Terence Tao

Terence Chi-Shen Tao is an Australian and American mathematician. He won the Fields Medal in 2006 for work spanning partial differential equations, combinatorics, harmonic analysis, and additive number theory. He teaches at the University of California, Los Angeles, where he holds the James and Carol Collins Chair. One of his best-known results is the Green–Tao theorem, which he proved with Ben Green in 2004, showing that prime numbers contain arbitrarily long arithmetic progressions.

Tao was born to Chinese immigrant parents and grew up in Adelaide, South Australia. His father, Billy Tao, was a paediatrician born in Shanghai who earned a medical degree from the University of Hong Kong. His mother, Grace Leong, was born in Hong Kong and earned a first-class honours bachelor’s degree in mathematics and physics from the same university, later teaching those subjects in secondary school. The two met as students at the University of Hong Kong and emigrated to Australia in 1972. Tao has two brothers, Trevor and Nigel, both of whom also competed for Australia at the International Mathematical Olympiad.

A child prodigy, Tao skipped five grades. He was taking university-level math courses by age nine. At eight, he scored a 760 on the SAT math section, one of only three children in the Johns Hopkins Study of Exceptional Talent program to reach 700 or higher. Julian Stanley, who directed the Study of Mathematically Precocious Youth, called Tao the most mathematically gifted student he had encountered in years. Tao became the youngest ever participant in the International Mathematical Olympiad at age ten, winning bronze in 1986, silver in 1987, and gold in 1988—he remains the youngest winner of each medal in the competition’s history.

At 14, Tao attended the Research Science Institute summer program. He earned bachelor’s and master’s degrees from Flinders University at 16, supervised by Garth Gaudry. A postgraduate Fulbright Scholarship took him to Princeton University, where he earned his PhD at 21 under Elias Stein. He joined UCLA’s faculty in 1996 and was promoted to full professor at 24, the youngest ever to hold that rank at the university. Tao is known for working across many fields and collaborating extensively; by 2006 he had co-authored with over 30 researchers, and by October 2015 that number had reached 68. His most notable collaboration is with Ben Green, with whom he proved the Green–Tao theorem. The theorem states that there exist arbitrarily long arithmetic progressions of prime numbers—for example, 3, 7, and 11 form a progression with spacing 4, but the next number, 15, is not prime. Green and Tao proved that such progressions of any length can always be found somewhere among the integers.

Other widely reported results include Tao’s demonstration of finite-time blowup for a modified version of the Navier–Stokes Millennium Problem; his 2015 resolution of the Erdős discrepancy problem using entropy estimates in analytic number theory; and his 2019 progress on the Collatz conjecture, showing that almost all Collatz orbits attain almost bounded values. In 2012, Green and Tao announced a proof of the orchard-planting problem, which asks for the maximum number of lines through exactly three points in a set of n points in the plane. In 2018, with Brad Rodgers, Tao proved that the de Bruijn–Newman constant is nonnegative—a result whose nonpositivity would be equivalent to the Riemann hypothesis. In 2020, he proved Sendov’s conjecture for polynomials of sufficiently high degree. In 2024 and 2025, he solved problems 121, 442, 135, 685, 69, and 1102 from the Erdős problems website.

Tao has received many honors, including the Fields Medal in 2006, the Royal Medal and the Breakthrough Prize in Mathematics in 2014, and a MacArthur Fellowship in 2006. His published research covers harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing, and analytic number theory.