### Terence Tao

Born 17 July 1975 in Adelaide (Australia)

Fields Medal (2006) “for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory”

Terence (‘Terry’) Tao is the son of professionals: his mother has a degree in Mathematics and Physics, while his father is a pediatrician. Both parents are from China and emigrated to Australia in 1972. Tao has two brothers who also excel in mathematics. All three took part in the International Mathematical Olympiads – at the age of ten in Terry’s particularly talented case. (Aged 12 he became the youngest winner of a gold medal at a Mathematical Olympiad, a record he holds to this day.) From the age of 11, he studied – at the same time as going to school – at Flinders University in Adelaide, where he took his Bachelor’s degree at the age of 17 (1991). One year later, he completed a Masters’ degree in Mathematics, with a thesis on ‘Convolution operators generated by right-monogenic and harmonic kernels’. He then began to work as an Assistant Researcher at Princeton (1993-1994) and earned his doctorate there in 1996 with a thesis on harmonic analysis. He subsequently worked as an Assistant Professor at the University of California at Los Angeles (UCLA) (1996-2000) and then became a full professor there. Since 2007 he has held the James and Carol Collins Chair at UCLA.

Terence Tao has won numerous awards, including fellowships from the Sloan Foundation (1999-2001), the Packard Foundation (1999-2006) and the Clay Mathematics Institute (2001-2003), and a variety of prizes in addition to the Fields Medal, including the Salem Prize (2000), the Bocher Memorial Prize of the American Mathematical Society (AMS) (2002), the Clay Research Award (2003), the Levi L. Conant Award from the AMS (along with Allen Knutson) (2004), the Ostrowski Prize (2007), the SIAM Pólya Prize (together with Emmanuel Candes, 2009), the King Faisal International Prize (2010) and the Crafoord Prize (2012).

Terry Tao is an exceptional talent; he has solved a number of difficult problems with particular creativity, in the areas of analysis, partial differential equations, combinatorics and number theory to name a few. But he also has a mathematical foresight like few others that allows him to read existing mathematical theorems in a new way and to make new cross connections. “I work in a number of areas, but I don’t view them as being disconnected; I tend to view mathematics as a unified subject and am particularly happy when I get the opportunity to work on a project that involves several fields at once,” Tao himself says. He often works in cooperation with others, is very communicative and to that end makes great use of the internet, maintaining an extensive blog where he discusses various mathematical questions.

Tao became famous with among other things a work on arithmetic progressions in the set of primes, co-authored with Ben Green. At first sight, this work from 2004 provides a proof that arbitrarily long sequences of numbers in the prime numbers exist such that each two consecutive numbers have the same distance from each other. However, behind this lies Tao’s attempts to better understand the boundary between structure and disorder: primes behave in many ways as if they were random numbers and yet obey on the other hand laws and structures.

Some of Tao’s work on matrices also concerned the line between structure and randomness. Matrices are tables full of numbers, that can be added and multiplied according to certain rules, but they can also be regarded as maps in space. At some points in space these maps operate like simple multiplications with a number; these numbers are then called ‘eigenvalues’. Tao showed together with Van H. Vu that in matrices with random entries, the eigenvalues are not random when the size of the matrices is allowed to grow, but lie instead within a clearly defined area. Together with Allen Knutson, he characterized the eigenvalues of special so-called Hermitian matrices and in this startling proof, combined combinatorics with geometry.

Tao also devoted himself for several years to the Kakeya problem, named after the Japanese mathematician Soichi Kakeya (1886-1947). Originally the problem was to determine the smallest area on which a needle can rotate once by 180 degrees. Amazingly, one can make this area arbitrarily small, but it then frays and becomes a fractal. So the question these days is different: What are the characteristics of sets of points which can accommodate a needle of a certain length in each spatial direction? This question is posed for both two dimensions (ie when the needle is on a table top) and higher dimensional spaces. Research in this area – which has important links with analysis – was significantly progressed by Tao’s work.

Tao lives in Los Angeles with his wife and two children.