Terence Chi-Shen Tao (; born 17 July 1975) is an Australian and American mathematician who was awarded the Fields Medal in 2006 for his contributions to partial differential equations, combinatorics, harmonic analysis, and additive number theory. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins Chair in the College of Letters and Sciences. Among his contributions to mathematics is the Green–Tao theorem on prime numbers, which he proved in 2004 in collaboration with Ben Green.

Tao was born to Chinese immigrant parents and raised in Adelaide, South Australia. After studying at Princeton and joining the faculty at UCLA, he went on to be a researcher, known for the diversity of his own interests and his collaborations with others. Tao has won many prizes for his work, including the Fields Medal in 2006 and the Royal Medal and Breakthrough Prize in Mathematics in 2014. He is a 2006 MacArthur Fellow.

Early life and career

Family

Tao was born to ethnic Chinese first-generation immigrants from Hong Kong to Australia. Tao's father, Billy Tao, was a Chinese paediatrician who was born in Shanghai and received a medical degree (MBBS) from the University of Hong Kong in 1969. Tao's mother, Grace Leong, was born in Hong Kong; she received a first-class honours bachelor's degree majoring in mathematics and physics from the University of Hong Kong. She was a secondary school teacher of mathematics and physics in Hong Kong. Billy and Grace met as students at the University of Hong Kong. They then emigrated from Hong Kong to Australia in 1972.

Childhood

A child prodigy, Terence Tao skipped five grades. Tao exhibited extraordinary mathematical abilities from an early age, attending university-level mathematics courses at the age of 9. He is one of only three children in the history of the Johns Hopkins Study of Exceptional Talent program to have achieved a score of 700 or greater on the SAT math section while just eight years old; Tao scored a 760. Julian Stanley, Director of the Study of Mathematically Precocious Youth, stated that Tao had the greatest mathematical reasoning ability he had found in years of intensive searching.

Tao was the youngest participant to date in the International Mathematical Olympiad, first competing at the age of ten; in 1986, 1987, and 1988, he won a bronze, silver, and gold medal, respectively. Tao remains the youngest winner of each of the three medals in the Olympiad's history.

Career

At age 14, Tao attended the Research Science Institute, a summer program for secondary students. In 1991, he received his bachelor's and master's degrees at the age of 16 from Flinders University under the direction of Garth Gaudry. In 1992, he won a postgraduate Fulbright Scholarship to undertake research in mathematics at Princeton University in the United States. From 1992 to 1996, Tao was a graduate student at Princeton University under the direction of Elias Stein, receiving his PhD at the age of 21.

Many other results of Tao have received mainstream attention in the scientific press, including:

  • his establishment of finite time blowup for a modification of the Navier–Stokes existence and smoothness Millennium Problem
  • his 2015 resolution of the Erdős discrepancy problem, which used entropy estimates within analytic number theory
  • his 2019 progress on the Collatz conjecture, in which he proved the probabilistic claim that almost all Collatz orbits attain almost bounded values.

Tao has also resolved or made progress on a number of conjectures. In 2012, Green and Tao announced proofs of the conjectured "orchard-planting problem," which asks for the maximum number of lines through exactly three points in a set of n points in the plane, not all on a line. In 2018, with Brad Rodgers, Tao showed that the de Bruijn–Newman constant, the nonpositivity of which is equivalent to the Riemann hypothesis, is nonnegative. In 2020, Tao proved Sendov's conjecture, concerning the locations of the roots and critical points of a complex polynomial, in the special case of polynomials with sufficiently high degree. In 2024 and 2025, Tao solved Erdős problems 121, 442, 135, 685, 69, and 1102.

Recognition

thumb|Tao at ICM 2006

Tao has won numerous awards and mathematician honours over the years. He is a Fellow of the Royal Society, the Australian Academy of Science (Corresponding Member), the National Academy of Sciences (Foreign member), the American Academy of Arts and Sciences, the American Philosophical Society, and the American Mathematical Society. In 2006 he received the Fields Medal; he was the first Australian, the first UCLA faculty member, and one of the youngest mathematicians to receive the award. He was also awarded the MacArthur Fellowship. In 2014, Tao was selected as one of the inaugural Breakthrough Prize laureates; he felt himself unqualified and unsuccessfully argued that the prize money be distributed among more researchers instead. After receiving the prize money, he used part of it to establish fellowships for students.

He has been featured in The New York Times, CNN, USA Today, Popular Science, and many other media outlets. Tao was a finalist to become Australian of the Year in 2007. In 2014, Tao received a CTY Distinguished Alumni Honor from Johns Hopkins Center for Gifted and Talented Youth in front of 979 attendees in 8th and 9th grade who were in the same program from which Tao graduated. In 2021, President Joe Biden announced Tao had been selected as one of 30 members of his President's Council of Advisors on Science and Technology, a body bringing together America's most distinguished leaders in science and technology.

As of 2026, Tao had published about four hundred thirty articles, along with nineteen books. He has an Erdős number of 2 and is a highly cited researcher.

Per the New York Times, "many regard Tao as the finest mathematician of his generation." writes of his ability: