Terence Tao
Professor of mathematics, UCLA · as of 2026-10-04 · source
Fields Medalist and the most prominent mathematician engaging with AI; his blog and Mathstodon posts are a main reference for judging AI maths claims.
News mentioning Terence Tao (30)
- arXiv limits submitters to two papers a month as AI-fuelled submissions hit 40,363 in September 2026 ★★★
On Oct 1, 2026 arXiv capped every submitter at two submissions per calendar month and three active submissions at a time. Monthly submissions doubled in two years, from 20,569 in September 2024 to 40,363 in September 2026, and arXiv cited a rise in thin, "salami" and "dense, AI-written" papers…
- Summer 2026 flood: dozens of named conjectures settled on arXiv with disclosed AI help (July–September catalogue) ★★★★
Between July and September 2026 arXiv saw a steady stream of papers that resolve a named conjecture or open question and disclose that a frontier model (mostly GPT-5.6 Sol/Pro and GPT-6 Astra, also Claude Fable 5/5.1, Opus 5/5.5, Gemini) found the key idea, the counterexample or the whole proof…
- Mathematicians' AGMAI publishes norms for AI labs releasing AI-generated results; Simons Institute TCS group issues 12 actions ★★★
On Sept 29, 2026 the Advisory Group on Mathematics and Artificial Intelligence (AGMAI; Tao, Gowers, Hairer, Witten and others) published general recommendations for AI companies releasing mathematical results. They ask labs to release significant results promptly, disclose models, prompts, compute…
- Caltech 'Mathathon' is reworked into 'Old Problems, New Proofs' after an open letter from mathematicians ★★
On Sept 28, 2026 Caltech's organizers and the signatories of an open letter against the AI-sponsored 'Mathathon' published a joint statement on Terence Tao's blog. The event is renamed 'Old Problems, New Proofs' (Nov 13–15, 2026). Participants learn existing hard proofs, then write new…
- ICIAM issues a Statement on Mathematics and Artificial Intelligence; LMS had commented on the Navier–Stokes episode ★★
On 24 Sep 2026 the International Council for Industrial and Applied Mathematics (ICIAM) published a Statement on Mathematics and AI, with a short and a long version. It holds that "understanding, validation, reliability, attribution and human judgement remain essential" and that mathematics must…
- OpenAI says an internal model resolved 100+ long-standing open problems in 24 days of training; no list released ★★★
On 21 Sep 2026 OpenAI said an unnamed internal model had resolved more than 100 long-standing open problems during about 24 days of training (28 Aug – 21 Sep). It released no list and no proofs, and did not define 'resolved'. It also formed a 9-member Advisory Group on Mathematics and AI at IAS…
- SAIR launches the Open Math Model initiative for community-governed open-weight math AI, plus Lean Kernel and Andrews–Curtis challenges ★★★
On 18 Sep 2026 Terence Tao announced that SAIR (Foundation for Science and AI Research), a nonprofit he co-founded, is speeding up an "Open Math Model" initiative. The goal is open-weight, community-governed AI models for everyday mathematical work (understanding proofs, checking references…
- 42 mathematician Fellows of the Royal Society, incl. Gowers, Hairer, Maynard and Scholze, call AI an 'emergency' in open letter to Paul Nurse ★★★★
On 16 Sep 2026 42 mathematical Fellows and Foreign Members of the Royal Society sent an open letter to its President, Sir Paul Nurse, expressing "extreme concern about the pace of development of AI". They wrote that in three months OpenAI's and Anthropic's models went from strong-student level to…
- Fields Medallists' open letter 'A Severe Misalignment of AI in Mathematics' criticises labs' race for famous problems ★★★
On 11 Sep 2026 about 25 Fields Medallists, including Terence Tao, Peter Scholze, Maryna Viazovska and Pierre Deligne, published an open letter criticising AI labs for treating famous open problems as marketing targets. It cited the Navier–Stokes announcement and the Jacobian-conjecture tweet. It…
- OpenAI claims a Millennium Prize problem: 10,000 AI agents prove forced Navier–Stokes blow-up; priority dispute erupts ★★★★★
On 8 Sep 2026 OpenAI released a 166-page paper and a Lean formalisation proving that the 3D incompressible Navier–Stokes equations with a smooth external force can develop a finite-time singularity from smooth initial data. This fits option (C) of Fefferman's official Clay problem statement. About…
- Caltech team (Anandkumar) reports a stable self-similar singularity candidate for the unforced 3D Euler equations on R³, found with PINNs and LLM help ★★★
On 7 Sep 2026, the evening before OpenAI's Navier–Stokes announcement, Anima Anandkumar's Caltech group posted a self-similar singular profile for the unforced incompressible 3D Euler equations on all of R³. Physics-informed neural networks found it, and LLMs helped simplify the bounds and…
- GPT-6 Astra lowers the bounded prime gaps record from 246 to 186 ★★★★
An OpenAI preprint (30 Aug 2026) claims lim inf (p_{n+1} − p_n) ≤ 186, improving Polymath8b's bound of 246, which had stood since 2014. It uses 'triply densely divisible' conditions feeding a multidimensional Selberg sieve and was announced with a Lean formalisation. Julia Stadlmann independently…
- Palomar launches: a registry of Lean-verified mathematics to curb misrepresented AI proof claims ★★★
On 18 Aug 2026 the Lean FRO and ICARM launched Palomar (palomar-registry.org), "the analogue of a preprint server for Lean proofs". It indexes GitHub repositories whose formal results are checked mechanically with Lean's Comparator tool and checked with an LLM for semantic alignment with the…
- Sendov's 1958 conjecture on polynomial roots proved with GPT-5.6 Pro; Tao simplifies and formalises it ★★★★
Lech Mazur posted a computer-assisted proof, generated with GPT-5.6 Pro, of Sendov's conjecture for all degrees: if every root of a polynomial lies in the closed unit disk, each root is within distance 1 of a critical point. Terence Tao called it 'remarkably elementary', simplified it, and used AI…
- HRT conjecture (1996) disproved: 12 time-frequency shifts of a Schwartz function are linearly dependent, found with ChatGPT-assisted guesswork ★★★
arXiv 2608.05044 (5 Aug 2026), by Markus Faulhuber, Philipp Petersen, Jordy Timo van Velthoven and Felix Voigtlaender, shows that finitely many time-frequency shifts of a Schwartz function can be linearly dependent. This disproves the Heil–Ramanathan–Topiwala (HRT) conjecture with an explicit…
- OpenAI's unreleased 'Astra' model claims ten advances in maths and theoretical CS, with Lean proofs ★★★★★
On 1 Aug 2026 OpenAI published 'Ten advances in mathematics and theoretical computer science' by an internal model, Astra (released as GPT-6 Astra on 3 Sep). It came with a 249-page manuscript and Lean 4 proofs. The claims include the first explicit non-sofic group, a disproof of Connes's rigidity…
- Hessian conjecture refuted in five variables, derived from Claude-found Jacobian counterexample ★★★
Five days after Levent Alpöge's Claude Fable 5-assisted counterexample to the Jacobian conjecture, Guowu Meng and Liang Yang used "Schur descent" on it to build a five-variable counterexample to the related Hessian conjecture. The Hessian conjecture now holds for n≤3, fails for n≥5, and is open…
- Terence Tao's ICM 2026 public lecture 'Mathematics in the age of AI' calls a crisis in the foundations of mathematical values ★★★
On 24 Jul 2026, at the International Congress of Mathematicians in Philadelphia, Terence Tao gave the public lecture "Mathematics in the age of AI". He argued that mathematics is entering a "crisis in the foundations of mathematical values and practices", comparable to the 1900–1930 foundations…
- 2026 Fields Medals go to Hong Wang, Yu Deng, John Pardon and Jacob Tsimerman at ICM Philadelphia ★★
At the opening of the International Congress of Mathematicians in Philadelphia on July 23, 2026, the IMU awarded the Fields Medals to Hong Wang, Yu Deng, John Pardon and Jacob Tsimerman. The awards are human results, but the congress was dominated by debate about AI in mathematics, and Tsimerman…
- Claude Fable 5 finds a counterexample to the Jacobian conjecture in dimension 3 ★★★★★
Anthropic mathematician Levent Alpöge posted an explicit polynomial map F: C³→C³ with constant Jacobian determinant −2 that is not injective, found with Claude Fable 5. This refutes Keller's 1939 Jacobian conjecture in every dimension n≥3; the two-variable case remains open. Within days…
- Leiden Declaration on Artificial Intelligence and Mathematics sets community norms for AI in maths (4,000+ signatories) ★★★
The Leiden Declaration on Artificial Intelligence and Mathematics, dated 2 Jun 2026 (Zenodo DOI 10.5281/zenodo.20302944), came out of a September 2025 Lorentz Center meeting in Leiden. It asks for transparent disclosure of AI use, proper attribution, peer-review standards, author rights over…
- OpenAI model disproves Erdős's 80-year-old unit distance conjecture ★★★★★
On 2026-05-20 OpenAI announced that an internal model found a counterexample to Erdős's 1946 unit-distance conjecture using algebraic number theory — widely described as the first historically significant proof produced by an AI; Timothy Gowers said he would recommend it to the Annals of…
- Amateur with GPT-5.4 Pro 'vibe-maths' a 60-year-old Erdős conjecture on primitive sets; Tao co-authors the paper ★★★★
23-year-old amateur Liam Price gave GPT-5.4 Pro a single prompt. In about 80 minutes it sketched a proof of Erdős problem #1196, the 1966 Erdős–Sárközy–Szemerédi conjectures on primitive sets and divisibility chains, using Markov chains with von Mangoldt weights. Professionals including Terence…
- GPT-5.5 Pro-assisted construction lowers the smallest known Borsuk counterexample dimension from 64 to 63 ★★★
In May 2026 Max Grinsztajn, assisted by OpenAI's GPT-5.5 Pro, built a 321-point set in R^63 that cannot be split into 64 parts of smaller diameter, so Borsuk's conjecture fails in dimension 63 (b(63) ≥ 65). The previous smallest known failing dimension, 64, had stood since 2013. A second…
- Erdős problem #728 solved near-autonomously by GPT-5.2 Pro and Harmonic's Aristotle, with a Lean proof ★★★★
On 4–6 Jan 2026 amateur Kevin Barreto relayed an informal argument from GPT-5.2 Pro to Harmonic's Aristotle, which formalised it in Lean. It was widely accepted as the first Erdős problem solved essentially autonomously by AI with no prior solution in the literature. Terence Tao said the win 'says…
- Genuine AI-assisted solutions to Erdős problems begin: #124 (Aristotle), #1026 (48-hour human–AI collaboration) ★★★★
In Nov–Dec 2025 AI tools produced the first genuinely new (if modest) solutions to Erdős problems. Harmonic's Aristotle proved a version of #124 in Lean autonomously (29 Nov). Erdős #1026 (posed 1975) was fully solved within ~48 hours by humans combining Aristotle, AlphaEvolve, GPT and…
- Tao, Gómez-Serrano, Georgiev and Wagner test AlphaEvolve on 67 maths problems ★★★
In 'Mathematical exploration and discovery at scale' (arXiv 2511.02864), Bogdan Georgiev, Javier Gómez-Serrano, Terence Tao and Adam Zsolt Wagner ran AlphaEvolve on 67 problems in analysis, combinatorics, geometry and number theory. It rediscovered the best known constructions in most cases and…
- OpenAI researchers claim GPT-5 'solved' 10 Erdős problems; the solutions were already in the literature ★★★
In mid-October 2025 OpenAI's Kevin Weil tweeted that GPT-5 'found solutions to 10 (!) previously unsolved Erdős problems'. Thomas Bloom, who runs erdosproblems.com, called this 'a dramatic misrepresentation': GPT-5 had found existing papers solving problems listed as open only because he did not…
- Math Inc's Gauss agent completes the Strong Prime Number Theorem formalisation in Lean in three weeks ★★★★
Math Inc (Christian Szegedy) announced that its autoformalization agent Gauss completed Terence Tao and Alex Kontorovich's Strong Prime Number Theorem project in Lean in about 3 weeks, producing ~25,000 lines of Lean and over 1,000 theorems and definitions. Human experts had worked on the project…
- OpenAI o3 scores 25% on FrontierMath research-level maths benchmark, amid funding disclosure controversy ★★★
Epoch AI's FrontierMath (Nov 2024) contains unpublished research-level problems on which models scored under 2%. On 20 Dec 2024 OpenAI claimed 25.2% for o3. It then emerged that OpenAI had funded the benchmark and had access to most problems. Released o3 scored lower in independent tests.
Posts (11)
- How AI does, and does not, change the way I do math original ↗ Rachel Webb (guest post on Terence Tao's blog) · blog · 2026-09-29
A mathematician's view, published on Terence Tao's widely read blog, of what LLMs change in research practice during the 2026 wave of AI-assisted proofs. - Announcing the Advisory Group on Mathematics and Artificial Intelligence original ↗ Terence Tao (for AGMAI) · blog · 2026-09-21
Nine leading mathematicians (Gowers, Hairer, Witten, Vakil, Wood…) formed an unpaid, independent group to advise OpenAI on releasing its 100+ claimed math results. - Why I didn't sign the Fields medallists' letter original ↗ Timothy Gowers @wtgowers · blog · 2026-09-17
The most prominent dissent from the Fields Medallists' declaration: a Fields medallist who agrees there is a crisis but rejects the letter's framing and demands. - Tao: 25 Fields Medalists make a joint declaration on Math and AI original ↗ Terence Tao @tao@mathstodon.xyz · other · 2026-09-11
Tao's announcement of the Fields Medallists' declaration 'A Severe Misalignment of AI in Mathematics', which says AI labs' race to solve famous problems is at odds with mathematics' goals. - OpenAI: 'We're sharing a solution to the Navier-Stokes Millennium Prize Problem' original ↗ OpenAI @OpenAI · x · 2026-09-08
OpenAI's announcement of an AI-produced proof claimed to solve a Clay Millennium problem, which set off a major controversy. - Buckmaster: Alpöge and I have made public three finite-time blowup results (with statement) original ↗ Tristan Buckmaster @tristanbuckmaster@mastodon.social · other · 2026-09-08
Buckmaster's release of the Euler/Boussinesq/IPM blow-up proofs and his statement accusing OpenAI, which started the Navier–Stokes priority controversy. - Finite time blowup with smooth forcing term for the incompressible porous medium, Boussinesq, and incompressible Euler equations original ↗ Terence Tao · blog · 2026-09-07
Tao's exposition of the Alpöge–Buckmaster AI-assisted blow-up results, which appeared a day before OpenAI's Navier–Stokes claim and anchor the priority dispute. - Tao: open problems have become a non-renewable resource original ↗ Terence Tao @tao@mathstodon.xyz · other · 2026-09-03
Tao's influential threads arguing that AI labs racing to 'solve' famous problems use up a non-renewable resource, with Navier–Stokes as the example. They set the terms of the September 2026 debate. - A digestion of the proof of Sendov's conjecture original ↗ Terence Tao · blog · 2026-08-12
Tao distils Lech Mazur's AI-generated proof of Sendov's conjecture (1958) into an elementary argument and a much shorter Lean formalisation. - A digestion of the Jacobian conjecture counterexample original ↗ Terence Tao · blog · 2026-07-21
Tao's expert explanation of the 3D Jacobian conjecture counterexample found with Claude Fable 5, the most-cited human 'digestion' of an AI-found disproof. - Math, Inc. original ↗ Math, Inc. @mathematics_inc · x · 2025-09-11
Cited as a source by: 2025-09-10-math-inc-gauss-strong-pnt
Videos (2)
- I've never made a video like this. Species | Documenting AGI · 2026-10-04
- Terence Tao: "Mathematics in the Age of AI" (ICM 2026) Alvaro Lozano-Robledo · 2026-07-27
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