John Jones, Jen Paulhus, David Roe, Andrew Sutherland, and I have launched the third SAIR challenge, this time aimed at attacking the notorious inverse Galois problem: competition.sair.foundation/competitions... terrytao.wordpress.com/2026/06/16/t... .

Discoveries | Inverse Galois Problem (IGP24) | SAIR Foundation

Read discoveries for Inverse Galois Problem (IGP24). IGP24, the Inverse Galois Problem in Degree 24. This is a mathematical discovery challenge: we are asking...

competition.sair.foundation

Alberto Alfarano, François Charton, Yongzheng Jia, Kristin Lauter, Cathy Li, Emily Wenger, are launching a challenge at SAIR on how efficiently neural networks can perform modular arithmetic: competition.sair.foundation/competitions... terrytao.wordpress.com/2026/06/08/m...

Modular Arithmetic Challenge | SAIR Foundation

The Modular Arithmetic Challenge asks a deceptively simple question — can a neural network learn to compute (a × b) mod p for integers hundreds of digits long...

competition.sair.foundation

Does this change my imaginary Erdos number to a complex number? Click the link to read the full comic on the site! COMIC ◆ www.smbc-comics.com/comic/sphere... PATREON ◆ www.patreon.com/ZachWeinersm... STORE ◆ smbc-store.myshopify.com

A #cosmicdistanceLadder post on the many ways we project our planet onto a plane. No projection can faithfully reproduce *all* the geometric features of a sphere, so each projection is a compromise; but some projections are still preferred for specific applications. www.instagram.com/p/DVC9SvxkXDs

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Create an account or log in to Instagram - Share what you're into with the people who get you.

instagram.com

We’re thrilled to announce that Terence Tao (@teorth.bsky.social)’s SIX MATH ESSENTIALS is available for preorder: us.macmillan.com/books/978037.... A whirlwind tour through six core ideas that have guided mathematicians from antiquity to the frontiers of what we know today. Pubs October 27, 2026.

Six Math Essentials

The “Mozart of mathematics” invites readers on a brief tour of six core ideas—numbers, algebra, geometry, probability, analysis, and dynamics—that ca...

us.macmillan.com

Tanya Klowden and I have uploaded a further sample chapter to our "cosmic distance ladder" book: terrytao.wordpress.com/books/climbi... . See also the blog post terrytao.wordpress.com/2025/11/21/c...

Climbing the cosmic distance ladder

Climbing the cosmic distance ladder Tanya Klowden and Terence Tao in preparation This project is based on a public lecture on the cosmic distance ladder that I have given on occasion. Working with …

terrytao.wordpress.com

A new paper with Bogdan Georgiev, Javier Gomez-Serrano, and Adam Zsolt Wagner: "Mathematical exploration and discovery at scale" arxiv.org/abs/2511.02864. Further discussion is at terrytao.wordpress.com/2025/11/05/m...

Mathematical exploration and discovery at scale

AlphaEvolve is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary framework that proposes, tests, and refines ...

arxiv.org

Calling Bay Area math enthusiasts interested in weekly sessions doing rigorous foundational mathematics the modern way - with computer-verified proofs in Lean. (An experiment in rigorous math education outside traditional academia)

I started a crowdsourced meta-project to list all the other crowdsourced mathematical research projects that are currently active and seeking participants: mathoverflow.net/questions/50...

List of crowdsourced math projects actively seeking participants

I believe that with the advent of modern online collaboration platforms (such as Github), proof assistant languages (such as Lean), and (potentially) AI tools, there are many emerging opportunities...

mathoverflow.net

A first proof-of-concept outcome for the erdosproblems.com - OEIS linkage project: with a useful assist from AI, the OEIS was used to locate a proof in the literature for an Erdos problem that was previously marked as "open". mathstodon.xyz/deck/@tao/11...

Thomas Bloom and I are launching a crowdsourced project to link up Thomas's erdosproblems.com site with the #OEIS, by systematically calculating the various integer sequences associated with the Erdos problems and crosschecking them against the OEIS database: terrytao.wordpress.com/2025/08/31/a...

SLMath (MSRI) announces three new research initiatives in Berkeley, California: Call for Proposals for AxIOM month-long programs to begin in Spring 2027, and applications for Summer 2026 PROOF and LATTICE independent research groups. Learn more at www.slmath.org/news-and-eve....

I wrote an op-ed on the world-class STEM research ecosystem in the United States, and how this ecosystem is now under attack on multiple fronts by the current administration: newsletter.ofthebrave.org/p/im-an-awar...

I’m an award-winning mathematician. Trump just cut my funding.

The “Mozart of Math” tried to stay out of politics. Then it came for his research.

newsletter.ofthebrave.org

#IPAM (the institute for pure and applied mathematics) is facing a critical shortfall for operating expenses due to an unexpected suspension of NSF funding www.ipam.ucla.edu/news/nsf-fun... . Donations for emergency continuity of operations funding can be made at giving.ucla.edu/Campaign/Donat

My thoughts on the crucial importance of methodology on self-reported AI performance on mathematics competitions, and my policy on commenting on such reports going forward: mathstodon.xyz/@tao/1148814...

The #SalemPrize for 2025 is now accepting nominations until September 15th. www.ias.edu/math/activit... (I am the chair of the Scientific Committee for the prize.) A bit more information in my blog post on this: terrytao.wordpress.com/2025/07/08/s...

Salem Prize

About

ias.edu

A new #CosmicDistanceLadder post to mark the summer solstice, on how astronomical measurements, from the time of Eratosthenes to the modern day, rely on the tireless (and often unsung) efforts of many careful and precise data collectors. www.instagram.com/p/DLG6a_WIWyb

I have just launched a "Lean companion" to my textbook "Analysis I": github.com/teorth/estim... . This gives a Lean translation (or paraphrasing) of the various definitions, theorems, and exercises in the textbook into Lean. Further discussion at terrytao.wordpress.com/2025/05/31/a...

A video on an actual formalization task from my Polynomial Freiman Ruzsa (PFR) project, which is sufficiently tricky (and sufficiently far from existing training data of current models) that one still has to largely formalize these proofs by "hand": www.youtube.com/watch?v=6uLX...

Formalizing a proof in Lean by hand

YouTube video by Terence Tao

youtube.com

A new #CosmicDistanceLadder post on how the distance ladder can also be used to measure cosmic durations, as well as cosmic distances. www.instagram.com/p/DJ2ra2soG4j

A third video in my occasional series on #Lean4 formalization workflows, this time focusing on how relying extensively on #GitHubCopilot fares against standard "epsilon delta" type problems in analysis. www.youtube.com/watch?v=c1ix...

Formalizing a proof in Lean using Github Copilot only

YouTube video by Terence Tao

youtube.com

A followup to my previous video, in which I now see how #Claude and #o4mini do at formalizing a slightly different proof of the same algebraic implication, after being given the initial informal and formal proofs as reference. www.youtube.com/watch?v=zZr5...

Formalizing a proof in Lean using Claude and o4

YouTube video by Terence Tao

youtube.com

As an experiment, I tried to use automated tools to formalize (in as "mindless" a fashion as possible) a one-page human written proof into Lean. You can watch the results here: www.youtube.com/watch?v=cyyR...

Formalizing a proof in Lean using Github copilot and canonical

YouTube video by Terence Tao

youtube.com

DARPA's "Exponentiating mathematics" (expMath) program, which is launching a challenge to develop and evaluate "AI collaborators" for assist in decomposing and formalizing informal mathematical proofs, is now taking short abstract proposal submissions: sam.gov/opp/869c8d73...

After 200 days, we finally have 100% completion on the primary goal of the Equational Theories Project to formally resolve >22 million implications between 4694 equational laws, using modern proof assistants, collaboration platforms, and automated theorem provers. teorth.github.io/equational_t...

A new #CosmicDistanceLadder post, on intriguing hints from the DESI survey data that suggests that the cosmological constant (aka "dark energy) might not, in fact, be constant after all. www.instagram.com/p/DIP0yy5oDUu

A new #CosmicDistanceLadder post on why lunar and solar eclipses tend to come in pairs (for instance, the solar eclipse next week is paired with the lunar eclipse from last week). www.instagram.com/p/DHkS3EcA40L

Cosmic Distance Calibration xkcd.com/3066

A new #CosmicDistanceLadder post, on how the recent lunar eclipse from the vantage point of the Earth becomes a solar eclipse from the vantage point of the Moon: www.instagram.com/p/DHR1tuWonDR/

Lunar eclipses, such as the one yesterday, were one of the earliest pieces of scientific evidence that the Earth was basically a round sphere, already known to Aristotle: regardless of the position of the eclipse in the light sky, the shadow of the Earth on the Moon was always circular.