Transcription
In July 1988, the International Mathematical Olympiad brought the most brilliant teenagers from around the world to Australia. They were there to solve problems that would break the minds of most university professors. Amidst the rows of awkward adolescents stood Terrence Tao. He looked out of place. He was small, quiet, and the youngest person in the room at just 13. Australian Prime Minister Bob Hawk crossed the stage clutching a gold medal. He placed the heavy ribbon around the boy's thin neck. The audience erupted. Terrence Tao had just become the youngest gold medalist in the history of the competition. Yet the boy did not grin for the cameras. He shook the prime minister's hand. A participant later remembered that Terry seemed almost confused by the noise. At an age when other boys were learning how to throw a cricket ball, Tao was already rewriting the rules of what a child's mind could do.
At 24 years old, Tao would go on to become a full professor at UCLA, the youngest person ever appointed to that rank in the university's history. Students assumed he was a TA. He was even younger than half of the students he taught. In 2006, at just 31, Tao won the Fields Medal, the highest honor in mathematics, often described as the Nobel Prize of Math, given only every four years to a few select mathematicians under 40. He has received a MacArthur Fellowship in 2006 known as the famous Genius Grant, the Royal Society's Royal Medal, the Crafford Prize in 2012, a prestigious international prize awarded by the Swedish Academy for Fields Not Covered by the Nobels, and the $3 million Breakthrough Prize in Mathematics in 2014.
The story of Terrence Tao is a story of a boy who once almost failed because he thought he could outrun the work. It is a story of a man who despite his talents had to completely reinvent himself to emerge as arguably the greatest mathematician of the 21st century. The roots of this story stretch back to Hong Kong. Billy and Grace Tao left the crowded streets of the city in 1972. They came to Adelaide in search of open space and opportunity. Billy was a pediatrician. Grace was a teacher of physics and mathematics. They were educated people who believed in the immigrant dream. They believed that hard work could open doors that had been bolted shut. They did not know that their first son would blow the doors off the hinges.
Terrence Chiantau was born on the 17th of July 1975. The signs of his genius appeared almost immediately. He did not play with blocks like a normal toddler. He arranged and counted them. He taught himself to read before he was 2 years old. His parents faced a terrifying choice. They had a child who could perform arithmetic before he could tie his shoes. The local schools did not know what to do with him. A 5-year-old Terry walked into a classroom and realized he was already years ahead of the curriculum. The teachers were baffled. Billy and Grace made a decision that would shape the rest of their lives. They created a curriculum at home. They let him move at his own speed. Billy Tao knew that burnout was the enemy of prodigies. He knew the history of children who shone too bright and burned to ash before they turned 20. He wanted his son to have a childhood. Terry played video games and learned computer programming at age six because he wanted to make things move on a screen. He taught himself the basic programming language from a manual. By day, he was a child. By late afternoon, he was auditing university courses at Flender University. The room at Flender University was filled with undergraduates in jeans and flannel shirts. They were 18 or 19 years old, and there in the front row sat a 9-year-old boy. His feet did not touch the floor. He listened quietly and took notes.
At age 8, Terry scored a 760 out of 800 on the math section of the SAT. This is a test designed for American high school seniors looking to enter university. Terry was eight. Researchers at Johns Hopkins University who met him thought he had the greatest mathematical reasoning ability they had ever seen, but raw ability was not enough. His father knew he needed mentors. He needed to see how the game was played at the highest level. Billy Tao took his son to America when Terry was nine. They went to Princeton to the Institute for Advanced Study. They met the gods of mathematics. They met Charles Fefferman and Enrico Bombiieri. These were men who had won Fields medals and defined the field. Feerman gave the kids some tricky pursuit of Asian problems way beyond simple math to see what he was really capable of. Terry totally nailed these complex puzzles which featured figures like lions chasing men in a small space. The amazing part, he didn't use the standard methods. He came up with his own clever ways to solve them. Feerman was blown away, later saying he was impressed that a 9-year-old could invent ideas you wouldn't find in any textbook. Bombiieri saw the tension in the small boy. The atmosphere at the Institute for Advanced Study can be suffocating. It is serious business. Bombiieri decided to break the ice. At one point in their interaction, the great mathematician jumped up and roared like a lion. He chased the 9-year-old around the office. The room exploded in laughter.
Then came Paul Erdus, the wandering Hungarian monk of mathematics, visited Adelaide in 1985. He was famous for his eccentricity and his brilliance. He called children epsilons because they were small quantities. He sat with 10-year-old Terry. They worked on problems together. Terry later said he looked like just another nice old man. He did not know he was sitting with a legend. Erdis treated him like an equal. He spoke to him as an adult. He wrote a letter later that predicted greatness. He said he was sure Terry would become a first rate mathematician. It was the blessing of the pope of mathematics.
Despite his impressive collection of medals and accolades, trouble was brewing for Terry. Terry Tao was merely coasting. He hadn't developed study habits because he had never needed them. The solutions simply materialized in his mind. He earned his bachelor's degree at 16 and his masters at 17. Then he headed to America, packing for Princeton to pursue his PhD. A teenager about to enter the most rigorous mathematics program globally, he mistakenly anticipated an easy experience. Princeton in 1992 was a cold bath. Terrence Tao walked into Fine Hall and looked at the faculty directory. He recognized half the names from the textbooks he had read. He felt a sudden shiver of intimidation. He was 17. The other graduate students were in their mid20s. They had lived lives they had failed before. Terry had never failed.
He chose to work with Elias Stein. Stein was a legend in harmonic analysis. He literally wrote the book on the subject. Stein was a kind man with a sharp mind. But the work was hard. The problems at Princeton weren't like 4-hour Olympiad puzzles with clear-cut solutions. They were tricky, ongoing issues in math that really required a ton of hard work and sticking with it. Terry did not have grit. He spent his time playing computer games like Civilization and Tetris. He joined a film club. He played foosball in the student lounge. He avoided the library. He was living on his own for the first time. His father had to come to New Jersey for the first week to help him set up a bank account and learn to do laundry. The genius of the Olympiad was struggling to function as an adult. When the time came for his general exams, he studied for a few weeks. He walked into the oral exam room with the confidence of a prodigy. He almost flamed out. The professors asked him questions he could not answer. He froze. He stumbled through the solutions. He managed to pass, but it was a near thing. Elias Stein sat him down afterward. The older man was gentle but firm. He told Terry that the performance was disappointing. It was the wakeup call he needed. Tao realized that the magic trick was over. He could not rely on raw processing power anymore. He had to learn the craft. He began to work and listen. He learned that research is not a sprint. It is a marathon through a jungle at night. You do not know where you are going. You hit dead ends. You have to backtrack. You have to hack through the vines of confusion. Stein taught him how to see the big picture. He taught him to respect the literature. He showed Terry that mathematics is a conversation across centuries. You cannot speak if you do not listen to what has been said before. Tao recalled standing in line at Stein's office hours. He would bring a thorny problem to the master. Stein would listen for 5 minutes. Then he would reach into a filing cabinet and pull out an old paper. He would know exactly what technique would crack the lock. Tao began to read. He became a researcher by absorbing the work of others. This involved developing the rigor to write proofs and the patience to endure the tedious task of checking details. He finished his PhD at 21. He finally became a mathematician.
Moving to Los Angeles in 1996, he joined the faculty at UCLA. The campus with its sunny and bright atmosphere offered a contrast to the Greystone of Princeton and the quiet suburbs of Adelaide. In the chaos of the city, Tao thrived. He became a full professor at 24. He was the youngest person ever appointed to that rank in the history of the university. He wore t-shirts, sneakers, and rode a bike to campus with a backpack slung over one shoulder. Students in the hallways mistook him for a teaching assistant. His office became a legend. Papers were piled in teetering towers. Books were scattered on every surface. It looked like the aftermath of a paper explosion. A journalist once visited him and found Tao was clad in khakis and a royal blue polo shirt. He was friendly and unassuming, but the room around him was pure entropy.
Tao developed a reputation as a machine. He did not work on one problem at a time. He worked on 10 or 20. He rotated through them like a chef managing pots on a stove. If he got stuck on a problem in number theory, he would switch to a problem in partial differential equations. If he got stuck there, he would move to harmonic analysis. Tao distinguished himself as a prolific collaborator in contrast to most mathematicians who tend to closely guard their ideas for fear of being scooped. Unlike his peers, Tao freely shared his intellectual property, engaging in open discussions with anyone interested. He would literally invite others into his thought process at the blackboard. Word got around in math circles that if you were stuck on a problem, you just had to get Terry interested. He would listen for a few minutes. He would stare at the ceiling. Then he would say something that forced the door open. He could see the hidden threads that connected everything to everything else. The results began to pour out of him. The volume was staggering and the quality was terrifying. He was publishing 50 papers a year. These were major breakthroughs. His colleague John Garnett said that in a good year he might write three papers. Terry wrote 56 in 2 years and they were all brilliant.
In 2004 he teamed up with Ben Green. They decided to tackle the prime numbers. The primes are the atoms of arithmetic. They are the building blocks of all numbers. 2 3 5 7 and so on. They seem to appear at random. There is no simple formula to predict where the next one will be. As you go higher, they get rarer. Mathematicians had wondered for centuries if there was a pattern. Could you find a sequence of primes that were evenly spaced? This is called an arithmetic progression. Could you find three primes in a row with the same gap? Yes. 3 5 7 The gap is two. Could you find four? Yes. Could you find 10? Could you find a 100? Green and Tao tackled a problem that had persisted for centuries. Their approach was novel, utilizing methods from both erotic theory and combinotaurics. In doing so, they forged a connection between two academic areas that seldom intersected. They proved that you could find a sequence of any length you wanted. You could find a billion primes in a perfect row if you looked far enough. They did not find the primes themselves. They proved they had to exist. The green tow theorem rocked the math world. It was a discovery of deep beauty. The New York Times ran a story on it. They explained to the public that somewhere in the infinity of integers, there were regiments of primes marching in perfect step.
Then came compressed sensing. This discovery began at a preschool. While picking up his son from preschool, mathematician Terrence Tao encountered Emanuel Candes, a fellow mathematician. Candez was facing a challenge related to MRI machines, determining if a highresolution image could be rebuilt from limited data. Conventional wisdom said no. This is known as the Nyquis Shannon sampling theorem. It says that to build a clear picture, you need a lot of samples. If you skimp on the data, the picture will be blurry. Candace suspected this might not always be true. He thought that if the image had a certain structure, you might be able to guess the missing parts. Even with all the noise from parents and kids, Tao listened carefully to the problem and got the gist. He told Candess he was skeptical. He thought the task was impossible before heading home. But the problem kept nagging at him. Eventually, he connected it to highdimensional geometry, which gave him a workaround for the system. If the image was sparse, it meant it contained less information than it appeared. Most of the data was zero or close to zero. You could find the picture in the data if you knew how to look. He wrote to Candice the next day. He had solved it. Together, they built the field of compressed sensing. It changed the way doctors take MRI scans. It allowed machines to see more while looking less that saved lives.
He has also taken on the Navier Stokes equations which describe fluid dynamics, the flow of water, air, and oil. These are considered the most challenging equations in physics and are designated as one of the Millennium Prize problems. The Clay Mathematics Institute offers a $1 million prize for the solution. The core question is straightforward. Are the governing equations always valid? Or can a fluid's movement become so intricate that the mathematics fails? Specifically, is it possible for the fluid's velocity to reach infinity within a finite time, a phenomenon known as a blowup? Though Tao did not ultimately solve the problem, he devised a thought experiment to test its boundaries. The exploding water computer. He envisioned a computer constructed from water to illustrate how energy could potentially concentrate in smaller and smaller eddies. A large whirlpool driving a small one, which in turn drives a tiny one. If perfectly constructed, the energy would accelerate, suggesting the equations underpinning the physics might be more fragile than previously thought.
The awards have been raining on him since that IMO gold medal win in 88. In 2006, his exceptional intellect won the MacArthur Fellowship, popularly known as the Genius Grant. That same year, in August, the math world gathered in Madrid for its Super Bowl, the International Congress of Mathematicians. Terry Tao, then 31, was awarded the Fields Medal. The citation for the medal was an unprecedented catalog of achievements recognizing his total dominance across disperate fields, partial differential equations, combinotaurics, harmonic analysis, and number theory. During his speech, he focused on acknowledging his mentors and collaborators, consistently attempting to deflect the spotlight. He is known to dislike the word genius, finding it a lazy descriptor that unfortunately creates a barrier between the public and mathematics. He started a blog called What's New? It is the most important website in mathematics. He once wrote an essay titled does one have to be a genius to do maths? His answer was an emphatic no. He believes that success comes from hard work, asking questions, and making mistakes. He posts his own rejections. He admitted that he still submits papers that get turned down. He showed the world that even Terrence Tao has bad days.
Tao initiated the Polymath projects, recognizing the potential of the internet to transform mathematical collaboration. This concept was tested in 2009 when Timothy Gowowers questioned the feasibility of massively collaborative mathematics. Tao eagerly participated. They posted a challenging problem online, inviting contributions from anyone interested in assisting with the solution. The result was electric. They solved problems in weeks that would have taken years for a lone genius. In 2013, a mathematician named Yang Jiang proved that there were infinitely many pairs of primes with a gap of 70 million. It was a huge breakthrough, but 70 million is a large number. Mathematicians wanted to get it smaller. The world watched as the number dropped. It went from 70 million to 60 million, then to 10,000, then to 600, then to 246. Tao orchestrated it all.
He is 50 years old now, still writing and thinking. He's a huge bike guy, riding his cycle to work every day. He's married to Laura, who is an engineer at NASA, and they have two kids. When he's got free time, you can find him catching up on Doctor Who or playing board games like Settlers of Katan. He knows he's not immortal, so he makes sure to get his rest. Colleagues say that if you met him at a party, you would never guess who he is. He is softspoken and polite. He listens more than he talks. In 2014, he won the prestigious Breakthrough Prize known as Oscars of Science, which included a $3 million award. The ceremony was a glitzy affair featuring movie stars. Rather than keeping the prize money, he chose to donate part of it. He dedicated the funds to supporting the future by establishing a fellowship program for graduate students.
Is he the greatest mathematician of all time? It is a question that people love to ask. It is a question that makes mathematicians squirm. How do you compare him to Gaus or Oiler? British mathematician Timothy Gowowers has compared Tao to David Hilbert. Hilbert was the last man to know all of mathematics. Gowowers says that it is hard to find a gap in Tao's knowledge. If you find one, it will be filled a year later. Charles Fefferman says that Tao is the ultimate problem solver. If you are stuck, you call Terry. He is the breaker of log jams. So what will he solve next? Tao is looking at artificial intelligence these days. He is also interested in the twin prime conjecture which basically asks are there an endless number of prime pairs that are only two apart. He's also wondering if working with computers could help crack these kinds of problems. Another thing he's mulling over is the kalat's conjecture. If you keep having an even number or doing three * + one to an odd number, will you always end up back at one? Tao has shown it works for almost all numbers. But nailing down that final solid proof is still a challenge. This was the story of Terrence Tao, the Mozart of math, the epsilon, the professor, the connector, the greatest of his time.