He received the Salem Prize in 2000, the Bôcher Prize in 2002, and the Clay Research Award in 2003, for his contributions to analysis including work on the Kakeya conjecture and wave maps. In 2005 he received the American Mathematical Society's Levi L. Conant Prize with Allen Knutson, and in 2006 he was awarded the SASTRA Ramanujan Prize.
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. The New York Times described it this way:
“ In 2004, Dr. 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.) Dr. 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. ”
For this and other work, he was awarded the Australian Mathematical Society Medal.
In 2006, at the 25th International Congress of Mathematicians in Madrid, he became one of the youngest, the first Australian, and the first UCLA faculty member ever to be awarded a Fields Medal. An article by New Scientist writes of his ability:
“ 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,” says Fefferman. ”
Tao was a finalist to become Australian of the Year in 2007.