Terence Chi-Shen Tao (Chinese: 陶哲轩; pinyin: Táo Zhéxuān; 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 earning his doctorate in mathematics from Princeton University 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. Tao's published research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing, and analytic number theory.
Early life and career
Family 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. Tao also has two brothers, Trevor and Nigel, who are currently living in Australia. Both formerly represented Australia at the International Mathematical Olympiad.
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. In 1996, he joined the faculty of the University of California, Los Angeles. In 1999, when he was 24, he was promoted to full professor at UCLA and remains the youngest person ever appointed to that rank by the institution. He became known for fruitful collaborations and working in multiple specializations; by 2006, Tao had co-authored publications with over 30 other researchers, reaching 68 co-authors by October 2015. Tao has had a particularly extensive collaboration with British mathematician Ben J. Green; together they proved the Green–Tao theorem, which is well known among both amateur and professional mathematicians. This theorem states that there are arbitrarily long arithmetic progressions of prime numbers. The New York Times described it this way:
In 2004, Dr. Tao, along with Ben Green, a mathematician now at the University of Oxford in England, solved a problem related to the Twin Prime Conjecture by looking at prime number progressions—series of numbers equally spaced. (For example, 3, 7 and 11 constitute a progression of prime numbers with a spacing of 4; the next number in the sequence, 15, is not prime.) Dr. Tao and Dr. Green proved that it is always possible to find, somewhere in the infinity of integers, a progression of prime numbers of equal spacing and any length. 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 problems 121, 442, 135, 685, 69, and 1102 from the Erdős problems website.
Recognition
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