New York Times features mathematician Terence Tao

The New York Times has published a feature article on mathematician Terence Tao of UCLA, regarded by some as the most brilliant mathematician alive.

Terence Tao was born in Adelaide, Australia, the son of Chinese immigrants. His intelligence and mathematical precocity were evident at a very young age. He taught himself to read at age 2. At the age of 7, the local newspaper showed a photo of him in an 11th grade mathematics class, kneeling on his chair should that he could reach his desk. A few months later, he was promoted to 12th grade. At the age of 10, Tao was the youngest person in history to win a medal in the International Mathematical Olympiad. At 15 he published a book on mathematical problem solving. By age 17, he had finished a master’s degree (with a thesis on “harmonic kernels”), and by 21 he had received a Ph.D. from Princeton University.

Tao’s accomplishments, even at age 40, are most impressive. In 2006, he received the Fields Medal (considered the equivalent of the Nobel Prize for mathematics) and in 2014 received one of the inaugural Breakthrough Prizes in mathematics (for which he received USD$3 million from Russian billionaire Yuri Milner). Even among Fields medalists, he is viewed with respect verging on awe.

Tao’s mathematical work spans harmonic analysis, partial differential equations, combinatorics, ergodic Ramsey theory, random matrix theory, analytic number theory, and compressed sensing among others. Perhaps his best-known result is the Green-Tao theorem, which is that the sequence of prime numbers contains arbitrarily long arithmetic progressions, or, in other words, that given any n, there is some m and k such that the sequence (m, m+k, m+2k, …, m+k(n-1)) are all prime numbers.

But Tao has made seminal contributions in many other fields as well. His work on Horn’s conjecture, which he co-authored with a foosball friend from graduate school, was so different from his established field of study that his Fields Medal citation gave the analogy of “a leading English novelist suddenly producing the definitive Russian novel.”

Tao operates a lively mathematical blog and stays in close contact with the Australian mathematical community. For instance, he is one of the keynote speakers at the 2015 annual Australian Mathematics Society meeting at Flinders University (his alma mater).

Defying the stereotype of mathematicians as closeted “nerds,” Tao is, as described by a colleague, “super-normal.” He is married, with two children (one of whom has appeared in television commercials), and works very effectively with other mathematicians. Indeed, many regard his greatest strength to be his talent for collaboration, for organizing teams of mathematicians to address new problems.

One example was in May 2013, when the previously unheralded mathematician Yitang Zhang proved that there are infinitely many gaps of prime numbers that do not exceed 70 million. At this point, Terence Tao joined with the Polymath project, an online collaboration of volunteer mathematicians to reduce this bound. By early 2014, Tao and others on the team had reduced the 70,000,000 figure to a mere 246.

Reflecting on his career to date, Tao realizes that his earlier training in mathematics did not prepare him for the truly imaginative and intuitive nature of real research mathematics. Tao had imagined that “a committee would hand me problems to solve.”

Tao now sees mathematics in a light similar to that described by Princeton’s Charles Fefferman, who gives the analogy of “playing chess with the devil.” The devil may be vastly superior at chess, but you have advantage that you can take back moves if you wish, while the devil cannot. In your first few games, the devil crushes you, pouncing on any oversight or mistake, but eventually you discover a weak link, and force the devil to shift strategy, until you finally defeat him in a checkmate.

In one of Tao’s most recent forays, he is struck by the fact that waves of water do not exhibit destructive vortices, so he is convinced there must be something fundamental we do not understand about the Navier-Stokes equations that govern fluid motion, and he is pursuing several lines of investigation. But Tao says that he “has been here before,” thinking that he had found a route through the opponent’s defenses, only to realize that he was being led into an ambush. As he explains, “you learn to get suspicious.”

Numerous additional facts and perspectives are in Gareth Cook’s very informative and well-written article in the New York Times.

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