# The work of Terence Tao

### Charles Fefferman

Princeton University, USA

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## Abstract

Mathematics at the highest level has several flavors. On seeing it, one might say:

- (A) What amazing technical power!
- (B) What a grand synthesis!
- (C) How could anyone not have seen this before?
- (D) Where on earth did this come from?

The work of Terence Tao encompasses all of the above. One cannot hope to capture its extraordinary range in a few pages. My goal here is simply to exhibit a few contributions by Tao and his collaborators, sufficient to produce all the reactions (A)... (D). I shall discuss the Kakeya problem, nonlinear Schrödinger equations and arithmetic progressions of primes.