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Terence Tao: The Mozart of Mathematics

Terence "Terry" Chi-Shen Tao FAA FRS  (born 17 July 1975, Adelaide), is an Australian mathematician working in harmonic analysis, partial differential equations, additive combinatorics, ergodic Ramsey theory, random matrix theory, and analytic number theory. He currently holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles.


Tao was a child prodigy. When Terry was two years old his parents realised that he was different from other children. They saw him teaching five year old children to spell and to add numbers and, when they asked him how he had learnt these skills, he replied that he had been watching Sesame Street on television. When he was three and a half years old his parents sent him to a private school but, six weeks later, they realised that he was not ready for schooling and also that the teachers did not know how to teach someone like him. So they removed him from the school and he did not start schooling again until he was, like other children, five years old. In the article Educational Studies in Mathematics, which is an evaluation of Terry's mathematical abilities just before his eighth birthday by which time he was attending Blackwood High School, Adelaide, Ken Clements writes that when he went into his home, Terry was:

... sitting in the far corner of a room reading a hardback book with the title 'Calculus'. Terence was small, even for a seven-year-old. After meeting his two brothers, I was accompanied by Terence to his father's study, where, after a brief chat, I began my usual assessment procedure for exceptionally bright primary school-age children.

Clements discovered that Terry knew the definition of a group and could solve graph sketching problems using the differential calculus. He wondered how much his mother was teaching him but found that her role

... is more one of guiding and stimulating Terence's development than one of teaching him. She said that Terence likes to read mathematics by himself, and he often spent three or four hours after school reading mathematics textbooks.

paul erodos+terence tao

Image : Child Tao with Paul Erdos

He is one of only two children (besides Lenhard Ng) in the history of the Johns Hopkins' Study of Exceptional Talent program to have achieved a score of 700 or greater on the SAT math section while just 8 years old (he scored a 760). In 1986, 1987, and 1988, Tao was the youngest participant to date in the International Mathematical Olympiad, first competing at the age of ten, winning a bronze, silver, and gold medal respectively. He remains the youngest winner of each of the three medals in the olympiad's history winning the gold medal when he barely turned fourteen.

At the age of fourteen he began full-time university studies at Flinders University and was awarded a B.Sc. with Honours in December 1991. He continued to study at Flinders University for a Master's Degree advised by Garth Gaudry and was awarded the degree in August 1992 having written the thesis Convolution operators generated by right-monogenic and harmonic kernels. He was awarded the University Medal by Flinders University and a Fulbright Postgraduate Scholarship to enable him to undertake research in the United States.

Terence Tao - UCLA Math Department - 090629 for University Communications

Tao undertook research at Princeton University advised by Elias Stein. He was an assistant researcher at Princeton during 1993-94 and he was awarded a Sloan Postgraduate Fellowship in 1995. He was awarded his doctorate in June 1996 for his thesis Three regularity results in harmonic analysis. In 1996 his research papers began to appear in print, four papers being published in that year. These are: Weak-type endpoint bounds for Riesz means; (with Andrew C Millard) On the structure of projective group representations in quaternionic Hilbert space; On the almost everywhere convergence of wavelet summation methods; and Convolution operators on Lipschitz graphs with harmonic kernels.

Following the award of his doctorate, Tao was appointed Hedrick Assistant Professor at the University of California at Los Angeles, a position he held from 1996 to 1998. He continued as an assistant professor at the University of California at Los Angeles where, at the age of twenty-four, he was promoted to full professor in 2000. In 2007 he was named the James and Carol Collins Professor there.
"Terry is like Mozart; mathematics just flows out of him," said John Garnett, professor and former chair of mathematics at UCLA, "except without Mozart's personality problems; everyone likes him. Mathematicians with Terry's talent appear only once in a generation. He's an incredible talent, and probably the best mathematician in the world right now. Terry can unravel an enormously complicated mathematical problem and reduce it to something very simple."

He received the 2006 Fields medal, the Nobel Prize of mathematics,

... for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory.

The article , describing the award of the Fields Medal, gives this overview:

"Terence Tao is a supreme problem-solver whose spectacular work has had an impact across several mathematical areas. He combines sheer technical power, an other-worldly ingenuity for hitting upon new ideas, and a startlingly natural point of view that leaves other mathematicians wondering, " Why didn't anyone see that before?" At 31 years of age, Tao has written over eighty research papers, with over thirty collaborators, and his interests range over a wide swath of mathematics, including harmonic analysis, nonlinear partial differential equations, and combinatorics. " I work in a number of areas, but I don't view them as being disconnected," he said in an interview published in the Clay Mathematics Institute Annual Report. " 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’s work is characterized by a high degree of originality and a diversity that crosses research boundaries, together with an ability to work in collaboration with other specialists.

In 2004, Ben Green and Tao released a preprint proving what is now known as the Green–Tao theorem. This theorem states that there are arbitrarily long arithmetic progressions of prime numbers. An area to which Tao has made many contributions is that of the Kakeya problem. This problem, originally posed in 2 dimensions, asked for the minimum area of a shape in which one can rotate a needle through 180° . The answer is rather surprising, in fact you can make the area less than any chosen number. Tao has worked on the n-dimensional Kakeya problem where again the minimum volume can be made as small as one chooses, but the fractal dimension of the shape is unknown. This problem sounds rather specialised, but on the contrary there are surprising connections to Fourier analysis and nonlinear waves.

Tao lecture MIT

Another area in which Tao has worked is solving special cases of the equations of general relativity describing gravity. Imposing cylindrical symmetry on the equations leads to the "wave maps" problem where, although it has yet to be solved, Tao's contributions have led to a great resurgence of interest since his ideas seem to have made a solution possible. Another area where Tao has introduced novel ideas, giving the subject a whole new look, is the theory of the nonlinear Schrödinger equations. These equations have considerable practical applications and again Tao's insights have shed considerable light on the behaviour of a particular Schrödinger equation.
Terence has received a number of prizes,these include:
The Salem Prize (2000); the Bôcher Memorial Prize from the American Mathematical Society (2002); the Clay Research Award from the Clay Mathematical Institute (2003); the Levi L Conant Award from the American Mathematical Society (2005); the Australian Mathematical Society Medal (2005); the ISAAC Award from the International Society of Analysis, its Application and Computation (2005); the SASTRA Ramanujan Prize (2006); the Fields Medal (2006); the Ostrowski Prize from the Ostrowski Foundation (2007); the Alan T Waterman Award from the National Science Foundation (2008); the Onsager Medal(2008); the Information Theory Society Paper Award (2008); the Convocation Award from Flinders University Alumni Association (2008); the King Faisal International Prize (Mathematics) (2010); the Nemmers Prize in Mathematics from Northwestern University (2010); and the George Polya Prize from the Society for Industrial and Applied Mathematics (2010). In addition he has received a Sloan Foundation research Fellowship (1999-2001), a Foundation Fellowship from the David and Lucille Packard Foundation (1999-2006), and a MacArthur Fellowship from the MacArthur Foundation (2007-11). He has been elected to the Australian Academy of Sciences (2006), to a fellowship of the Royal Society (2007), to the National Academy of Sciences (2008), and to the American Academy of Arts and Sciences (2009). He was a finalist in Australian of the Year in 2007.

Terence is held by a number of mathematicians as Midas as whatever topic he gets interested, the obstacles gets reduced and the field blossoms out. Now the mathematicians try to get Terence interested in their topics so that he apply his genius and get something out of the mess in his own magical way. In Charles Fefferman's own words,

"Such is Tao's reputation that mathematicians now compete to interest him in their problems, and he is becoming a kind of Mr Fix-it for frustrated researchers. If you're stuck on a problem, then one way out is to interest Terence Tao."


Source: Various Online & Offline sources



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