math content is what makes me interested to math. Yeah, thanks, dude. Thank you. That really honestly means a lot to me cuz I'm practicing. I'm practicing like how to teach or how to try to get people interested in math. Um, yeah, potentially famish. I just blew up a couple of days ago. It's It's kind of scary to me a little bit. It's really fun. It's really fun, but it's just like, oh my gosh, what what those numbers are really big [laughter] compared to before. Um, it's awesome. Thought you were talking to yourself. No, no, no, no, no, no, no, no. Um, yeah. Oh, here we go. Here we go. I know. I have an idea. I have an idea. My bad. Um, this one. Okay, so the iPad is dead. The iPad is dead right now. [music] So that's why I switched away. Um, but hey, I'm a classical guitarist. If anybody wants to follow my classical guitar content, um, I am a I'm an enthusiast. That's what my teacher calls me. I call myself a hobbyist or an amateur, but I love it. you know, all the music we're listening to, um, we recorded live on my primary channel, uh, JC Practices. So, um, I'm I'm trying to catch up on chat. So, now you can read chat. That's what I'm trying to get at. I'm sorry, I didn't realize that you couldn't see chat. Uh, someday Leo will help me figure out how to get Twitch and YouTube interled here. >> [sighs] >> We'll do it soon. We'll we'll we'll figure it out. We'll figure it out. Um, dialectics or in math speak would just be logic. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. For me, every color speed up. I don't know what that means. Textbooks, computer science. Nice recommendation. Oh, is that siper? Yeah, bro. That sip. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. This is a beautiful book. This is actually literally a very beautiful book about the theory of computation. So, if you're interested in computers, this is about theoretical computers and it's a it's a very nice book. Very, very nice. So this is the one I would recommend if somebody is interested in um studying computer science. I would start here. Start with this book. It's very nice. Um, if you don't like that book, I wouldn't I wouldn't study computer science. Um, yeah, we talked about the definition of a function. You saw my video about lang and you ordered it. Heck yeah, dude. Heck yeah. Heck yeah. You've been avoiding math your entire life, but you felt you feel left out. Um, TCS is pretty broad. Leo, are you going to stream? Dude, can I raid you, Leo? Cuz I got to go to sleep. I need somebody to encourage me to wrap this up. Um, funeral for iPad on Sunday night. Uh, yeah. Yeah, theoretical computer science really is an offshoot of um really is an offshoot of math. Like it truly is math. Like in the past, people like Turing were just called mathematicians. Like the field of computer science hadn't been invented yet or termed yet. Uh, they were just mathematicians. And then that turns out to be very useful like all of that theory that they built like kind of you know the father of theoretical computer science. Your hobbies are math and editing like video editing. Do you want to help me with video editing? Potentially famish. I hate video editing. I'm I'm getting decently good at it. Um, but it takes so much time for me, man. And I'd rather be studying math or playing the guitar, you know, I enjoy it. I'm I'm growing to enjoy it, but editing, if you meant editing like that, um, man, hats off. Like, it it can be a fun hobby, right? Even if AI gets better at it soon, which I know it's getting it's getting decently good. It's it's already getting pretty good at that. Um, 3,000 likes. That's amazing. Thanks for starting with first principles. Yeah, dude. Yeah. Yeah. Hell yeah, dude. Please make a playlist. I will do that. I will do that. Hey, hey, Ethan. Ethan, Christopher, good to see you, dude. You've been coding a bunch and you're tired. Yeah, keep up that grind, man. Keep up that grind. Um, thanks for joining today. All right, you got to go to actual real world work. I feel you. Um, yeah, I got to go bed. All right, bye everyone. I had a lot of fun. Um, yo, did you do the edits for cutting out blank space for you talking? Um, yeah, yes and no. Um, I know that there's AI for that, but dude, AI is so lame, man. It's so boring. Like, I just don't like using AI. Like, cuz I still have to go into the video like the the blank spaces. Great song. Um, but the blank spaces of the uh of the video are the easy part. That's the easy part. Um, I mean it's tedious for sure. I would save 30 minutes or something. The hard part is cutting phrases and like just I don't know. It's hard to describe, but it's more it's more than just the blank spaces. And then on top of that, for for some videos, I'm somewhat of a perfectionist and like I want to like really fine-tune exactly how much blank space to have. Like I want control over that, but I just don't do it, you [music] know? Like my goal is to not edit at all. Like the intro video, episode zero, is highly edited. It is like retention edited. It's like lots of cuts. Cut out all the ums. Like it wasn't intentionally just like, "Oh, I want to be snappy in like a Mr. Beast math video or something." It's just that I said um a lot or I talk like a normal human who has spaces in between words and that doesn't really work on YouTube. So, I had to go in there and fix some things. And then, well, I was like, "Well, while I'm here and fixing some things, let's like try to make it snappy. I mostly skipped cutting up link spaces in this like 1 hour plus video I've been working on. Don't do that. Just don't do that. People like humanity. If you're posting a 1-hour video, just don't. Just just [music] don't do it. Like people like the imperfection. People like the blank spaces and the fact that this is two and a half hours long. um if you're making if you're trying to [music] post uh like I filmed 18 minutes for that um episode zero and I cut it down to 14 I think I think it went from 18 to 14 and two of that like 18 to 16 was just like kind of mistakes or like easy fillers like like easy like obviously I don't want to say um here or um I lost a train of thought. I don't think I lost any trains of thought, but like bigger [music] edits, like the easy edits were 2 minutes and then the hard edits were how do I shave off a bit more to reduce the timestamp in the thumbnail? Cuz like it's not just the the the picture of the thumbnail, it's the picture, the title, and how long the video is. Like those three things are so like key. I as I understand it, you know, to trying to get somebody to click on a damn thing, like how much time is this going to to be I don't know, you know, like [music] 18 minutes versus 14 minutes might be the difference or like 18 versus or 16 versus 14 or something. So I like at some point I was like, I just want to cut out some of this stuff. Like I like this line, but it doesn't need to be there. Let's cut that just to try to get to like 1459 or something. Um to to try to make it a bit more clickable, but I'm there's no world in which I'm doing that for the for the lectures. Uh episode zero edited, episode one, single take, no edits, no post-prouction at all. Um, and that's the bar that I want to hit. I want to get to that level because I want to give live lectures to little children. I want to teach a middle school classroom of kids. And you don't get to like refilm a line, you know, if you're giving a presentation like first this attitude came from me wanting to give presentations at tech companies or pitching to an investor or something like in some sort of highstakes scenario to try to be able to speak decently articulate articulately um case in point without saying ums and things like that or just be able to randomly get into interesting conversation. Um, yeah, I got to go to bed. That's where the idea of like to me it doesn't count unless it's live. It just doesn't count unless it's live because that's the format that I'm playing in. That's the like if it were speed running or something like competitive video games like there's the any% category versus um I don't know. I don't I don't watch that stuff that very much. Like there's a 100% versus any%. There's task versus human with glitches without glitches. Like you know those different categories, right? Um, I want to make unedited live single first take performances. [snorts] Um, that's the that's the long that's the bar that I'm trying to practice at. And so live streams are great at that, dude. Like live streaming is a great way, I think, to to practice. It's a yappathon. Like literally like just yapping, right? Um, ums and mistakes make it real. Exactly. It proves that you're not ChachiPT. I mean, ChachiPT is going to be really good at putting ums in the right places, you know? Like, it's going to get really good at that, too. But like with live streaming, like I just don't see it happening anytime soon that somebody could deep fake a low latency live stream. That is just dude, if somebody can deep fake a freaking low latency live stream, like the entire world is burning at that point, dude. Like, so like live streaming proves that you're a human, you know? And like so much more of YouTube. There were some comments from people saying that um oh wow the algorithm blessed me. There's no AI slop voice in this or something and I was like yeah dude like I think you're going to like the live streams cuz it's human and we say um all the time. That's normal. That is super normal. Um started leaving in breaths and adding contractions to my voiceovers. Nice. Nice. I'm I'm starting to leave in more ums here and there in my editing as well because it's it sounds more natural. Like I'm leaving there's some gaps like little spaces between sentences or mids sentence where I'll I'll like cut the gap in half, you know? I don't cut the gap completely, but like just like just a little bit, you know, just like half of that length. Um, so we can deep fake K. I don't see that happening anytime. I mean, if you're a if you're like a VTuber, it would be like really easy to deep fake that. And people are doing that now. There's like one V YouTuber on Twitch who's got like a million followers or something like I don't know their name. I forget what it's called, but it's like a big deal that there's this VTuber. Sorry, not V. Of course, there's lots of YouTubers, but there's an AI VTuber um that's 100% ChachyPT or Claude or whatever, you know. Probably Claude. So, um I I like I like the format of live streaming. I think YouTube has so much potential for growth as a live streaming platform. I really do. [music] cuz uh it's just it's such a cool medium that a lot of people have never seen before. Okay. What the thing is I sometimes learn coding languages but quit because I don't have much projects to work on. Yeah. Cyber potato. That's a skill that takes time to develop. It just does. Uh finished my physics BS like eight years ago. Nice. And you're trying to practice math for fun. Dude, you found the right place. What's up, Tom? Tom. Uh, dude, thanks for joining. It's nice to meet you. Uh, yeah. Yeah, I I think I've met so many people uh I've met so many people, especially at tech companies, who study math for fun. Like, I think it's a very popular thing. It's maybe it's not the majority of people, but it's a very popular thing that people study math or physics or chess, you know, for fun and and they just do it on their own because they think that they can learn it with Khan Academy. And it's like, dude, you don't even know what you don't know. Dude, you don't even know what you don't know. If you think Khan Academy is how you can learn math for fun, yeah, Khan Academy sounds fun. Khan Academy is fun. That would be fun. But like, dude, have you ever tried real math? Dude, have you ever have you ever tried yellow math? Like, this stuff, yellow math is cool. Yellow math is really good. You'll get completely hooked once you start yellow math. Um, it's like I don't know, proof oriented. The Springer, is it pronounced Springer? Springer. Uh this publishing house uh is famous for this style of yellow books. Um, this is one of them for they don't even rate it like high school or anything. This is a unique special book that doesn't really fit neatly into high school, undergraduate, graduate level, but a lot of I have a lot of these that are like graduate level books. this thing um takes the idea of algebra. So, usually in high school, algebra is just like part of what you study before you go to trigonometry, geometry, and pre-calculus and stuff like that. [snorts] Um, algebra is like you learn algebra 1 and algebra 2. Later on, when you're a real math major, when when you're like in grad school, you do an entire year-long course on algebra. And like, you don't even know what you don't know. This stuff is so pretty and really, really hard and really, really different than what you might be imagining. But it's still at the end of the day algebra. It's still the same algebra. It's just different. But there's a reason we use the same word for both of them. There's like a good reason for [music] that. I got to go to bed. Things have changed. Yeah. Your old way is now being taken by AI. Oh, the the way that you used to to do voiceovers is now sounding like AI. That's like me with m dashes, dude. I would never actually hit the m dash character, though. I've always used hyphens. Just like a simple like dude, I'm not a nerd. Like just like you don't have to do the long weird dash that not everybody knows how to type. Just use a rig regular little small dash. Like I'll die on this hill. I will die on that hill. Like I love the dash as a writing device. M dash or small dash, whatever you want to use. Um, and now AI is taking that. So, so I make it a point to use an M dash in all of my [music] freaking video titles. Like every video title uses M dashes and it's like, yeah, you can't like you will take these dashes from my cold lifeless hands, you know. Um perhaps best use of math now is just making sure you can still think. Yeah. And a lot of people are going to feel like like work is starting to feel like Tik Tok or something like that that they need to exercise their brain. And I think math for fun is just the best way to just keep your brain sharp. Like math as a hobby, great idea. Good idea. Very good idea. TMW yellow math. What is What does that mean? Tomorrow yellow math. No, tomorrow. Well, I don't know. Can you get a job with automated theorem proving? Yeah, but then it's kind of like you're putting yourself out of a job, right? That's sort of sad. Like I don't really want to work in that kind of software. Um, it's pronounced Springer. Thank you. Uh, books are more fun than any X Academy. Yeah. Yeah. Just paper books, dude. This was published 50 years ago and it's better than ever, I think. Oh, wait. No, not this one. I don't know. That one maybe, too. But this one was published 50 years ago, and it's just it's better than ever. I really think that this book is better than ever. Um, yeah, it's it's better than Khan Academy, etc. Like Khan Academy is great, but like books are better. Like why why did we move away from books? You up late yesterday? Yeah, Luna woke me up. [snorts] Who's the guy on the left hand side? That's me and my cat Luna. She woke me up and then I checked my phone and then I couldn't fall asleep again cuz phone hygiene is a thing. Don't look at your phone in the middle of the night. I just [music] couldn't go back to bed. Um, yeah, dude. Do your VTuber thing just every now and then flash back to your camera just to prove it to people that you're actually a human. Just like every now and then, you know, you don't need to do it for the entire stream. Um, I I think people would enjoy that. I think people would uh appreciate that. Yeah, you've got Griffiths. Um, I don't have Griffiths. I I keep collecting all these damn books that I uh that I'm not reading like The Great Gatsby or something like it's just that I will read this book eventually. But I've got Jackson back there. The yellow or the the blue book right there, that's Jackson someday. Like that's a commitment for me. Like I I did take an upper division uh quantum course with that pink one over there. Um, but I dropped out of the Jackson uh course in order to to do a philosophy class instead. And um I don't know, man. I mean, no regrets there, but someday I want to learn Jackson's ENM like hardcore stuff. Like scary scary math. Um, oh yeah, and you said that too at the end. Maybe I'll make it to Jackson someday. Me too. You and like let's start the Jackson study group someday. Someday. [sighs] Yeah. You're a hyphen hog. I've never heard the term, but I love it. A hyphen hog. That's great. Yeah, you have to add the imperfections back in, which is weird. Yeah. Yeah, that's funny. That moment when yellow math. Oh, that's funny. Uh, I really like those parsing exercises and proof theory. Oo, that sounds fun. Like logic stuff. Yeah, what's up, Vob Edits? Um, yeah, you are a bit late, but you could rewind if you want. Today was a really fun stream. I just wanted to do one hour, but we ended up we're almost at three now. It's crazy. Um, yeah, I got I'm just going to prove it because it's fun for me. I don't do too much physics. I do want to learn like proper classical mechanics someday, but like I don't know, more than anything, like someday I want to tackle these two. They're so pretty, too. Like look at those colors, dude. They look nice. just like I love all these like big bold color books, right? Like it they if nothing else they just look nice in my opinion back there against like the black bookshelf. So right now they're just decoration. But someday someday we will hit Jackson. Mark my words. Even if it's just one exercise. Where the math at? Um, my iPad ran out of batteries and I have to go to sleep now. [laughter] Uh, Gamalin and Green. I don't know that one. Oh, that one. Yeah, yeah, yeah. I I've barely read that one, but I do want to learn topology with that um someday. Someday. We just used it to to write down the formal definition of a limit uh in topology terms because there's so many different ways to write down the definition of a limit in different math worlds like different contexts, different number systems. Um, and like topology is one of the the coolest and weirdest ones. Um, so that's why I had gamlin and green in that thumbnail. Like that was a that was a really fun stream where we um compared the definition of limit everywhere. Uh Sixers probably has about five diagonalization pro. Dude, didn't you say that you were going to someday um do a whole video focused on diagonalization? I don't know anything about Tarski. Some famous physicist says, "A physicist is anyone who studied ENM through Jackson." That is such a gatekeeper. That's hardcore. Oh my gosh. A physicist, you're only a physicist if you have studied Jackson. Man, I would drop out. [laughter] Like, I wouldn't I would not have made it. Um, what's uh what am I searching for right now? What am I looking for? Yeah, channel's going crazy. It's It's really weird. Um I mean, I'm so grateful and excited about it, but yeah, it's shocking to me. What was I going to look for, dude? Leo, that sounds Dude, just film it and then film it again and make it shorter. Yo, what math do I do? I do basic mathematics this week. This week we're doing um middle school, high schoolish math done, right? Like starting from the ground up with numbers, like just adding numbers. I promise you it's more interesting than you might think. Um, so if you want to see what we're talking about, check out this video. Where did I put it? This one. All right, episode one is out right now in my brand new series on introduction to real mathematics um or proof oriented math and we restart and this is meant to be accessible to anybody um literally from the very beginning integers I promise you it might be more interesting than you think um it's really cool I geek out about it. I study this kind of math for fun. So, this week we're doing high school math. Next week we are doing college math. I don't know what book we're going to pick. Calculus, linear algebra, group theory, abstract algebra. Um, and then the following week we're going to do some graduate level math and that's going to be hard. um to do some representation theory, which is like brand new math for me. I've never learned it before, and try to learn live some graduate level math. And then once we're done with that grad level math, then we come back and then we're back to stuff that I do understand. Uh and then we go back to college and then we go back to graduate school and then, [music] you know, back and forth forever and ever. Um, I would say the notion of self- reference like the liars paradox is one of the most important things to see in [music] TCS. That's so cool. You just stumbled upon uh basic math and you love these types of live streams. Yeah, dude. If you have any other recommendations of streamers like math as a streaming category is so underrated. There's like a few others that I know like shout outs to Leo lectures, shout outs to K theory. If you enjoyed this, I think that you'll enjoy those fine gentlemen [music] as well. How can I How do I type? YouTube.comctures. Um, YouTube.com/k Theory. [music] Yeah, his isn't annoying. Like, I I don't remember his the numbers. See, you thought that they were letters, but they're numbers. Like dude, bro needs to just find some different num find different numbers that people can remember or try to find another one that doesn't have numbers so I can just type it, you know, or write it on the iPad. I have to look it up every time. Um like bro needs to make it 123 or uh 235 or something. 314 like oh pi like 314 like it's cra like maybe his numbers mean something in representation theory and it's like bro has lost the plot. No dude it's not for you it's for the other people. You know what I mean? Like I I hope we can get K in the in the weekend um hangouts soon. Is he streaming? That was the other thing I wanted to check on. Is anybody streaming? It's like impossible to find out in a moment if somebody I know is streaming to raid them. [music] Nope, doesn't look like it. So, I think we're good for today. 8604 ain't anything. [music] There must be something. That's That's hilarious. Um, all right. Okay. theory huge ass. Yeah, that [music] just something like something like that. Just K Theory. Um K Theory bro [music] like dude K Theory bro. That sounds That sounds like a great handle. Like he's the K Theory bro. I don't know. The Okay theory. Um, all right y'all. I had so much fun today. I think that we're finally caught up. Um, thank you for watching. Um, uh, if you know anybody who likes math, uh, share this with them. You know, it's really nice to to be growing this community. I think it's it's so freaking dope. Like, math hobbyists, it's it's underrated. Underrated, you know? Like, it's nice to just build a space where we can just hang out and chill and geek out about stuff like this. So, thanks for watching. Bye. I gotta go. Bye. Bye. [music] Bye.