Others are areas that he appears to understand at the deep intuitive level of an expert despite officially not working in those areas. Some of these are areas to which he has made fundamental contributions. Tao's mathematical knowledge has an extraordinary combination of breadth and depth: he can write confidently and authoritatively on topics as diverse as partial differential equations, analytic number theory, the geometry of 3-manifolds, nonstandard analysis, group theory, model theory, quantum mechanics, probability, ergodic theory, combinatorics, harmonic analysis, image processing, functional analysis, and many others. Recognitionīritish mathematician and Fields medalist Timothy Gowers remarked on Tao's breadth of knowledge: In 2020, Tao proved Sendov's conjecture for large. In 2018, with Brad Rodgers, Tao improved the best available lower bound for the de Bruijn–Newman constant. In 2012, Green and Tao announced proofs of the conjectured "orchard-planting problem," which asks for the maximum number of lines through exactly 3 points in a set of n points in the plane, not all on a line. Tao has also resolved or made progress on a number of conjectures. his 2019 progress on the Collatz conjecture, in which he proved the probabilistic claim that almost all Collatz orbits attain almost bounded values.his 2015 resolution of the Erdős discrepancy problem, which used entropy estimates within analytic number theory.his establishment of finite time blowup for a modification of the famous Navier–Stokes existence and smoothness Millennium Problem.
Many other results of Tao have received mainstream attention in the scientific press, including: 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. (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, along with Ben Green, a mathematician now at the University of Cambridge in England, solved a problem related to the Twin Prime Conjecture by looking at prime number progressions-series of numbers equally spaced. The New York Times described it this way: This theorem states that there are arbitrarily long arithmetic progressions of prime numbers.
#TERRY TAO MATH PROFESSIONAL#
Green together they proved the Green–Tao theorem, which is well-known among both amateur and professional mathematicians. Tao has had a particularly extensive collaboration with British mathematician Ben J. He is known for his collaborative mindset by 2006, Tao had worked with over 30 others in his discoveries, reaching 68 co-authors by October 2015.
#TERRY TAO MATH FULL#
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. In 1996, he joined the faculty of the University of California, Los Angeles. 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 1992, he won a Postgraduate Fulbright Scholarship to undertake research in mathematics at Princeton University in the United States. 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. Tao (second from left) with UCLA undergraduate students in 2021Īt age 14, Tao attended the Research Science Institute, a summer program for secondary students. He is widely regarded as one of the greatest living mathematicians and has been referred to as the " Mozart of mathematics". Tao has been the author or co-author of over three hundred research papers. He won the Fields Medal in 2006 and won the Royal Medal and Breakthrough Prize in Mathematics in 2014. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing and analytic 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. Terence " Terry" Chi-Shen Tao FAA FRS ( Chinese: 陶哲軒 born 17 July 1975) is an Australian mathematician. Three Regularity Results in Harmonic Analysis (1996) Global Australian of the Year Award (2022) Kilby Signal Processing Medal (2021)Įducation & Reseach award finalist (2022) Australian Mathematical Society Medal (2005)
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