Terence Tao

Book pages (bibliographic details and errata) and other collected pages, generated from a database maintained by the author.

Distinguished Professor and James and Carol Collins Chair, Department of Mathematics, UCLA
Director of Special Projects, Institute for Pure and Applied Mathematics, UCLA
Co-Founder, Foundation for Science & AI Research

Papers and preprints — a searchable, tag-organized database of 553 works.

Biography and CV — short and extended bios, plus short and full curriculum vitae.

Contact and policies — how to reach me, and my correspondence policies.

Travel — upcoming engagements and a log of 374 past trips.

Collaborative projects — 9 active and completed online projects.

Interactive tools — 28 experimental math apps and games, old and newly ported.

Mastodon posts and other links — Selected Mastodon posts and other links, organized loosely by theme.

Books (19)

1992 Solving Mathematical Problems: A personal perspective — book details
2000 Three Regularity Results in Harmonic Analysis — book details
2006 Additive Combinatorics · with Van Vu — 131 corrections
2006 Analysis I — 141 corrections
2006 Analysis II — 110 corrections
2006 Nonlinear dispersive equations: local and global analysis — 192 corrections
2006 Solving Mathematical Problems (Second edition) — 40 corrections
2008 Structure and Randomness: pages from year one of a mathematical blog — 23 corrections
2009 Poincaré’s legacies: pages from year two of a mathematical blog — 96 corrections
2010 An epsilon of room: pages from year three of a mathematical blog — 224 corrections
2011 An introduction to measure theory — 125 corrections
2012 Higher order Fourier analysis — 20 corrections
2012 Topics in random matrix theory — 88 corrections
2013 Compactness and contradiction — 15 corrections
2014 Hilbert’s fifth problem and related topics — 17 corrections
2015 Expansion in finite simple groups of Lie type — 33 corrections
2026 Six Math Essentials — book details
in preparation Climbing the cosmic distance ladder · with Tanya Klowden — book details
in preparation Spending symmetry — 12 corrections

Teaching (68)

Spring 2026 Math 246C · Complex analysis
Fall 2025 Math 245A · Measure theory
Winter 2025 Math 254A · Analytic number theory
Fall 2024 Math 246A · Complex analysis
Winter 2024 Math 246B · Complex analysis
Fall 2023 Math 246A · Complex analysis
Spring 2023 Math 246C · Complex analysis
Fall 2022 Math 254A · Analytic prime number theory
Spring 2022 Math 246C · Complex analysis
Winter 2022 Math 246B · Complex analysis
Fall 2021 Math 246A · Complex analysis
Winter 2021 Math 246B · Complex analysis
Fall 2020 Math 246A · Complex analysis
Spring 2020 Math 247B · Graduate Fourier analysis
Fall 2019 Math 254A · Analytic number theory
Winter 2019 Math 255B · Incompressible Euler equations
Fall 2018 Math 254A · Incompressible fluids
Spring 2018 Math 246C · Complex analysis
Spring 2017 Math 245C · Real analysis
Fall 2016 Math 246A · Complex analysis
Spring 2016 Math 245C · Real analysis
Fall 2015 Math 275A · Probability
Winter 2015 Math 254A · Analytic prime number theory
Spring 2014 Math 245C · Real analysis
Winter 2014 Math 245B · Real analysis
Spring 2013 Math 245C · Real analysis
Winter 2013 Math 245B · Real analysis
Winter 2012 Math 254B · Expansion in groups of Lie type
Fall 2011 Math 254A · Hilbert's fifth problem
Spring 2011 Math 245C · Real analysis
Fall 2010 Math 245A · Real analysis
Spring 2010 Math 254B · Higher order Fourier analysis
Winter 2010 Math 254A · Random matrices
Spring 2009 Math 245C · Graduate real analysis
Winter 2009 Math 245B · Graduate real analysis
Spring 2008 Math 285G · Poincaré conjecture
Winter 2008 Math 254A · Ergodic theory
Winter 2007 Math 247B · Graduate Fourier analysis
Fall 2006 Math 247A · Graduate Fourier analysis
Spring 2006 Math 251B · Introduction to PDE
Winter 2006 Math 251A · Introduction to PDE
Spring 2005 Math 245C · Real analysis
Winter 2005 Math 33A · Linear algebra
Winter 2005 Math 245B · Real analysis
Fall 2004 Math 245A · Real analysis
Winter 2004 Math 133 · Fourier analysis
Winter 2004 Math 245B · Real analysis
Semester 2 2003 Math 3228 · Complex variables (Honors) (ANU)
Spring 2003 Math 131BH · Honors real analysis
Winter 2003 Math 131AH · Honors real analysis
Winter 2003 Math 254A · Additive combinatorics
Fall 2002 Math 115A · Linear algebra
Winter 2001 Math 254A · Time-frequency analysis
Semester 2 2000 Math 2620 · Higher complex analysis (UNSW)
Spring 2000 Math 199 · Problem solving
Spring 2000 Math 121 · Introduction to topology
Winter 2000 Math 132 · Complex analysis
Semester 2 1999 Math 2620 · Higher complex analysis (UNSW)
Spring 1999 Math 254B · Restriction/Kakeya
Winter 1999 Math 254A · Oscillatory integrals
Fall 1998 Math 132 · Complex analysis
Spring 1998 Math 32A · Calculus of several variables
Spring 1998 Math 132 · Complex analysis
Winter 1998 Math 32A · Calculus of several variables
Spring 1997 Math 132 · Complex analysis
Spring 1997 Math 121 · Introduction to topology
Winter 1997 Math 31B · Calculus and analytic geometry (Honors)
Fall 1996 Math 132 · Complex analysis

Students (3 current)

Arian Nadjimzadah · PhD, 2024–
Ben Goldman · PhD, advanced to candidacy 2025; co-advised with Dominique Maldague
Siddharth Mulherkar · PhD, advanced to candidacy 2024

Former students (36)

2023–2026 Rushil Raghavan · PhD
2022–2026 Zi Li Lim · PhD
2022–2025 Ben Johnsrude · PhD — Topics in the theory of Fourier decoupling
2022–2025 James Leng · PhD — Szemerédi's theorem, primes, and nilsequences
2021–2023 Jaume de Dios · PhD — Uniform estimates for operators involving polynomial curves; decoupling estimates for fractal and product sets
2020–2023 Stan Palasek · PhD — Some quantitative regularity theorems for the Navier–Stokes equations
2019–2021 Alex Dobner · PhD — Zeros of Riemann zeta-type functions
2019–2021 Redmond McNamara · PhD — Dynamical methods for the Sarnak and Chowla conjectures
2018–2021 Khang Huynh · PhD — Intrinsic harmonic analysis on manifolds with boundary, and Onsager's conjecture
2018–2021 Bjoern Bringmann · PhD — Probabilistic perspectives on dispersive partial differential equations
2017–2019 Zane Li · PhD — Decoupling for the parabola and connections to efficient congruencing
2015–2017 Stephen Ge · PhD — The eigenvalue spacing of IID random matrices and related least singular value results
2015–2017 Yilong Yang · PhD — Shapes of finite groups through covering properties and Cayley graphs
2013–2016 Nick Cook · PhD — Spectral properties of non-Hermitian random matrices
2014–2016 Jordy Greenblatt · PhD — Dimensional asymptotics for norms of maximal averaging operators on Cartesian powers of finite graphs
2013–2015 Ben Krause · PhD — Some results in pointwise ergodic theory
2013–2015 Anand Rajagopalan · PhD — Outlier eigenvalue fluctuations of perturbed IID matrices
2012–2015 Jacques Benatar · PhD — The existence of small gaps in subsets of the integers
2012–2015 Pietro Carolino · PhD — The structure of locally compact groups
2011–2013 Brad Rodgers · PhD — The statistics of the Riemann zeta function and related topics
2009–2013 Josh Zahl · PhD — Some algebraic and geometric variants of restriction and Kakeya problems
2008–2011 Kenny Maples · PhD — Arithmetic properties of random matrices
2008–2011 Zaher Hani · PhD — Global and dynamical aspects of nonlinear Schrödinger equations on compact manifolds
2008–2011 Paul Smith · PhD — Subthreshold geometric renormalization and energy-critical Schrödinger maps
2007–2010 Le Thai Hoang · PhD — Topics in additive combinatorics in finite fields
2006–2010 Tim Austin · PhD — Multiple recurrence and the structure of probability-preserving systems
2006–2008 Tristan Roy · PhD — Global well-posedness of the defocusing cubic wave equation in dimension 3
2006–2008 Soonsik Kwon · PhD — Low-regularity problems of fifth-order KdV and modified KdV equations
2006–2008 Shuanglin Shao · PhD — Restriction estimates for paraboloids and cones in the cylindrically symmetric case
2005 Umut Isik · Undergraduate — Maximal non-commuting subsets of groups
2003–2006 Jon Bueti · PhD — Finite field x-ray and k-plane estimates
2003–2006 Monica Visan · PhD — Critical nonlinear Schrödinger equations in higher dimensions
2002–2003 Roman Sasyk · PhD; co-advised with Sorin Popa — Operator algebra methods in ergodic theory
2002–2004 Julia Garibaldi · PhD; co-advised with John Garnett — Erdős distance problem for convex metrics
2000–2001 Thomas Lam · Honours undergraduate — Cycles of even length in graphs
2000 Deborah Cromer · Honours undergraduate — Uniform distribution of sequences mod 1

Editorial roles (3 active)

Advice on submitting papers to journals

Forum of Mathematics (Cambridge University Press) · Editor (since 2012)
Dynamics of Partial Differential Equations · Associate Editor (since 2003)
American Journal of Mathematics · Associate Editor (since 2002)

Former editorial roles (5)

2015–2025 Discrete Analysis · Editor
2007–2025 Analysis & PDE · Editor
2005–2011 J. Amer. Math. Soc. · Editor
2003–2008 International Mathematics Research Surveys · Advisory Board
2002–2004 J. Amer. Math. Soc. · Associate Editor