ADDITIVE COMBINATORICS TERENCE TAO PDF

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Both formerly represented Australia at the International Mathematical Olympiad. When he was 15, he published his first assistant paper. From to , Tao was a graduate student at Princeton University under the direction of Elias Stein , receiving his PhD at the age of In , 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.

Green of Oxford University; together they proved the Green—Tao theorem. Known for his collaborative mindset, by , Tao had worked with over 30 others in his discoveries, [17] reaching 68 co-authors by October Some of these are areas to which he has made fundamental contributions.

Others are areas that he appears to understand at the deep intuitive level of an expert despite officially not working in those areas. How he does all this, as well as writing papers and books at a prodigious rate, is a complete mystery.

Tao has won numerous honours and awards over the years. In , Tao proved for the Collatz Conjecture using probability that almost all Collatz orbits attain almost bounded values. This theorem states that there are arbitrarily long arithmetic progressions of prime numbers.

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.

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. 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. He was the first Australian, the first UCLA faculty member, and one of the youngest mathematicians to receive the award.

In April , Tao received the Alan T. Waterman Award , which recognizes an early career scientist for outstanding contributions in their field. Vu solved the circular law conjecture. In , joint work with Ben Green culminated in the proof of the Hardy-Littlewood prime tuples conjecture for any linear system of finite complexity. That same year, Tao published the first monograph on the topic of higher order Fourier analysis.

That year, Tao presented work on a possible attack on the Navier—Stokes existence and smoothness Millennium Problem, by establishing finite time blowup for an averaged three-dimensional Navier-Stokes equation. That year he also, jointly with several co-authors, proved several results on short and long prime gaps.

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