Terence Tao

SUMMARY: One of the most accomplished contemporary mathematicians, Terence Tao is a groundbreaking number theorist as well as a popular blogger.

Terence Chi-Shen “Terry” Tao (1975–) is a South Australian–born mathematician. Some rank Tao among the greatest living mathematicians in the early part of the twenty-first century. A child prodigy, he was taking college-level mathematics classes as early as nine years old and was awarded a Ph.D. from Princeton University at the age of twenty. He began teaching as a professor at the University of California, Los Angeles, in 1994 and became a full faculty member in 1999 at twenty-four years old. As a mathematician and writer, he is extremely productive and has contributed elegant solutions to difficult problems in diverse areas in mathematics. His primary research interests are analytic number theory, harmonic analysis, combinatorics, and partial differential equations.

Honors and Contributions

Dr. Tao’s contributions to mathematics, and his awards for them, are numerous. In 2006, Terence Tao was awarded the Fields Medal. The Fields Medal is sometimes called the “Nobel Prize of mathematics” and is generally regarded as the most prestigious award in mathematics. It is awarded once a year for superlative achievement by a mathematician up to the age of 40. At the age of 13, Tao won a gold medal at the International Mathematics Olympiad, an annual competition intended to challenge the world’s brightest students of high-school age; as of 2010 he remained the youngest person to ever win such a gold medal. His accolades also include the Salem Prize, the Clay Research Award, the SASTRA Ramanujan Award, the Australian Mathematical Society Medal, and the King Faisal International Prize. Tao has been pleased with his success, but he would like to continue focusing on mathematics research rather than reflect on his achievements. In 2014, Tao received a CTY Distinguished Alumni Honor from Johns Hopkins Center for Gifted and Talented Youth, the program from which he graduated. He received the award in front of nearly one thousand students who were also in the same program. In 2021, he was selected by President Joe Biden as a member of the President's Council of Advisors on Science and Technology.

One particularly significant contribution by Terence Tao to number theory came in 2004. In joint work with Ben Green, he proved a remarkable result about arithmetic progressions of prime numbers. An arithmetic progression is a sequence of numbers with a constant difference between them. For example, 5, 11, 17, 23, 29 is an arithmetic progression with length 5 and constant difference 6. The five numbers in the sequence are prime. Green and Tao proved that it is possible to find arithmetic progressions of five primes, or 50 primes, or 50,000 primes. Indeed, they showed that arithmetic progressions of primes exist that are as long as desired. Understanding the distribution of the prime numbers is of paramount importance in number theory, and results of this type are often notoriously difficult to establish.

Communication and Strategy

In addition to all his papers and books, Terence Tao is a very well-respected and prolific blogger. On the “What’s New” blog, Terence Tao frequently posts remarks on his ongoing projects, links to and commentary on current articles, and other mathematical topics. There are numerous active mathematical blogs at all levels of sophistication, but many consider “What’s New” to be the “grandfather” of mathematical blogging. “What’s New” is considered by many active mathematicians to be an important and influential source of information. The American Mathematics Society has published sixteen books of excerpts from his blog.

While he has been described as the “Mozart of Math” because of his creativity and the mathematics that seems to flow out of him, Tao attributes his success to strategies that enable him to break up difficult problems into easier ones. Often, he focuses on one question at a time and tries a variety of techniques. He stated: “When I was a kid, I had a romanticized notion of mathematics—that hard problems were solved in Eureka moments of inspiration. With me, it’s always, ‘let’s try this that gets me part of the way. Or, that doesn’t work, so now let’s try this. Oh, there’s a little shortcut here.’”

As an authority in the world of mathematics, Tao's thoughts and opinions are not taken lightly. As artificial intelligences (AI) have grown, particularly in their ability to communicate and engage in live interaction, Tao was questioned on his impression of AI's mathematical abilities. Though he compared AI to a somewhat competent graduate studies student, he noted the potential for collaboration when it comes to mathematicians and AI-generative software. In this way, AI would not do the thinking or computing for people, but would instead act as a conduit and partner whom people could work with.

Bibliography

Cook, Gareth. “The Singular Mind of Terry Tao.” The New York Times, 24 July 2015, www.nytimes.com/2015/07/26/magazine/the-singular-mind-of-terry-tao.html. Accessed 4 Oct. 2024.

Green, Ben, and Terence Tao. “The Primes Contain Arbitrarily Long Arithmetic Progressions.” Annals of Math 167 (2008).

“Mathematical Minds: Terence Tao.” Interview with the Gazette of the Australian Mathematical Society 36, no. 5 (2009).

Tao, Terence. Poincaré’s legacies: Pages From Year Two of a Mathematical Blog. Providence, RI: American Mathematical Society, 2009.

———. Solving Mathematical Problems. 2nd ed. Oxford, England: Oxford University Press, 2006.

———. Structure and Randomness: Pages From Year One of a Mathematical Blog. Providence, RI: American Mathematical Society, 2008.

———. What's New, Word Press, terrytao.wordpress.com/. Accessed 4 Oct. 2024.

Wong, Matteo. “We’re Entering Uncharted Territory for Math.” The Atlantic, 4 Oct. 2024, www.theatlantic.com/technology/archive/2024/10/terence-tao-ai-interview/680153/. Accessed 4 Oct. 2024.