Transcription
The thing about math, right? Especially if you're talking about pure math, the experience as a student is that you are going through a textbook. It starts with saying, "Here's the axioms of this field," and then, "We're going to deduce from those axioms like various different lemas and theorems and proceed from that."
And with that as the framing, you get the impression that you could have just come up with any axioms, just make up some pile of axioms, deduce what follows from them. The space of possible like math is unfathomably huge. And so you need some process that calls down what are the useful things to maybe pursue.
And so one of the things that I think is all too often missing in those pure math textbooks is the basically the motivating problem. Why is it that this was the set of axioms people found to be useful and not something else?
The framework for Quantum Information Theory, it's like you marry together linear algebra and probability. That's great. But there's all sorts of other things where you could kind of try to cram them together and maybe get some sort of math out. And the the question becomes, is it worth your time to do that?