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In number theory, the Green–Tao theorem, proved by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long arithmetic progressions. In other words, for every natural number k {\displaystyle k} , there exist arithmetic progressions of primes with k {\displaystyle k} terms.
Terence Chi-Shen Tao FAA FRS (Chinese: 陶哲軒; born 17 July 1975) is an Australian-American mathematician, Fields medalist, and 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.
In September 2013, Ben Green and Terence Tao published a paper in which they prove that for all point sets of sufficient size, n > n 0, there are at most + = + 3-point lines which matches the lower bound established by Burr, Grünbaum and Sloane. [2]
This work was further developed by Ben Green and Terence Tao, leading to the Green–Tao theorem. In 2003, Gowers established a regularity lemma for hypergraphs, [15] analogous to the Szemerédi regularity lemma for graphs. In 2005, he introduced [16] the notion of a quasirandom group.
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In August 2014, Maynard (independently of Ford, Green, Konyagin and Tao) resolved a longstanding conjecture of Erdős on large gaps between primes, and received the largest Erdős prize ($10,000) ever offered. [13] [14] In 2014, he was awarded the SASTRA Ramanujan Prize. [1] [15] In 2015, he was awarded a Whitehead Prize [16] and in 2016 an EMS ...
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Terence Tao Australia: 1986 Bronze 10 years, 363 days Raúl Chávez Sarmiento Peru: 2009 Bronze 11 years, 271 days Terence Tao Australia: 1987 Silver 11 years, 364 days Alex Chui Hong Kong: 2020 Silver 12 years, 156 days Akshay Venkatesh Australia: 1994 Bronze 12 years, 241 days Yeoh Zi Song Malaysia: 2014 Bronze 12 years, 245 days