Terence Tao

Terence Tao is an Australian-American mathematician, one of the leading experts in harmonic analysis, combinatorics, and partial differential equations. In the context of the Navier–Stokes problem, he is known for his 2016 work, in which he proved the possibility of blow-up (loss of regularity) for averaged (smoothed) Navier–Stokes equations. This was an important step in understanding potential singularity mechanisms, although not for the original equations. Tao showed that if one considers Navier–Stokes equations with a certain type of averaging, one can construct solutions that become unbounded in finite time. This result demonstrated that standard methods based on energy estimates cannot rule out blow-up in general. Tao's work stimulated further research, including attempts to find counterexamples to global regularity.

Biography

Terence Chi-Shen Tao was born on July 17, 1975, in Adelaide, Australia. A child prodigy: at age 9 he began attending university courses, at 16 he received bachelor's and master's degrees from Flinders University, and at 21 he earned a PhD from Princeton University under the supervision of Elias Stein. Since 1996 he has been working at the University of California, Los Angeles (UCLA). In 2006 he was awarded the Fields Medal, as well as many other prestigious awards, including the Breakthrough Prize (2014).

Key discoveries

Proof of the possibility of finite-time blow-up for averaged Navier–Stokes equations (2016).
Fields Medal 2006 for contributions to number theory, harmonic analysis, and combinatorics.
Green–Tao theorem on the existence of arbitrarily long arithmetic progressions in the primes (jointly with Ben Green, 2004).

Biography

Key discoveries

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