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Ben Joseph Green FRS (born 27 February 1977) is a British mathematician, specialising in combinatorics and number theory. He is the Waynflete Professor of Pure Mathematics at the University of Oxford .
Any given arithmetic progression of primes has a finite length. In 2004, Ben J. Green and Terence Tao settled an old conjecture by proving the Green–Tao theorem: The primes contain arbitrarily long arithmetic progressions. [1] It follows immediately that there are infinitely many AP-k for any k.
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.
The Green–Tao theorem, proved by Ben Green and Terence Tao in 2004, [3] states that the sequence of prime numbers contains arbitrarily long arithmetic progressions. In other words, there exist arithmetic progressions of primes, with k terms, where k can be any natural number. The proof is an extension of Szemerédi's theorem.
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.
2000 Terence Tao F; 2001 Oded Schramm and Stanislav Smirnov F; 2002 Xavier Tolsa; 2003 Elon Lindenstrauss F and Kannan Soundararajan; 2004 no prize; 2005 Ben J. Green; 2006 Stefanie Petermichl and Artur Avila F; 2007 Akshay Venkatesh F; 2008 Bo'az Klartag and Assaf Naor; 2009 no prize; 2010 Nalini Anantharaman; 2011 Zhan Dapeng and Julien ...
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
One of his most famous results is the Green-Tao theorem (proven in collaboration with Ben Green), which pertains to the twin prime conjecture. [21] Erik Demaine (1981–) was identified as a prodigy at the age of 7 [22] and earned his PhD in computer science at 20. [23] He is now a computer scientist at MIT.