Terence Tao

Professor of Mathematics; James and Carol Collins Chair, University of California, Los Angeles

tao@math.ucla.edu · https://www.math.ucla.edu/~tao/

Biography

Terence Tao was born in Adelaide, Australia in 1975. He has been a professor of mathematics at UCLA since 1999, having completed his PhD under Elias Stein at Princeton in 1996. Tao's areas of research include harmonic analysis, PDE, combinatorics, and number theory. He has received a number of awards, including the Salem Prize in 2000, the Fields Medal in 2006, the MacArthur Fellowship in 2007, the Crafoord Prize in 2012, and the Breakthrough Prize in Mathematics in 2015. Terence Tao also holds the James and Carol Collins Chair in mathematics at UCLA, and is a Fellow of the Royal Society, the Australian Academy of Sciences, the National Academy of Sciences, and the American Academy of Arts and Sciences. From 2020 to 2024, he served on the President's Council of Advisors on Science and Technology.

Research interests

PrimaryOscillatory integrals and Kakeya maximal functions; Nonlinear dispersive equations; Multilinear operators (e.g. the bilinear Hilbert transform); Arithmetic combinatorics, and connections with number theory and ergodic theory; Compressed sensing

Education

1996Ph.D., Princeton University (advisor: Elias Stein)
Thesis: Three regularity results in harmonic analysis

1992M.Sc., Flinders University (advisor: Garth Gaudry)
Thesis: Convolution operators generated by right-monogenic and harmonic kernels

1991B.Sc. (Hons), Flinders University (advisor: Garth Gaudry)

Appointments

1992–1994Assistant Researcher, Flinders Medical Centre

1993–1994Assistant Researcher, Princeton University

1996–1998Hedrick Assistant Professor, UCLA

1997–1997Member (Fall), MSRI

1999–1999Acting Assistant Professor, UCLA

1999–1999Visiting Fellow, UNSW

2000–2000Assistant Professor, UCLA

2000–2000Visiting Professor, UNSW

2000–2009Professor, UCLA

2009–Distinguished Professor, UCLA

2001–2003CMI Long-term Prize Fellow, Clay Mathematics Institute

2001–2003Honorary Professor, Australian National University

Awards and honors (selected)

2000Salem Prize — Salem Prize

2002Bôcher Memorial Prize — American Mathematical Society

2003Clay Research Award — Clay Mathematics Institute

2006Fields Medal — International Mathematical Union

2006SASTRA Ramanujan Prize — SASTRA

2007–2011MacArthur Fellowship — MacArthur Foundation

2007Ostrowski Prize — Ostrowski Foundation

2007–Fellow — The Royal Society

2008–2010Alan T. Waterman Award — National Science Foundation

2008–Foreign Affiliate (regular member since 2022) — National Academy of Sciences

2009Member — American Academy of Arts and Sciences

2010King Faisal International Prize (Mathematics) — King Faisal Foundation

2010Nemmers Prize — Northwestern University

2012Crafoord Prize (Mathematics) — Royal Swedish Academy of Sciences

2014Royal Medal — The Royal Society

2015Breakthrough Prize in Mathematics — Breakthrough Prize

2019Riemann Prize — RISM

2020Princess of Asturias Award for Technical and Scientific Research — Princess of Asturias Foundation

2020János Bolyai International Mathematical Prize — Hungarian Academy of Sciences

2023Grande Médaille — French Academy of Sciences

2026Companion of the Order of Australia — Australia

Books

2026Six Math Essentials — Quanta Books

2015Expansion in finite simple groups of Lie type — American Mathematical Society

2014Hilbert’s fifth problem and related topics — American Mathematical Society

2013Compactness and contradiction — American Mathematical Society

2012Higher order Fourier analysis — American Mathematical Society

2012Topics in random matrix theory — American Mathematical Society

2011An introduction to measure theory — American Mathematical Society

2010An epsilon of room: pages from year three of a mathematical blog — American Mathematical Society

2009Poincaré’s legacies: pages from year two of a mathematical blog — American Mathematical Society

2008Structure and Randomness: pages from year one of a mathematical blog — American Mathematical Society

2006Additive Combinatorics (with Van Vu) — Cambridge University Press

2006Analysis I — Hindustan Book Agency

2006Analysis II — Hindustan Book Agency

2006Nonlinear dispersive equations: local and global analysis — American Mathematical Society

2006Solving Mathematical Problems (Second edition) — Oxford University Press

2000Three Regularity Results in Harmonic Analysis — World Scientific Publishing Co.

1992Solving Mathematical Problems: A personal perspective — Deakin University Press

Climbing the cosmic distance ladder (with Tanya Klowden) — Yale University Press

Spending symmetry

Selected publications

1998The honeycomb model of GL_n(C) tensor products I. Proof of the saturation conjecture. with Allen Knutson. J. Amer. Math. Soc.12 (1999), 1055–1090

2003A sum-product estimate for finite fields, and applications. with Jean Bourgain, Nets Katz. GAFA 14 (2004), 27–57

2004The primes contain arbitrarily long arithmetic progressions. with Ben Green. Annals of Math. 167 (2008), 481–547

2005Decoding by Linear Programming. with Emmanuel Candes. IEEE Inf. Theory 51 (2005), 4203–4215

2006The primes contain arbitrarily long polynomial progressions. with Tamar Ziegler. Acta Math. 201 (2008), 213—305.Errata: Acta Math. 210, (2013), Page 403–404

2010An inverse theorem for the Gowers U^s+1[N] norm. with Ben Green, Tamar Ziegler. Annals of Math. 176 (2012), no. 2, 1231–1372.

2011The structure of approximate groups. with Emmanuel Breuillard, Ben Green. Publ. Math. Inst. Hautes Études Sci. 116 (2012), 115–221

2012Every odd number greater than 1 is the sum of at most five primes. Mathematics of Computation 83 (2014), 997–1038

2014Finite time blowup for an averaged three-dimensional Navier-Stokes equation. J. Amer. Math. Soc. 29 (2016), no. 3, 601–674.

2019Almost all orbits of the Collatz map attain almost bounded values. Forum Math. Pi 10 (2022), Paper No. e12, 56 pp.

2023On a conjecture of Marton. with Timothy Gowers, Ben Green, Freddie Manners. Submitted, Annals Math.

2014Variants of the Selberg sieve, and bounded intervals containing many primes. with D.H.J. Polymath. Research in the Mathematical Sciences 1:12 (2014)

Selected from 377 papers.

Students

39 doctoral and undergraduate students supervised (full list on the full CV).

Professional service and editorial (selected)

2025–Co-founder — Foundation for Science and AI Research (SAIR)

2025–Scientific Advisory Board — Mathlib Initiative

2021–2024President's Council of Advisors on Science and Technology — Office of Science and Technology Policy

2019–2025Structure Committee (Chair, 2019–2024) — International Mathematical Union

2016–2018Fields Medal Committee — International Mathematical Union

2015–2025Editor — Discrete Analysis

2012–Editor — Forum of Mathematics (Cambridge University Press)

2011–2013Abel Prize Committee — Norwegian Academy of Sciences

2008–2010ICM 2010 Program Committee — International Mathematical Union

2007–2025Editor — Analysis & PDE

2005–2011Editor — J. Amer. Math. Soc.

2003–Associate Editor — Dynamics of Partial Differential Equations

2002–2004Associate Editor — J. Amer. Math. Soc.

2002–Associate Editor — American Journal of Mathematics