A Severe Misalignment of AI in Mathematics is a declaration about artificial intelligence and mathematical research, published on September 11, 2026 at mathandai.org with 25 initial signatories, each listed with the year of a Fields Medal.[1] It does not dispute that recent AI systems have solved hard open problems. Its complaint is about what disappears when a result arrives without the process that normally surrounds one: attribution to the work it builds on, a written account other mathematicians can read and simplify, and the slow transfer of ideas through talks, discussion, and the training of students.[1]

Terence Tao, one of the signatories, published the same text on his blog the same day with a short framing note of his own, and announced it on Mastodon at 17:40 UTC on September 11.[2][3] It spread quickly outside mathematics. A Hacker News submission linking to mathandai.org went up five minutes after Tao's Mastodon post and had 1,219 points and 1,201 comments when read on September 13, 2026.[4] The Economist published a piece on the declaration the same day, and a French version of the text appeared in Le Monde as a signed opinion piece.[2][5][6]

The argument

The declaration opens by conceding the capability rather than questioning it: "Over the last few months, the mathematical capabilities of LLMs have improved dramatically, to the point that they can solve major outstanding problems in many fields of mathematics." The objection is to the use being made of that capability. "However, the push by AI companies to solve mathematical problems as a benchmark is detrimental to the science of mathematics, and to the mathematical community. The goals of the AI companies and the goals of the mathematical community are severely misaligned." The signatories place this inside a wider pattern: "We see these as part of broader alignment issues impacting other scientific and creative professions, as well as the whole of society."[1]

Most of the text is then spent describing what mathematicians take a solved problem to be for. Famous problems have served as "landmarks and lighthouses" for measuring understanding, and solving one has been "a certain sign of new insights and interesting methods, which would then be studied by a community of mathematicians, through a long and arduous process of talks, discussions, simplifications." The end of that process is a textbook presentation a graduate or even undergraduate student can study, and some ideas travel further still, becoming tools "understood and used by the whole population" decades or centuries later. The declaration calls students and ideas "the most precious resources of our profession" and says the processes that develop them "invariably take time and are based on human interaction."[1]

The specific harm identified is that a proof detached from that process does not feed it. "But solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. Forgetting this in the world of AI may turn the tool against the primary goal." The declaration warns that "the mass production at faster and faster pace" of "true/false" statements "could destroy fertile ground instead of breathing life into new ideas." It then makes the practical complaint most often quoted from it: "Often these solutions are announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others. As in all creative professions, this raises severe attribution and plagiarism questions." Without mathematicians willing to develop such results and fit them into the existing body of knowledge, it argues, "AI-conceived ideas would never become fully alive and the crucial human transmission chain between mathematicians would be lost."[1]

The closing paragraphs are not a rejection of the technology. "AI offers the potential of enhancing and accelerating genuine mathematical study and understanding," the declaration says, and mathematics "will need to adapt to these changes in several ways." Whether the outcome is beneficial or destructive "will in large part be determined by the decisions of the humans in control of this new technology." The final sentence asks that the issues be addressed urgently by the mathematical community, by the companies building the technology, and by a society that will meet the same problem in other kinds of intellectual work.[1] The text itself names no company, model, or specific result.[1]

Signatories

The 25 initial signatories are listed with their Fields Medal years. Tao described the group in his own note as "all Fields Medallists."[1][2]

Signatory	Fields Medal
Artur Avila	2014
Manjul Bhargava	2014
Caucher Birkar	2018
Pierre Deligne	1978
Yu Deng	2026
Simon Donaldson	1986
Hugo Duminil-Copin	2022
Alessio Figalli	2018
Martin Hairer	2014
June Huh	2022
Maxim Kontsevich	1998
Elon Lindenstrauss	2010
Pierre-Louis Lions	1994
James Maynard	2022
Curtis McMullen	1998
Shigefumi Mori	1990
Ngô Bảo Châu	2010
Andrei Okounkov	2006
Peter Scholze	2018
Stanislav Smirnov	2010
Terence Tao	2006
Maryna Viazovska	2022
Cédric Villani	2010
Wendelin Werner	2006
Efim Zelmanov	1994

Every one of those 25 name and year pairs matches the International Mathematical Union's chronological list of Fields Medallists.[7] Tao's copy of the list on his blog gives one name in a shorter form, "Curt McMullen", where mathandai.org has "Curtis McMullen"; the entries refer to the same person.[1][2] The medal years run from 1978 to 2026, and two complete four-person cohorts signed, those of 2010 and 2022.[1][7] Yu Deng, the most recently decorated signatory, is one of four people the IMU awarded a Fields Medal in 2026, alongside John Pardon, Jacob Tsimerman, and Hong Wang.[7]

How it came about

Tao's blog post is explicit about how quickly the statement was assembled, and about what that cost. He wrote that he was "proud to be among the list of 25 initial signatories" to a declaration "which grew out of discussions between ourselves over the last week," then added a caveat in parentheses: "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."[2] The comparison is to the Leiden Declaration of June 2026, which came out of a conference and a named working group rather than a week of discussion among a small group.

Events behind it

Two announcements by OpenAI shaped the context. On August 1, 2026 the company published "Ten advances in mathematics and theoretical computer science," saying the results "were achieved by an internal version of Astra, our next major model," the model later released as GPT-6 Astra. Each of the ten came with a Lean certificate in a public repository.[8] That post also set out an attribution position: "We helped prepare the manuscripts and formalize the proofs in Lean, and we take responsibility for their correctness, while the mathematical arguments themselves were generated by our system."[8]

Then on September 8, 2026, three days before the declaration, OpenAI announced a proposed solution to the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems, describing it as "an AI-generated solution" released "including a writeup and a formal proof in Lean."[9] The manuscript's author line reads simply "OPENAI", with no individual authors named.[19] The announcement was followed immediately by a public dispute over priority, data provenance, and proposed authorship arrangements involving Tristan Buckmaster and Levent Alpöge, who had been working on closely related forced fluid-equation problems, and the Clay Mathematics Institute had not accepted the proposed solution.[20][21]

The Hodge conjecture companion post

On the same day as the declaration, Tao published a guest post by Burt Totaro titled "On the Hodge conjecture." It applies the declaration's argument to one problem rather than stating it in general. Totaro asks the reader to imagine a counterfactual world in which, the day after the conjecture was stated, an "inhuman oracle" answered it and the problem was considered settled. Looking at the real world instead, he writes, "we can see, by examining our real world, the vast body of mathematical knowledge that would have been lost," because "what we want from a great conjecture is a challenge that inspires all kinds of other discoveries, even if the original question remains open."[10]

The post makes that case with mathematics rather than assertion. Totaro notes that progress on the conjecture itself has been limited: after Lefschetz's (1,1)-theorem, from work around 1924, settled the cases of codimension-1 and dimension-1 algebraic cycles, the first open case, codimension-2 cycles on a variety of complex dimension 4, "still seems far out of reach" for arbitrary varieties. What the conjecture produced instead were whole theories, among them Phillip Griffiths's variations of Hodge structure from the 1960s and Pierre Deligne's absolute Hodge cycles, along with Claire Voisin's more recent work applying Hodge theory to algebraic cycles. His main recent example is Eyal Markman's 2025 proof of the Hodge conjecture for abelian varieties of dimension 4 and 5, which Totaro calls "a monumental piece of work that builds on many earlier developments." He traces the chain behind it: Andre Weil's 1977 identification of abelian varieties of Weil type; Ben Moonen and Yuri Zarhin's 1995 result that in low dimensions such as 4 the general case would follow from that special class; the semi-regularity property defined by Spencer Bloch in 1972 and extended by Ragnar-Olaf Buchweitz and Hubert Flenner in 2003, long thought too strong a condition to apply to hard cases; Markman's construction of enough semi-regular sheaves to make it apply; and an extension of the Buchweitz and Flenner theorem to twisted sheaves that Markman needed and that Jonathan Pridham supplied in 2024.[10] None of that lineage would exist if the answer had simply been handed over.

Totaro's description of the present moment is carefully limited, which matters because the subject has attracted speculation. He writes: "It now seems possible that AI companies will burn through vast resources in order to prove some new fact about the Hodge conjecture."[10] He makes no claim that any company has attempted or completed such a proof. His conclusion is that "there is reason to worry about the commercial pressure on AI companies to claim advances at high speed and the knock-on effect this has on mathematicians," and he closes: "The power of mathematical ideas comes from a continual negotiation among people. What we care about are not so much isolated facts, but rather the ideas and inspiration that the search leads to."[10]

The post opens with a one-line editorial note from Tao saying that it was initially written in a different file format and converted using AI, a detail that sits oddly with the subject matter. The same note appears on "After Math," a guest post Tao published the following day.[10][11]

Endorsement and uptake

The declaration page invites anyone who supports the text to endorse it, and the site publishes the resulting roll. Endorsement requires either signing in with an ORCID iD, in which case the name comes from the ORCID record and appears immediately alongside the iD, or confirming an email address at an academic or research institution. The published fields are title, name, and affiliation; the site says the email address is used only to confirm and manage the endorsement and is never published, and endorsers can later change or withdraw their entry.[12][13]

The roll listed 5,876 endorsers when read on September 13, 2026, paginated 150 at a time, with affiliations spanning university mathematics departments, research institutes, and industry.[12] That count is a running total on a live page and will not match a figure read on another date.

Relation to the Leiden Declaration

The Leiden Declaration on Artificial Intelligence and Mathematics, dated June 2, 2026 and endorsed by the International Mathematical Union, is the earlier statement Tao referred to. It grew out of a September 2025 Lorentz Center conference at Leiden University titled "Mechanization and Mathematical Research" and was drafted by a named 16-member working group.[14] The two documents differ more in form than in sympathy. Leiden is long and prescriptive, organized into separate recommendation sets for individual mathematicians, mathematical organizations and funders, policymakers, and commercial AI developers, with specific asks: disclose tool use in papers, retain human responsibility for correctness, put active effort into attribution where automated tools fail at it, insist on appropriate publication outlets.[14] The September declaration is a single short argument with no recommendation list.

Leiden also anticipated the practice the later declaration objects to. It notes that mathematics is used "to advertise the capabilities of commercial artificial intelligence systems in public communications and public relations campaigns," and that what makes mathematics attractive for general-purpose AI development is that the correctness of formalized proofs "can be checked automatically, without the need for human oversight," giving an effectively unlimited training signal.[14] OpenAI acknowledged that document directly in its August 1 post, writing that "there are many views as to the role of AI in mathematics, and we have deep respect and understanding for those concerned with its impact, including the signers of the Leiden declaration on AI and Mathematics."[8] Leiden remained open for signature through the later episode: its list showed 4,013 signatories when read on September 13, 2026, including entries dated that same day.[15]

Reception

Named responses appeared within a day, and several agreed with the diagnosis while disputing the framing.

Lior Pachter, Bren Professor of Computational Biology at Caltech, who says he worked in the UC Berkeley mathematics department for 18 years, opened a September 12 post with "They are right," then turned the declaration's own standard back on the profession. If conceptual understanding were really the goal, he argued, the community would in fact have treated students and ideas as its most precious resources, and he set out cases where it did not: Juliusz Schauder, denied an invitation from Princeton and murdered by the Germans; Olga Ladyzhenskaya, shortlisted for the 1958 Fields Medal and passed over for Klaus Roth and René Thom; Karen Uhlenbeck, told on the job market that "people did not hire women"; Julia Robinson, barred by Berkeley from teaching mathematics for 35 years. Pachter also noted the irony that a statement criticizing rushed announcements had itself been released quickly for want of time to consult, and objected to the signatories identifying themselves by medal rather than affiliation, since "mathematical ability is not the same as mathematical responsibility." He observed that only one of the 25 signatories is a woman. His conclusion was that alignment with the mathematics community as it exists should not be the target: "AI companies and mathematicians should instead be asking what both ought to be aligned to: understanding, attribution, intellectual generosity, and the nurturing of students and ideas, and not merely the production or recognition of results."[16]

Silvia De Toffoli of the University School for Advanced Studies IUSS Pavia and Eamon Duede of Princeton University and Purdue University turned the declaration's concern into a formal distinction in their September 12 guest post on Tao's blog. They separate a logical notion of proof, which a Lean formalization satisfies exactly and which "secures certainty," from an intelligible notion, which supplies knowledge of what makes a proposition true in ideas experts can grasp, communicate, and build on. Historically the two ran together, because nobody could produce a very complicated formal proof without first grasping the shareable ideas behind it; with AI they can come apart, leaving "formal proofs that float free from any intelligible proof." Their verdict on the Navier-Stokes announcement: "At this moment, it is an answer, not a solution." Their conclusion is that "AI presents mathematics not with an ending but with a choice about what mathematical practice should become."[11]

Brian Leiter reposted an extended excerpt on his philosophy blog on September 12, adding that "some of their case applies, I would venture, to philosophy."[17]

Tao's post also linked a short interview with James Maynard, one of the signatories, published by Oxford Mathematics as a YouTube Short titled "AI does the math."[2][18]

The Hacker News thread is evidence of how far the statement travelled rather than a record of expert opinion, and the several thousand endorsements are a measure of assent rather than of argument. The substantive public disagreement in the first days was about who should be speaking and about what an AI-generated proof actually delivers, not about whether the results are correct.

See also

References

"A Severe Misalignment of AI in Mathematics." Math and AI. https://mathandai.org/ (read September 13, 2026)
Terence Tao. "A Severe Misalignment of AI in Mathematics." What's new, September 11, 2026. https://terrytao.wordpress.com/2026/09/11/a-severe-misalignment-of-ai-in-mathematics/
Terence Tao. Post announcing the declaration. Mathstodon, September 11, 2026, 17:40 UTC. https://mathstodon.xyz/@tao/117253629967855195
"A misalignment of AI in mathematics." Hacker News item 49662371, submitted September 11, 2026, 17:45 UTC. https://news.ycombinator.com/item?id=49662371 (score and comment count read September 13, 2026)
"Top mathematicians are outraged by OpenAI's methods." The Economist, September 11, 2026. https://www.economist.com/science-and-technology/2026/09/11/top-mathematicians-are-outraged-by-openais-methods
Collectif. "La mise en garde de 25 medailles Fields: Les objectifs des entreprises d'IA et ceux de la communaute mathematique divergent profondement." Le Monde, Idees, published September 11, 2026, 18:00 UTC. https://www.lemonde.fr/idees/article/2026/09/11/la-mise-en-garde-de-25-medailles-fields-les-objectifs-des-entreprises-d-ia-et-ceux-de-la-communaute-mathematique-divergent-profondement_6770630_3232.html
International Mathematical Union. "Fields Medal" (chronological list of Fields Medallists) and "Fields Medals 2026." https://www.mathunion.org/imu-awards/fields-medal and https://www.mathunion.org/imu-awards/fields-medal/fields-medals-2026 (read September 13, 2026)
OpenAI. "Ten advances in mathematics and theoretical computer science." August 1, 2026. https://openai.com/index/ten-advances-in-mathematics/
OpenAI. "On the Navier-Stokes Millennium Prize Problem." September 8, 2026. https://openai.com/index/navier-stokes-solution/
Burt Totaro. "On the Hodge conjecture." Guest post, What's new, September 11, 2026. https://terrytao.wordpress.com/2026/09/11/on-the-hodge-conjecture/
Silvia De Toffoli and Eamon Duede. "After Math." Guest post, What's new, September 12, 2026. https://terrytao.wordpress.com/2026/09/12/after-math/
"Endorsers." Math and AI. https://mathandai.org/endorsers.php (read September 13, 2026)
"Endorse the Declaration." Math and AI. https://mathandai.org/sign.php (read September 13, 2026)
"Leiden Declaration on Artificial Intelligence and Mathematics." June 2, 2026. DOI 10.5281/zenodo.20302944. https://leidendeclaration.ai/
"Signatories." Leiden Declaration on Artificial Intelligence and Mathematics. https://leidendeclaration.ai/signatories (read September 13, 2026)
Lior Pachter. "Align AI and Mathematics to Something Else." Bits of DNA, September 12, 2026. https://liorpachter.wordpress.com/2026/09/12/align-ai-and-mathematics-to-something-else/
Brian Leiter. "A Severe Misalignment of AI in Mathematics." Leiter Reports, September 12, 2026. https://leiterreports.com/2026/09/12/a-severe-misalignment-of-ai-in-mathematics/
Oxford Mathematics. "AI does the math." YouTube. https://www.youtube.com/shorts/R9VQnNv5SoI (title and channel confirmed via the YouTube oEmbed endpoint, September 13, 2026)
OpenAI. "Finite Time Blowup for Navier-Stokes." Manuscript PDF, September 2026. https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8a9a/navier-stokes.pdf
Tristan Buckmaster. Public statement on finite-time blowup for forced fluid equations and interactions with OpenAI. September 7, 2026. https://cims.nyu.edu/~tristanb/statement.pdf
Clay Mathematics Institute. "Navier-Stokes announcement." September 11, 2026. https://www.claymath.org/news/navier-stokes-announcement/

Editing: A Severe Misalignment of AI in Mathematics