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
Weβre thrilled to announce that Terence Tao (@teorth.bsky.social)βs 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.
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...
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...
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...
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...
Simons Laufer Mathematical Sciences Institute (SLMath) - AxIOM Month-Long Programs: Call for Proposals for Spring 2027 and beyond - PROOF and LATTICE summer research for teams: Call for Applications for Summer 2026
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 have some related posts on this at mathstodon.xyz/@tao/1149568... and mathstodon.xyz/deck/@tao/11...
#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...
If you click on the link and go to the second slide you will see the second part of the sentence (after the ellipsis ...), which mentions the tropic of Cancer.
First page of the instagram post
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...
The first page of the instagram post on how we measure cosmological durations.
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...
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...
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...
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...
The dashboard of the project reports a 100.00% completion rate.
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
First page of the instagram post
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
First page of the instagram post
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.
A new post on my #CosmicDistanceLadder Instagram with Tanya Klowden on the parallels (but also differences) between ancient Greek and ancient Indian astronomy. www.instagram.com/p/DGzJs02AbBA
