# Terence Tao

> Source: https://aiwiki.ai/wiki/terence_tao
> Updated: 2026-09-13
> Fact-checked: 2026-07-24
> Categories: AI for Science, Mathematics, People
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> Cite as: AI Wiki. "Terence Tao." aiwiki.ai, 13 Sept 2026. https://aiwiki.ai/wiki/terence_tao
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Terence Tao (born 1975 in Adelaide, Australia) is a mathematician at the University of California, Los Angeles, where he is a Distinguished Professor and holds the James and Carol Collins Chair in the College of Letters and Sciences [1][5]. He received the Fields Medal in 2006 [2][3] and is known outside his own subject for the Green-Tao theorem, proved with Ben Green in a 2004 preprint, which shows that the prime numbers contain arithmetic progressions of every finite length [3][4].

Since 2023 Tao has also written extensively in public about artificial intelligence and its use in mathematics. His involvement takes several distinct forms. He organizes large formalization projects in the [Lean](https://aiwiki.ai/wiki/lean) proof assistant; he publishes hands-on evaluations of frontier models applied to genuine research tasks; he helps run competitions, registries and benchmarks that measure machine performance on [mathematical reasoning](https://aiwiki.ai/wiki/mathematical_reasoning); and he writes dated commentary, mostly on his blog What's new and on Mastodon, about what the tools can and cannot do [7][9][13][15].

What distinguishes that commentary is that it is dated, specific and frequently revised in public. In September 2024 he likened one narrow kind of AI assistance to advising a "mediocre, but not completely incompetent, (static simulation of a) graduate student", edited the post days later to add the bracketed qualifiers that secondary coverage usually drops, and posted a separate apology for the comparison he had drawn [15]. By June 2026 he was reporting that autoformalization tools could finish virtually every formalization task he issued within hours, while producing proofs bloated enough to slow his build times [23]. He has been publicly critical of uncontrolled benchmark comparisons, and of his own group's results when they came back weak [18][21]. On 11 September 2026 he was one of 25 initial signatories, all of them Fields Medallists, to a declaration titled "A Severe Misalignment of AI in Mathematics", which argues that the goals of AI companies and those of the mathematical community have come apart [33][34].

## Background and mathematical career

Tao competed in the [International Mathematical Olympiad](https://aiwiki.ai/wiki/international_mathematical_olympiad) three times as a schoolchild, at the ages of ten, eleven and twelve, taking a bronze medal in 1986, a silver in 1987 and a gold in 1988; his own biography page describes him as still the youngest gold medallist in the competition's history [1][3]. He completed a B.Sc. (Hons) at Flinders University in December 1991 and an M.Sc. there in August 1992 under Garth Gaudry, then a Ph.D. at Princeton University in June 1996 under Elias Stein [1][28]. He joined UCLA in 1996 as a Hedrick Assistant Professor and has been a full professor there since 2000 [1][3].

The Clay Mathematics Institute, which appointed him a Clay Research Fellow for a three-year term beginning in 2001 and gave him the 2003 Clay Research Award, describes his work as split between real-variable harmonic analysis, the analysis of non-linear dispersive and wave equations, and the combinatorics arising from the representation theory and symplectic geometry of U(n) [28]. Alongside the Fields Medal he was named to the MacArthur Foundation's 2006 class of fellows [2], and he served on the President's Council of Advisors on Science and Technology (PCAST) under the Biden administration [5]. His own biography page records an appointment as a Companion of the Order of Australia in 2026 [3]. In January 2026 he described himself as writing "in my capacity as Director of Special Projects at IPAM", UCLA's Institute for Pure and Applied Mathematics, when launching the formalization network described below [32]. He writes the blog What's new and has posted to the Mastodon instance mathstodon.xyz since November 2022, where much of his commentary on AI appears [30].

## Formalization and the Lean projects

### The Polynomial Freiman-Ruzsa formalization

On 9 November 2023, Tao, Timothy Gowers, Ben Green and Freddie Manners posted a proof of a conjecture of Katalin Marton, widely known as the polynomial Freiman-Ruzsa conjecture, in characteristic 2 [8]. Days later Tao announced a project with Yael Dillies and Bhavik Mehta to formalize the argument in Lean 4, coordinated through a GitHub repository and Patrick Massot's Blueprint tool, which renders a human-readable version of the proof as a dependency graph whose nodes turn green as each step is verified [9][11].

The goal Tao set was to get all the bubbles leading up to and including the "pfr" bubble at the bottom of that graph coloured green [9]. He noted that the blueprint structure lets contributors work on different parts of a proof asynchronously, without waiting for earlier stages to be fully formalized, and that a proof-assistant project "makes large-scale mathematical collaboration possible without necessarily having a pre-established level of trust amongst the collaborators" [9]. On 5 December 2023 he reported that the project had succeeded after three weeks, with the dependency graph fully green and the Lean compiler confirming that the conjecture followed from the standard axioms [10].

The repository has since run further stages. A second stage formalized several consequences of the result and an argument of Jyun-Jie Liao reducing the covering exponent from 12 to 11; the repository now describes work on an extension to other bounded torsion groups and on a further refinement of Liao's that improves the exponent to 9 [11]. The repository also carries a Challenge and Solution pair submitted to the Palomar registry described below [11].

### The Equational Theories Project

On 25 September 2024 Tao proposed a larger experiment: a crowdsourced attempt to settle every implication among the 4,694 equational laws of order at most four, meaning the laws on magmas that use the magma operation at most four times [12][13]. In the announcement he argued that proof assistant languages such as Lean "provide a potential way to overcome these obstacles, and allow for large-scale collaborations involving professional mathematicians, the broader public, and/or AI tools", while warning that such tools "can 'hallucinate' plausible-looking, but nonsensical arguments, which therefore need additional verification" [12].

The Equational Theories Project (ETP) launched that same month, hosted in a repository under Tao's GitHub account [13][14]. Its primary goal was reached on 14 April 2025, when all 22,028,942 implications between the 4,694 laws had been determined, with every proof or refutation formalized in Lean [13]. Over fifty contributors took part, coordinating through a channel on the Lean Zulip forum and a single GitHub repository [13]. The report contrasts this with the earlier Polymath model of open online collaboration, which required human moderators to review and integrate contributions and which the authors judged would not scale to a project demanding the verification of over twenty million statements [13]. The 4,694 laws resolved into 1,415 equivalence classes [13].

The project's own report, posted to arXiv in December 2025 with several dozen named authors, is unusually candid about where machine learning helped and where it did not. Most of the automation came from conventional [automated theorem provers](https://aiwiki.ai/wiki/automated_theorem_proving) and related solvers, among them Vampire, Prover9 and Mace4, the SMT solver Z3 and the SAT solver Kissat, not from neural systems [13]. [Large language models](https://aiwiki.ai/wiki/large_language_model) were used "in a fairly limited fashion": for writing initial code behind the project's visualization tools, for autocompletion during formalization via [GitHub Copilot](https://aiwiki.ai/wiki/github_copilot), and in one case where [ChatGPT](https://aiwiki.ai/wiki/chatgpt) guessed a complete rewriting system for a particular law that could then be formally verified [13]. On the hard cases, the report states, "we found that LLMs did not provide useful suggestions beyond what the human participants could already propose". Elsewhere it records that automated theorem provers turned out to be "significantly more effective at this task (at least if one restricted to publicly available LLMs), and the project largely moved away from the use of such LLMs (other than to help create the code for the visualization tools)" [13].

One machine learning result did stand out. A five-layer convolutional network trained on character-level tokenizations of equation pairs predicted implication status on a held-out test set with 99.7 percent accuracy, and still reached 92.2 percent when trained on 0.1 percent of the data [13]. The authors suggest such a model could guide the extension of the graph to order 5 by letting the automated provers focus first on the network's predicted status for each implication [13].

Revisiting the report on 7 September 2026, Tao drew attention to a remark at the back of it about the opportunity cost of the project's own choices: by deploying automated theorem provers early, he wrote, "we might have settled some implications that had more interesting human-readable proofs that we missed" [13][64]. He added his own assessment that if the ETP were run in 2026, "it is likely that modern LLMs would very quickly resolve almost all of the implications studied, and the few remaining holdouts would likely then fall in a matter of days with additional LLM compute", and sketched two ways the problem set could be enlarged: order-five laws, which he put at roughly 3 billion implications, or pairs of order-four laws, at roughly 40 billion [64].

### The Integrated Explicit Analytic Number Theory Network

On 15 January 2026, writing in his capacity as Director of Special Projects at IPAM, Tao launched the Integrated Explicit Analytic Number Theory Network (IEANTN), partially hosted inside the existing Prime Number Theorem And More (PNT+) formalization project [31][32]. Explicit analytic number theory makes every constant in an estimate numerical rather than asymptotic, which Tao described as requiring "a significant amount of careful book-keeping and numerical optimization" and as historically error-prone enough that downstream papers often rely on inputs a decade or more out of date [32]. He framed the project as "an appropriate application of modern AI and formalization tools", meant "not to replace the most enjoyable aspects of human mathematical research, but rather to allow extremely tedious and time-consuming, but still necessary, mathematical tasks to be offloaded to semi-automated or fully automated tools" [32].

The project has two halves. The first is a crowdsourced Lean formalization of a network of inter-related explicit results, coordinated through GitHub issues that are labelled by size from XS to XL so that beginners can pick small tasks [32]. The second, run at IPAM with financial and technical support from Math Inc., is to extract from the formalized network an interactive spreadsheet of estimates in which changing one input, such as the numerical threshold to which the Riemann hypothesis has been verified, propagates automatically through the dependent bounds [32]. AI use is permitted on the formalization tasks but must be disclosed, and contributors are required to edit the generated code to remove excessive bloat [32].

Writing about the project on 21 June 2026, Tao said that "autoformalization has reached the point where virtually every formalization task I had issued could be completed within hours", leaving its queue of unclaimed formalization tasks essentially empty [23]. The tools, he noted, "tended to create quite bloated proofs, often hundreds of lines longer than what a human would choose to do, with a lot of redundancy, with many lemmas not stated at the natural level of abstraction"; since each such proof adds tens of seconds to the total build time, the cumulative effect had become noticeable and hard to review [23]. He added a distinction that recurs in his writing: agents can execute a refactor he explains to them, but "they struggle to spontaneously discover such refactors on their own" [23]. He set the episode against a line he attributed to Blaise Pascal in 1657, that it is now easier to generate long correct proofs than short ones, which widens what he calls the impedance mismatch between proof generation, verification and digestion [23].

### Palomar

On 18 August 2026 Tao announced that Palomar, a registry of Lean-verified mathematics incubated by the Lean FRO and by ICARM, was open for submissions, and that he serves on its scientific advisory board alongside Jeremy Avigad, Matthew Ballard, Jaume de Dios, Nestor Guillen, Bryna Kra, Kim Morrison, Ravi Vakil and Akshay Venkatesh [36]. He described the motivation as the difficulty of checking, for a non-expert, that a given Lean repository really proves what it claims: one has to confirm that the proofs typecheck, that they contain no "cheats" such as extra axioms, and that the formal statements match the informal description [36].

Palomar registers snapshots of external GitHub repositories, identified by commit, that contain a short human-readable "challenge file" stating the claimed results in Lean, a solution module proving them, and a formalization.yaml file describing the results informally along with metadata and disclosures [36]. Submissions are checked mechanically with the Lean tool Comparator, and the match between the informal description and the formal statement is checked by a large language model [36]. Tao stressed that neither check substitutes for peer review: "Palomar is not a peer-reviewed journal" [36]. He said he had submitted his own formalization of the proof of Sendov's conjecture as a test, and called it "a zeroth approximation" of a preprint server for Lean proofs [36].

### Other repositories

Tao maintains a Lean companion to his textbook Analysis I as a public repository [26], and a community GitHub repository for the erdosproblems.com database is hosted under his account [29].

## Public evaluations of AI systems

### 2023: a forecast

In an essay for Microsoft's AI Anthology published on 12 June 2023, Tao wrote that when integrated with tools such as formal proof verifiers, internet search and symbolic math packages, "2026-level AI, when used properly, will be a trustworthy co-author in mathematical research, and in many other fields as well" [7]. The same essay records that the stylistic signals he normally relies on to smell out a hopelessly incorrect argument "are of little use with LLM-generated mathematics", and that only line-by-line reading can tell whether there is substance [7].

### 2024: o1 and the graduate student comparison

On 13 September 2024 Tao posted three experiments with a prototype version of OpenAI's [o1](https://aiwiki.ai/wiki/o1), which he had been granted access to [15]. On a semantic search task that earlier models had answered with "hallucinated nonsense", o1 identified the relevant theorem (Cramer's theorem) and gave what Tao called a perfectly satisfactory answer [15]. On a complex analysis problem the results were "better than previous models, but still slightly disappointing": the model "could work its way to a correct (and well-written) solution if provided a lot of hints and prodding, but did not generate the key conceptual ideas on its own, and did make some non-trivial mistakes" [15].

His summary was the sentence that circulated most widely: "The experience seemed roughly on par with trying to advise a mediocre, but not completely incompetent, (static simulation of a) graduate student. However, this was an improvement over previous models, whose capability was closer to an actually incompetent (static simulation of a) graduate student" [15]. Secondary coverage often drops the "(static simulation of a)" qualifiers, which Tao himself added to the post on 19 September 2024 and flagged with a note reading "[Parenthetical clarifications added - 9/19/2024]" [15]. The same post continued that "it may only take one or two further iterations of improved capability (and integration with other tools, such as computer algebra packages and proof assistants) until the level of '(static simulation of a) competent graduate student' is reached, at which point I could see this tool being of significant use in research level tasks" [15]. The earlier, weaker performance he was contrasting against was that of [GPT-4](https://aiwiki.ai/wiki/gpt-4), which he had asked to assist in writing up a proof of the same complex analysis problem in an earlier experiment [15].

On 16 September 2024 he posted an apology for having implied that human graduate students can be ranked on "a static, one dimensional level of 'competence'", arguing that the ability to contribute to an existing research project is "only one aspect of graduate study, and a relatively minor one at that", and that the decisive difference is growth: "while modern AI tools have some ability to incorporate feedback into their responses, each individual model does not truly have the capability for long term growth, and so can be sensibly evaluated using static metrics of performance" [15].

Asked on 14 September 2024 to make the comparison concrete, he said he was considering one specific metric, the extent to which an assistant can help with subtasks of a research project directed by an expert, and offered a numerical version: with the latest tools "the effort put in to get the model to produce useful output is still some multiple (but not an enormous multiple now, say 2x to 5x) of the effort needed to properly prompt and verify the output", and he saw "no reason to prevent this ratio from falling below 1x in a few years, which I think could be a tipping point for broader adoption of these tools in my field" [15]. He added that the ratio was already below one for some subtasks such as semantic search, data formatting and generating numerical code [15]. A third experiment asked o1 to break a formalization task in Lean into sublemmas; the model understood the task but produced code with errors, which Tao attributed to its training data on Lean and [Mathlib](https://aiwiki.ai/wiki/mathlib) being a year or more out of date [15].

### FrontierMath

Tao was one of four mathematicians interviewed by [Epoch AI](https://aiwiki.ai/wiki/epoch_ai) for the paper introducing [FrontierMath](https://aiwiki.ai/wiki/frontiermath), the research-level benchmark posted on 7 November 2024, and he also contributed several problems to it [6]. Shown a selection of questions, he said: "These are extremely challenging. I think that in the near term basically the only way to solve them, short of having a real domain expert in the area, is by a combination of a semi-expert like a graduate student in a related field, maybe paired with some combination of a modern AI and lots of other algebra packages..." [6]. He expected the benchmark to "resist AIs for several years at least", citing the near absence of relevant training data: for many problems, he said, it is "almost nonexistent...you're talking like a dozen papers with relevant things" [6]. At launch, the paper reported that leading models solved under 2 percent of the problems [6].

The paper records two quantified expectations from him. On advanced graduate-level questions, guiding a system of that era to a correct solution took "about five times as much effort" as solving the problem directly, a ratio he expected to fall below one on certain problems within a few years; and he and Evan Chen both suggested that human experts working with AI systems could tackle FrontierMath problems within around three years, well before fully autonomous solutions [6]. He also raised the economics. Commenting on systems such as [AlphaProof](https://aiwiki.ai/wiki/alphaproof), he observed that "if your amazing tool takes three days of compute off of all of Google to solve each problem...then that's less of a useful tool" [6].

### AlphaProof and the Olympiad

On 26 July 2024, after [Google DeepMind](https://aiwiki.ai/wiki/google_deepmind) announced that AlphaProof and [AlphaGeometry 2](https://aiwiki.ai/wiki/alphageometry_2) had together solved four of six IMO problems for 28 of 42 points, one short of the gold threshold [17], Tao posted preliminary impressions [16]. He called it "great work, shifting once again our expectations of which benchmark challenges are within reach of either AI-assisted or fully autonomous methods", judged that "IMO level geometry problems are now effectively a solved problem for specialized AI tools", and qualified that formalizable IMO problems were now "at least somewhat amenable to AI attacks (though currently requiring genuinely significant amounts of compute per problem, and human assistance on the formalization side)" [16]. He suggested the database of generated formal proofs "could be a useful resource if shared more openly", and noted that the approach leaned more on reinforcement learning than on language models, in the spirit of AlphaGo [16].

A year later he set out a longer caution. On 19 July 2025 he noted that the 66th IMO had run without an official controlled competition for AI models, although "several AI companies have submitted solutions to many of the IMO questions, though with no regulation on how much compute or human assistance was used", and said he hoped for a controlled environment the following year, possibly using the AIMO format [27]. In a three-part thread later the same day he laid out a human metaphor: a team of contestants given days instead of hours, allowed tools and internet access, permitted to collaborate, prompted by their team leader, and free to submit only their best solution or none at all. Under such formats, he wrote, "a student or team of students who might not even always reach bronze medal performance if taking the competition under standard test conditions might instead reach reliable gold medal performance" [18]. His conclusion: "in the absence of a controlled test methodology that was not self-selected by the competing teams, one should be wary of making overly simplistic apples-to-apples comparisons between the performance of various AI models on competitions such as the IMO, or between such models and the human contestants", adding that he would not comment on self-reported results whose methodology had not been disclosed in advance [18]. He stressed in an edit that the remarks were not specific to any single result [18].

## Digesting AI-generated results

During 2026 Tao published a series of posts he called "digestions": human expositions of results that had been produced with heavy AI assistance, written to place them in the context of the existing literature and to isolate the ideas. Each carries an explicit disclosure of his own AI use.

In "A digestion of unit distance constructions" (3 July 2026) he worked through a construction of point sets with many unit distances that a team from OpenAI had produced, a weaker variant that he says was "later observed using the Mythos AI", and Paul Erdős's original construction, presenting the three as points on a continuum distinguished by whether the number of primes or the degree of a field extension is sent to infinity [44]. He noted that the Mythos variant could plausibly have been found first in an alternate order of events, by humans or by machines, and then refined into the OpenAI construction "once the significance of Golod-Shafarevich towers was realized" [44]. His disclosure reads: "AI tools were useful for providing initial summaries of these arguments, as well as on explaining various fundamentals of algebraic number theory to me" [44].

"A digestion of the Jacobian conjecture counterexample" (21 July 2026) carries the disclosure "I used an AI chatbot to discuss various aspects of this problem and to confirm several of the calculations made here" [45]. On "A partial digestion of the HRT counterexample" (6 August 2026) he wrote that the result was unsurprisingly AI-assisted but that "the authors have disclosed their AI use responsibly, with the final arguments written by hand with a readable overview of the argument, as well as proper discussion of methods, relation to past literature, and other independent numerical checks on the result" [46].

The longest of the series is "A digestion of the proof of Sendov's conjecture" (12 August 2026) [47]. Tao had previously proved Sendov's conjecture for sufficiently large degree by an argument that used analytic continuation and so did not quantify the threshold; Brown and Xiang had settled small degrees [47]. He reports that Lech Mazur used an AI tool to close the intermediate range, with the proof verified in Lean, but that "the AI-generated proof was not human-digested to be in the form of a publication-ready preprint", and that it took Tao several days, with heavy AI assistance of his own, to place it in context and simplify it [47]. One consequence of the digestion, he writes, is that the argument establishes the stronger interior form of the conjecture, resolving both Sendov's conjecture and the Phelps-Rodriguez conjecture in full generality; the resulting proof uses no complex analysis beyond the fundamental theorem of algebra and basic Möbius transformations [47]. Using an AI agent he then reformalized the whole argument in Lean in about 15,000 lines, against roughly 90,000 for the original formalization [47].

## Literature search and problem databases

In October 2025 Tao set out a general position on where AI would pay off first: the most productive near-term uses in mathematics would come "not from applying the most powerful models to the most challenging problems", but "from using medium-powered tools to accelerate and scale up more mundane and time-consuming, but still essential, research tasks" [19]. The fact that a human expert could in principle have produced the same output "is actually a feature rather than a bug", because it makes the output cheap to check [19].

His worked example was literature review on erdosproblems.com, a database of over a thousand problems attributed to Paul Erdős, about 600 of them then marked open [19]. Contributors began systematically running an AI deep research tool across the problem list, with human review before anything was posted [19]. Six problems had their status upgraded from open to solved as a result, and a dozen or so others gained newly located references [19]. He also argued that systematic tool use makes negative results reportable: a search that finds nothing is worth recording, and rarely gets recorded when a human does it [19].

He returned to the database on 22 January 2026, writing that it "has become a real hotbed of activity in recent months, particularly as some of the easiest of the outstanding open problems have turned out to be amenable to various AI-assisted approaches", and drawing the lesson that a well curated database of precise problems lets other parties, human or machine, make systematic progress on some fraction of them [59]. He proposed a second such database, a crowdsourced repository of optimization constants recording the best known upper and lower bounds for constants defined by optimization problems, to encourage attempts to improve the state of the art [59].

## AlphaEvolve and machine-driven exploration

Tao is a coauthor of "Mathematical exploration and discovery at scale", posted on 3 November 2025 with Bogdan Georgiev, Javier Gómez-Serrano and Adam Zsolt Wagner, which applies DeepMind's [AlphaEvolve](https://aiwiki.ai/wiki/alphaevolve) evolutionary coding agent to 67 problems across mathematical analysis, combinatorics, geometry and number theory [20]. The system "rediscovered the best known solutions in most of the cases and discovered improved solutions in several", and in some instances generalized results from finitely many input values into a formula valid for all of them [20]. The paper also combines AlphaEvolve with Deep Think and AlphaProof so that proof assistants and [reasoning models](https://aiwiki.ai/wiki/reasoning_models) supply automated proof generation on top of the search [20].

## Benchmarking research-level mathematics

Tao's UCLA group operates one of the AI harnesses evaluated by First Proof, a foundation whose stated mission is to provide "independent, transparent, and rigorous engagement with the evolving capabilities of AI in research mathematics" and whose executive director is Mohammed Abouzaid of Stanford University [22]. Its editorial board selects previously unpublished research problems whose solutions are not public, tests the entered harnesses via API with one shot per question and no further interaction, and has the resulting solutions reviewed double blind by expert referees who score correctness, exposition and attribution separately [22][60]. Board members undertake not to accept paid engagements with AI companies while serving, and industry donations are used to pay the graders rather than the boards [22].

Reporting the second batch on 10 June 2026, Tao wrote that ten research-level questions were tested against four harnesses, including his UCLA team's, and that in aggregate 7 of the 10 problems were deemed to have at least one publication-level solution across the four [21]. His own team's harness solved 2 at an acceptable level, reached roughly "minor revisions needed" on 3 more, and drew rejections or major revisions on the other 5 [21]. The UCLA harness performed slightly better than the out-of-the-box frontier model, but "at much higher compute costs (a few hundred dollars per question, rather than tens)" [21].

He listed the weaknesses the referees exposed without softening them: "the general failure to cite appropriate relevant literature, and having poor exposition", including one correct solution flagged for spending far too much time on trivial steps [21]. He called those addressable, said the team planned to make more use of tools such as symbolic computation and literature search, and closed: "While our own performance was slightly disappointing, I hope to see many more scientifically rigorous benchmarking exercises like this in the future" [21]. First Proof announced a third batch on 25 August 2026, with testing scheduled for early October 2026 and results, referee reports and human solutions due for publication on 14 October 2026 [60].

## SAIR Foundation challenges

Tao serves on the board of the SAIR Foundation, the Foundation for Science and AI Research, and has co-organized a sequence of its mathematical competitions [37][41]. The pattern he describes is a problem whose solutions are cheap to verify mechanically but hard to find, opened to human and machine entrants alike.

| Launched | Challenge | Co-organizers named by Tao | Design |
|---|---|---|---|
| 13 March 2026 | Mathematics Distillation Challenge (equational theories) | Damek Davis [37] | Stage 1 asked for a "cheat sheet" of at most 10 kilobytes that raises a cheap model's accuracy on ETP-style true-false questions; Tao reported that small open models scored about 50 percent unaided and 55-60 percent with a good prompt [37] |
| 8 June 2026 | Modular Arithmetic Challenge | Alberto Alfarano, François Charton, Yongzheng Jia, Kristin Lauter, Cathy Li, Emily Wenger [38] | Submit a fixed-weight neural network that performs modular multiplication for a prime modulus of up to about a thousand digits, with the main computation required to be neural rather than scripted [38] |
| 16 June 2026 | Inverse Galois Challenge (IGP24), with the LMFDB | John Jones, Jen Paulhus, David Roe, Andrew Sutherland [39] | Locate integer polynomials realizing as many as possible of the 25,000 transitive permutation groups of degree 24 as Galois groups, verified by MAGMA and PARI/GP rather than Lean [39] |
| 11 September 2026 | Andrews-Curtis Conjecture Challenge, with the Math-AI group at Caltech | Sergei Gukov, Lucas Fagan [40] | A Discovery Track over a pool of 10,115 balanced two-generator presentations of the trivial group, scored on the shortest verified trivialization path, plus a Proof Track for proofs or disproofs; closes 30 November 2026 [40] |

Writing on 13 March 2026, Tao placed the distillation challenge in a line running from the Polymath projects through collaborative formalization to the ETP, as a way of doing mathematics "with a broad community of mathematically minded people on problems which may not be as deep as the problems one traditionally works on, but still are of mathematical interest" [37]. On 8 June 2026 he reported that stage 1 of the distillation challenge was complete and that stage 2, requiring Lean proofs or disproofs rather than true-false answers, was under way [38].

On 3 September 2026 he described a tradeoff the inverse Galois challenge had forced. Because its first stage was run as a competition in which contestants did not share their polynomials, the organizers could measure the difficulty of each Galois group by the number of contestants who found a polynomial for it, producing what he called a map of the difficulty landscape [48]. Releasing the polynomials to enable a collaborative second stage, he wrote, "permanently degraded the ability to crowdsource this type of difficulty map in the future": a tradeoff he and his co-organizers "viewed as one worth making, but the decision was not taken lightly" [48]. Answering a commenter on 12 September 2026 who asked whether the mathematical community might train its own models, he wrote that "the SAIR foundation I am working with are currently negotiating with several academics and smaller companies on precisely this" and that he hoped to announce something soon [56].

## Writing on the purpose and value of mathematics

With Tanya Klowden, Tao posted "Mathematical methods and human thought in the age of AI" to arXiv on 27 March 2026, an unabridged version of a solicited article for a forthcoming Blackwell Companion to the Philosophy of Mathematics [42][43]. He wrote that he rarely produces article-length philosophical essays, that this one took over a year, and that at the field's current pace "some of it is already slightly out of date" [43]. The paper argues that AI is "a natural evolution of human tools developed throughout history to facilitate the creation, organization, and dissemination of ideas", and that its development must "remain fundamentally human-centered" [42]. The point Tao singled out in the blog post was that AI tools should be judged not only "through the technical lens of what microscale problems they solve" but "through the macroscopic humanitarian lens of how our society, our shared body of knowledge and understanding, and our species benefits (or is harmed) as a whole" [43].

He is also on the scientific board of Mathematical Discourse, a peer-reviewed journal that publishes video recordings of research talks, announced on his blog on 22 August 2026 with the stated goal of promoting "a culture which values communication as an essential part of the research process" [58].

## 2026: open problems as a non-renewable resource

Through early September 2026 Tao developed, in a sequence of dated Mastodon threads, an argument that the supply of fruitful open problems is being depleted. On 3 September 2026 he opened with the observation that answering a question can carry irreversible costs, drawing analogies to film spoilers and to leaked competition information, and concluded that "analogously to pre-atomic steel", open problems in mathematics generated before the AI era "have become something resembling a non-renewable resource" [48]. Citing an essay by Hugo Duminil-Copin, he wrote that "the indiscriminate automated strip-mining of open problems for solutions may destroy the ecosystem from which the next generation of mathematical techniques, problems, and practitioners would have developed", and raised the possibility that "it may become necessary to declare certain classes of mathematical problems off-limits to automated solvers", while conceding this would be hard to enforce [48].

The same day he applied the argument to the global regularity problem for the incompressible Navier-Stokes equations, writing that until recently the problem "was on track to be one of the most promising examples of an AI-assisted success story" but that there was now "an increasingly realistic scenario in which a primarily AI-generated solution to the problem appears, but in a fashion that contaminates the problem as a source of further advances" [49]. On 5 September 2026 he appended a clarification to the thread: "in response to recent rumors about a possible solution to the Navier-Stokes problem: I am not aware of any significant developments in this regard; the above discussion is hypothetical, but not completely implausible at the current level of development of AI technology" [49]. Both of those posts predate OpenAI's announcement of 8 September 2026, which the wiki covers at [OpenAI Navier-Stokes proposed solution](https://aiwiki.ai/wiki/openai_navier_stokes_proposed_solution). He worked the argument out in more detail on the bounded gaps between primes problem. On 1 September 2026 he had described a preprint of Julia Stadlmann that shaved the Polymath8b bound of 246, standing since 2014, down to 240, and noted that she had used traditional numerical computation but not modern AI tools, and that the paper, "being human-written, was far easier to read for experts than an AI-generated analogue" [68]. Two days later he wrote that "no fewer than three separate AI companies" had raced to announce numerically stronger improvements on the same result, and that he was glad Stadlmann had finished "just in time before the problem became contaminated", because the transferable insights in her paper "would have been significantly harder to extract in the counterfactual situation in which the AI-generated proofs were released first" [69]. The general form of the claim, in the same thread, is that the production of answers and the production of insight have become "negatively correlated": further optimization toward generating answers for a problem "can now decrease the amount of insight one could have gained from the study of" it [69]. He added that nothing about AI use forces that tradeoff, citing literature search as an established counterexample, and blamed "the current incentive to race for priority for solutions above all other concerns" [69]. On 5 September 2026 he proposed an alternative: "rather than being the first to announce solutions to unsolved math problems, be the first to announce a new mathematical insight" [63].

On 8 September 2026 he extended the argument to the difficulty landscape of a field. Every advance reduces the difficulty of solving problems, which flattens the landscape and makes promising questions harder to identify; ordinarily a new tool also extends the reach of results and creates fresh boundaries to explore, but he wrote that the current era lacks clear frontiers separating AI-feasible from AI-hard problems, "in part due to the rapidly changing nature of the technology, but also compounded by the refusal of AI companies to disclose their negative results, or reveal the process towards obtaining their solutions" [50]. He concluded that "it is now the identification of a promising problem which is the scarce and precious resource", warned that "even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential", and proposed that classes of problems be designated as requiring analysis rather than raw solutions, comparing this to a food drive that sets standards beyond mere edibility [50].

## Fluid equations and the September 2026 blowup results

On 7 September 2026 Tao published a technical summary of work by Levent Alpöge and Tristan Buckmaster, building on earlier work of Diego Córdoba and Luis Martínez-Zoroa, which demonstrates finite time blowup with a smooth forcing term for three model equations: the incompressible porous medium equation, the two-dimensional Boussinesq equation and the three-dimensional incompressible Euler equations [51]. He wrote that it is "now widely expected" that smooth initial data and a smooth forcing term making the Navier-Stokes equations develop singularities in finite time should be constructible, and that while these authors "do not quite achieve these goals yet, they have made enough of a breakthrough that it looks very feasible to complete these goals in the near future" [51]. The arguments have been formalized in Lean [51].

He was explicit about the AI involvement and about the writing. The arguments "are heavily AI-assisted", he wrote, but the authors had spent weeks turning what they themselves called "the worst writeup we had ever seen in the history of mathematics" into something of professional quality, and were forced to release preliminary preprints before that work was finished "due to external events" [51]. He added that Buckmaster had explained the main ideas to him in a half-hour phone call, "which made a refreshing change from AI-based communication modalities" [52], and set out his own reason for writing the summary: he would attempt "a quick summary of some of the main ideas, the highlighting of which I view as the main value of such work; the actual solving of these problems is only a proxy goal for the primary goal of developing mathematical understanding and insight" [51].

An edit to the post, and a Mastodon note the next day, flagged an independent preprint by Vignesh Ganeshram, Valentin Duruisseaux and Anima Anandkumar pursuing the other main route to blowup, in which a numerical or machine learning method locates an approximately self-similar profile which is then shown to be stable enough to perturb into a genuine solution [51][52]. Tao described that work as using a physics-informed neural network to find a numerically stable candidate, with rigorous stability still lacking, and as "relatively AI-light compared with other recent results, being restricted largely to secondary tasks such as literature review and Lean formalization" [52]. Anandkumar, in a guest post Tao hosted on 10 September 2026, wrote that she had sent the work to Tom Hou and to Tao for feedback and that Tao had encouraged the group to release it publicly [55].

## The September 2026 declaration

On 11 September 2026 Tao published the declaration "A Severe Misalignment of AI in Mathematics" on his blog and on the site mathandai.org [33][34]. He introduced it in his own voice, describing himself as proud "to be among the list of 25 initial signatories", all of them Fields Medallists, "to the declaration below, which grew out of discussions between ourselves over the last week" [33]. He noted that the group invites further signatures, as with the [Leiden Declaration](https://aiwiki.ai/wiki/leiden_declaration), and flagged the speed of the process as a cost: "It is unfortunate that we did not have the time to have a more consultative process, as with Leiden; but we decided that the urgency of the situation was such that we needed to release a statement sooner rather than later" [33]. He pointed readers to a report in The Economist published the same day under the headline "Top mathematicians are outraged by OpenAI's methods", to a short interview with James Maynard, and to a French version of the declaration published in Le Monde [33][61]. He repeated the announcement on Mastodon, again inviting signatories [35]. The declaration itself, its argument and its signatory list are covered at [A Severe Misalignment of AI in Mathematics](https://aiwiki.ai/wiki/a_severe_misalignment_of_ai_in_mathematics).

## Opening the blog to other mathematicians

Between 10 and 13 September 2026 Tao published nine guest posts on What's new, most of them on AI and mathematics. Each is prefaced with a bracketed note naming the author and disclosing that "This blog post was initially written in a different file format and converted using AI", signed with his initial.

| Date | Author | Post |
|---|---|---|
| 10 September 2026 | Anima Anandkumar | Stable singularity of the Euler equations on R^3 [55] |
| 11 September 2026 | Lucas Fagan | SAIR competition: Andrews-Curtis challenge [40] |
| 11 September 2026 | Burt Totaro | On the Hodge conjecture [53] |
| 11 September 2026 | Andreas Thom | On the existence of non-sofic groups [54] |
| 12 September 2026 | Claire Voisin | The status of the Hodge conjecture [62] |
| 12 September 2026 | Steven Strogatz | Wimbledon, the U.S. Open, and the future of mathematics [65] |
| 12 September 2026 | Silvia De Toffoli and Eamon Duede | After Math [66] |
| 13 September 2026 | Bryna Kra | "Deep theorems were scarce and difficult and so became an effective mechanism to identify deep thought. AI has broken this system." [67] |
| 13 September 2026 | Nestor Guillen | Happy, those able to know the causes of things (crossposted from his own blog) [70] |

Totaro's post, which he credits Tao with suggesting, reviews what is and is not known about the Hodge conjecture in order to ask what the mathematical community gains from hard problems, and closes with a worry "about the commercial pressure on AI companies to claim advances at high speed and the knock-on effect this has on mathematicians" [53]. Thom's post concerns the non-sofic groups construction that OpenAI announced in August 2026 as one of ten results from an internal Astra model, covered on the wiki at [GPT-6 Astra](https://aiwiki.ai/wiki/gpt_6_astra); Thom, whose joint work with Gábor Kun the OpenAI manuscript uses, describes objecting to the announcement's framing of a decade without progress, an exchange with Mark Sellke and Sébastien Bubeck, and his own conclusions about credit and publication in a world where "an AI system can produce a correct proof even if no human being discovered or even understood the argument in the usual sense" [54]. The views in these posts are the authors' own; Tao's role was to solicit and publish them.

Alongside the guest posts Tao started two crowdsourced reading lists. On 10 September 2026 he began collecting "useful online resources with regards to AI and mathematics in general", noting that he does not agree with all of the content he links and excluding his own writings, and moved further submissions to the comments once the volume grew [56]. On 12 September 2026 he started a companion list on "the purpose(s), value(s), and nature of mathematics", motivated by what he described as oversimplified perceptions visible in reactions to recent events, the first being that "mathematical research is about solving open problems" [57].

## Advocacy and everyday use

Tao contributed feedback to an early version of the Leiden Declaration on Artificial Intelligence and Mathematics, which went live and opened for signatures on 2 June 2026, though he was not part of the working group that drafted it [24]. He described its purpose as making explicit the goals and values that the mathematical community had previously left implicit, on the grounds that "increasingly powerful AI can be set to optimize (or over-optimize) many of the goals that are explicitly presented to them" [24]. He said he endorsed it wholeheartedly and had signed it, and singled out its recommendation to "participate in public discourse": mathematicians could once afford to discuss only safe technical topics in public, but "in the new era of 'proof abundance', it is increasingly important that we also debate the 'soft' aspects of our field, such as our goals and values" [24].

He also uses the tools for ordinary software work. In July 2026 he reported that a coding agent had ported roughly two dozen of his Java applets from 1999 into working JavaScript "in a matter of hours"; he found only one minor bug in the ported code, and the agent identified two bugs in his original 1999 code that he had not known about, which he judged "a net wash as far as code quality was concerned" [25]. He went on to have an agent build two new apps, including a special-relativity visualizer he had abandoned in 1999 because the code complexity defeated him, and said he might add such interactive visualizations to future papers since they are not mission-critical to a paper's argument [25].

## Selected AI-related activity

| Date | Activity | Outcome |
|---|---|---|
| June 2023 | Essay for Microsoft's AI Anthology | Predicted "2026-level AI" would be a trustworthy co-author [7] |
| November 2023 | PFR conjecture proved, then formalized in Lean 4 | Formalization completed in three weeks [8][10] |
| July 2024 | Commentary on AlphaProof and AlphaGeometry 2 | Called IMO geometry "effectively a solved problem" for specialized tools [16] |
| September 2024 | Hands-on evaluation of OpenAI o1 | "Mediocre, but not completely incompetent, (static simulation of a) graduate student" [15] |
| September 2024 | Launched the Equational Theories Project | 22,028,942 implications resolved and formalized by 14 April 2025 [12][13] |
| November 2024 | Interviewed for and contributed problems to FrontierMath | Expected it to "resist AIs for several years at least" [6] |
| July 2025 | Commentary after the 66th IMO | Warned against uncontrolled model-versus-human comparisons [18] |
| October 2025 | AI-assisted literature review on erdosproblems.com | Six problems reclassified from open to solved [19] |
| November 2025 | Coauthored AlphaEvolve mathematics paper | 67 problems; improved solutions found in several [20] |
| January 2026 | Launched IEANTN at IPAM | Crowdsourced Lean formalization plus a propagating spreadsheet of explicit estimates [32] |
| January 2026 | Proposed a crowdsourced optimization-constants repository | Second database modelled on erdosproblems.com [59] |
| March 2026 | First SAIR challenge, with Damek Davis | Distilling 22 million ETP results into a 10 kB cheat sheet [37] |
| March 2026 | Paper with Tanya Klowden on AI and the philosophy of mathematics | arXiv:2603.26524 [42] |
| June 2026 | First Proof second batch, UCLA harness | 2 of 10 solved acceptably; weak literature citation and exposition [21] |
| June 2026 | Report on autoformalization | Formalization queue cleared within hours, but proofs bloated [23] |
| June 2026 | Second and third SAIR challenges | Modular multiplication by neural network; inverse Galois with the LMFDB [38][39] |
| August 2026 | Palomar registry opens | Scientific advisory board; submitted his own Sendov formalization as a test [36] |
| August 2026 | Digestion of an AI-generated proof of Sendov's conjecture | Reformalized in about 15,000 Lean lines against roughly 90,000 [47] |
| September 2026 | Mastodon threads on problem scarcity | "Open problems ... have become something resembling a non-renewable resource" [48] |
| September 2026 | Summary of the Alpöge-Buckmaster blowup results | Finite time blowup with smooth forcing for IPM, Boussinesq and 3D Euler [51] |
| September 2026 | Signed "A Severe Misalignment of AI in Mathematics" | One of 25 initial Fields Medallist signatories [33][34] |
| September 2026 | Nine guest posts and two crowdsourced resource lists on his blog | Opened What's new as a venue for the community debate [53][54][56][57] |

## See also

- [Lean](https://aiwiki.ai/wiki/lean)
- [Mathematical reasoning](https://aiwiki.ai/wiki/mathematical_reasoning)
- [FrontierMath](https://aiwiki.ai/wiki/frontiermath)
- [AlphaProof](https://aiwiki.ai/wiki/alphaproof)
- [A Severe Misalignment of AI in Mathematics](https://aiwiki.ai/wiki/a_severe_misalignment_of_ai_in_mathematics)
- [Leiden Declaration on Artificial Intelligence and Mathematics](https://aiwiki.ai/wiki/leiden_declaration)
- [OpenAI Navier-Stokes proposed solution](https://aiwiki.ai/wiki/openai_navier_stokes_proposed_solution)
- [AI gold medals at the IMO 2025](https://aiwiki.ai/wiki/ai_imo_gold_2025)
- [AI for science](https://aiwiki.ai/wiki/ai_for_science)

## References

1. Terence Tao, curriculum vitae, Department of Mathematics, UCLA. https://www.math.ucla.edu/~tao/cv.html
2. MacArthur Foundation, "Terence Tao", MacArthur Fellows Class of 2006. https://www.macfound.org/fellows/class-of-2006/terence-tao
3. Terence Tao, "Biography", personal web pages (short and extended biographies). https://teorth.github.io/tao-web/bio.html
4. Ben Green and Terence Tao, "The primes contain arbitrarily long arithmetic progressions", arXiv:math/0404188, 8 April 2004. https://arxiv.org/abs/math/0404188
5. UCLA Department of Mathematics, faculty listing for Terence Tao ("Distinguished Professor & The James and Carol Collins Chair in the College of Letters and Sciences"). https://www.math.ucla.edu/people/ladder/tao
6. Elliot Glazer et al., "FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI", arXiv:2411.04872, 7 November 2024 (interviews with mathematicians in section 6). https://arxiv.org/abs/2411.04872
7. Terence Tao, "Embracing change and resetting expectations", Microsoft AI Anthology, 12 June 2023. https://unlocked.microsoft.com/ai-anthology/terence-tao/
8. W. T. Gowers, Ben Green, Freddie Manners and Terence Tao, "On a conjecture of Marton", arXiv:2311.05762, 9 November 2023. https://arxiv.org/abs/2311.05762
9. Terence Tao, "Formalizing the proof of PFR in Lean4 using Blueprint: a short tour", What's new, 18 November 2023. https://terrytao.wordpress.com/2023/11/18/formalizing-the-proof-of-pfr-in-lean4-using-blueprint-a-short-tour/
10. Terence Tao, post on Mastodon announcing completion of the PFR formalization, 5 December 2023. https://mathstodon.xyz/@tao/111526765350663641
11. teorth/pfr, "The Polynomial Freiman-Ruzsa Conjecture", GitHub repository README. https://github.com/teorth/pfr
12. Terence Tao, "A pilot project in universal algebra to explore new ways to collaborate and use machine assistance?", What's new, 25 September 2024. https://terrytao.wordpress.com/2024/09/25/a-pilot-project-in-universal-algebra-to-explore-new-ways-to-collaborate-and-use-machine-assistance/
13. Equational Theories Project contributors, "The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale", arXiv:2512.07087, 8 December 2025. https://arxiv.org/abs/2512.07087
14. Equational Theories Project, project home page. https://teorth.github.io/equational_theories/
15. Terence Tao, Mastodon thread on OpenAI o1, 13-16 September 2024 (with edits dated 19 September 2024). https://mathstodon.xyz/@tao/113132502735585408
16. Terence Tao, Mastodon thread on AlphaProof and AlphaGeometry 2, 26 July 2024. https://mathstodon.xyz/@tao/112850716240504978
17. Google DeepMind, "AI achieves silver-medal standard solving International Mathematical Olympiad problems", 25 July 2024. https://deepmind.google/discover/blog/ai-solves-imo-problems-at-silver-medal-level/
18. Terence Tao, Mastodon thread on AI performance and competition formats, 19 July 2025. https://mathstodon.xyz/@tao/114881418225852441
19. Terence Tao, Mastodon thread on AI-assisted literature review and the Erdős problems site, 16 October 2025. https://mathstodon.xyz/@tao/115385022005130505
20. Bogdan Georgiev, Javier Gómez-Serrano, Terence Tao and Adam Zsolt Wagner, "Mathematical exploration and discovery at scale", arXiv:2511.02864, 3 November 2025. https://arxiv.org/abs/2511.02864
21. Terence Tao, Mastodon post on the First Proof second batch, 10 June 2026. https://mathstodon.xyz/@tao/116727977488589991
22. First Proof, project home page (mission, editorial board, board of directors, ethics statement). https://1stproof.org/
23. Terence Tao, Mastodon thread on autoformalization and proof bloat in the IEANTN project, 21 June 2026. https://mathstodon.xyz/@tao/116789373239346609
24. Terence Tao, Mastodon thread on the Leiden Declaration on Artificial Intelligence and Mathematics, 2 June 2026. https://mathstodon.xyz/@tao/116681023979910132
25. Terence Tao, "Old and new apps, via modern coding agents", What's new, 11 July 2026. https://terrytao.wordpress.com/2026/07/11/old-and-new-apps-via-modern-coding-agents/
26. teorth/analysis, "A Lean companion to Analysis I", GitHub. https://github.com/teorth/analysis
27. Terence Tao, Mastodon post on the conclusion of the 66th IMO, 19 July 2025. https://mathstodon.xyz/@tao/114877789298562646
28. Clay Mathematics Institute, "Terence Tao", Research Fellows profile. https://www.claymath.org/people/terence-tao/
29. teorth/erdosproblems, "A community database for the problems on the erdosproblems.com site", GitHub. https://github.com/teorth/erdosproblems
30. Terence Tao, profile page (joined November 2022), mathstodon.xyz. https://mathstodon.xyz/@tao
31. Institute for Pure and Applied Mathematics, "Integrated Explicit Analytic Number Theory Network", special project page, UCLA. https://www.ipam.ucla.edu/news-research/special-projects/integrated-explicit-analytic-number-theory-network/
32. Terence Tao, "The integrated explicit analytic number theory network", What's new, 15 January 2026. https://terrytao.wordpress.com/2026/01/15/the-integrated-explicit-analytic-number-theory-network/
33. Terence Tao, "A Severe Misalignment of AI in Mathematics", What's new, 11 September 2026. https://terrytao.wordpress.com/2026/09/11/a-severe-misalignment-of-ai-in-mathematics/
34. "A Severe Misalignment of AI in Mathematics", declaration and endorsers, mathandai.org. https://mathandai.org/
35. Terence Tao, Mastodon post announcing the declaration, 11 September 2026. https://mathstodon.xyz/@tao/117253629967855195
36. Terence Tao, "Palomar: a registry of Lean verified mathematics", What's new, 18 August 2026. https://terrytao.wordpress.com/2026/08/18/palomar-a-registry-of-lean-verified-mathematics/
37. Terence Tao, "Mathematics distillation challenge: equational theories", What's new, 13 March 2026. https://terrytao.wordpress.com/2026/03/13/mathematics-distillation-challenge-equational-theories/
38. Terence Tao, "Modular arithmetic challenge", What's new, 8 June 2026. https://terrytao.wordpress.com/2026/06/08/modular-arithmetic-challenge/
39. Terence Tao, "Third SAIR competition: inverse Galois challenge", What's new, 16 June 2026. https://terrytao.wordpress.com/2026/06/16/third-sair-competition-inverse-galois-challenge/
40. Lucas Fagan, "SAIR competition: Andrews-Curtis challenge", guest post on What's new, 11 September 2026. https://terrytao.wordpress.com/2026/09/11/sair-competition-andrew-curtis-challenge/
41. SAIR, The Foundation for Science and AI Research, home page. https://sair.foundation/
42. Tanya Klowden and Terence Tao, "Mathematical methods and human thought in the age of AI", arXiv:2603.26524, 27 March 2026. https://arxiv.org/abs/2603.26524
43. Terence Tao, "Mathematical methods and human thought in the age of AI", What's new, 29 March 2026. https://terrytao.wordpress.com/2026/03/29/mathematical-methods-and-human-thought-in-the-age-of-ai/
44. Terence Tao, "A digestion of unit distance constructions", What's new, 3 July 2026. https://terrytao.wordpress.com/2026/07/03/a-digestion-of-unit-distance-constructions/
45. Terence Tao, "A digestion of the Jacobian conjecture counterexample", What's new, 21 July 2026. https://terrytao.wordpress.com/2026/07/21/a-digestion-of-the-jacobian-conjecture-counterexample/
46. Terence Tao, "A partial digestion of the HRT counterexample", What's new, 6 August 2026. https://terrytao.wordpress.com/2026/08/06/a-partial-digestion-of-the-hrt-counterexample/
47. Terence Tao, "A digestion of the proof of Sendov's conjecture", What's new, 12 August 2026. https://terrytao.wordpress.com/2026/08/12/a-digestion-of-the-proof-of-sendovs-conjecture/
48. Terence Tao, Mastodon thread on solved problems and non-renewable resources, 3 September 2026. https://mathstodon.xyz/@tao/117204929023813310
49. Terence Tao, Mastodon thread on Navier-Stokes regularity and opportunity cost, 3 September 2026, with a clarification on 5 September 2026. https://mathstodon.xyz/@tao/117207849921390904
50. Terence Tao, Mastodon thread on the difficulty landscape and the scarcity of promising problems, 8 September 2026. https://mathstodon.xyz/@tao/117237320796901560
51. Terence Tao, "Finite time blowup with smooth forcing term for the incompressible porous medium, Boussinesq, and incompressible Euler equations", What's new, 7 September 2026. https://terrytao.wordpress.com/2026/09/07/finite-time-blowup-with-smooth-forcing-term-for-the-incompressible-porous-medium-boussinesq-and-incompressible-euler-equations/
52. Terence Tao, Mastodon thread on the Alpöge-Buckmaster result and the Ganeshram-Duruisseaux-Anandkumar preprint, 8 September 2026. https://mathstodon.xyz/@tao/117233527638291447
53. Burt Totaro, "On the Hodge conjecture", guest post on What's new, 11 September 2026. https://terrytao.wordpress.com/2026/09/11/on-the-hodge-conjecture/
54. Andreas Thom, "On the existence of non-sofic groups", guest post on What's new, 11 September 2026. https://terrytao.wordpress.com/2026/09/11/on-the-existence-of-non-sofic-groups/
55. Anima Anandkumar, "Stable singularity of the Euler equations on R^3", guest post on What's new, 10 September 2026. https://terrytao.wordpress.com/2026/09/10/stable-singularity-of-the-euler-equations-on-r3/
56. Terence Tao, "Crowdsourcing a list of general resources on AI and mathematics", What's new, 10 September 2026 (including Tao's comment of 12 September 2026). https://terrytao.wordpress.com/2026/09/10/crowdsourcing-a-list-of-general-resources-on-ai-and-mathematics/
57. Terence Tao, "Crowdsourcing a list of general resources on the purpose, value, and nature of mathematics", What's new, 12 September 2026. https://terrytao.wordpress.com/2026/09/12/crowdsourcing-a-list-of-general-resources-on-the-purpose-value-and-nature-of-mathematics/
58. Katie Mann, Akshay Venkatesh and Rachel Webb, "Mathematical discourse", announcement posted on What's new, 22 August 2026. https://terrytao.wordpress.com/2026/08/22/mathematical-discourse/
59. Terence Tao, "A crowdsourced repository for optimization constants", What's new, 22 January 2026. https://terrytao.wordpress.com/2026/01/22/a-crowdsourced-repository-for-optimization-constants/
60. First Proof, "Third Batch Benchmark" (announced 25 August 2026; testing early October 2026, results 14 October 2026). https://1stproof.org/third-batch.html
61. "Top mathematicians are outraged by OpenAI's methods", The Economist, 11 September 2026 (linked from Tao's declaration post). https://www.economist.com/science-and-technology/2026/09/11/top-mathematicians-are-outraged-by-openais-methods
62. Claire Voisin, "The status of the Hodge conjecture", guest post on What's new, 12 September 2026. https://terrytao.wordpress.com/2026/09/12/the-status-of-the-hodge-conjecture/
63. Terence Tao, Mastodon post proposing a competition to announce new mathematical insights, 5 September 2026. https://mathstodon.xyz/@tao/117221032761877425
64. Terence Tao, Mastodon thread on the Equational Theories Project report and prospecting for new problems, 7 September 2026. https://mathstodon.xyz/@tao/117230983266837293
65. Steven Strogatz, "Wimbledon, the U.S. Open, and the future of mathematics", guest post on What's new, 12 September 2026. https://terrytao.wordpress.com/2026/09/12/wimbledon-the-u-s-open-and-the-future-of-mathematics/
66. Silvia De Toffoli and Eamon Duede, "After Math", guest post on What's new, 12 September 2026. https://terrytao.wordpress.com/2026/09/12/after-math/
67. Bryna Kra, "Deep theorems were scarce and difficult, and so became an effective mechanism to identify deep thought. AI has broken this system", guest post on What's new, 13 September 2026. https://terrytao.wordpress.com/2026/09/13/deep-theorems-were-scarce-and-difficult-and-so-became-an-effective-mechanism-to-identify-deep-thought-ai-has-broken-this-system/
68. Terence Tao, Mastodon thread on Julia Stadlmann's improvement to the bounded gaps between primes bound, 1 September 2026. https://mathstodon.xyz/@tao/117197525544971208
69. Terence Tao, Mastodon thread on answers versus insight in pure mathematics, 3 September 2026. https://mathstodon.xyz/@tao/117208617602946453
70. Nestor Guillen, "Happy, those able to know the causes of things", guest post on What's new, 13 September 2026. https://terrytao.wordpress.com/2026/09/13/happy-those-able-to-know-the-causes-of-things/