AHM Statement on OpenAI’s October 6 Release of Mathematical Documents

7 October, 2026 in guest blog, opinion | Tags: AI, Association for Human Mathematics | by Terence Tao

[This is a guest post by the Association for Human Mathematics, reposted from their statements page. This blog post was initially written in a different file format and converted using AI. — T.]

Yesterday, on October 6th, 2026, OpenAI — which is currently defending lawsuits against accusations of illegal plagiarism, copyright infringement, and trademark dilution — released a repository of manuscripts purporting to contain solutions to a number of high-profile problems in mathematics.

Mathematicians did not ask for this work to be done. The Advisory Group on Mathematics and Artificial Intelligence, from whom OpenAI has claimed to derive its legitimacy, opened their initial advisory statement by saying that frontier AI corporations should not test advanced mathematical problems on internal models. In ignoring the central premise of the Advisory Group’s position, OpenAI has indicated total disregard for the norms of scientific research — norms that guarantee that mathematics remains trustworthy, ethically researched, and in the public interest.

Mathematicians have a particular vision of progress that is informed by history and field-specific considerations. We reject OpenAI’s assertion that this release advances our subject, and we urge mathematicians and the public to view the value of this publication model with due skepticism.

Releasing over 700 files at once is not a demonstration of scholarship, but a demonstration of power. We urge mathematicians to discontinue their work with OpenAI and to return to a vision of science that centers human understanding.

Association for Human Mathematics Communications Working Group

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50178915)

Objection. Relevance.

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50178920)

they don’t own math anymore than astrophysicists own the sun

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50179238)

https://en.wikipedia.org/wiki/Yitang_Zhang

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50179292)

at least for legal and medical fields the AI icepicks itself out of respect so ppl dont ban AI here in maths they dont repsect mathematicians

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50179037)

rape is not about ...

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50179140)

oh the irony

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50179288)

🤔

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50178965)

Not flame that's actually what they're doing by their own admission lol the actual prompts are no more involved than that. And then they're just copy pasting the uploaded output online and calling it New Breakthroughs

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50178974)

Take your meds MiG.

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50179301)

ljl

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50179029)

an obvious problem is that this is still premised on the notion of 'progress' via 'development.' under that framework, it's not particularly important whether progress originates from people or machines. the objection that machines will churn out stuff which will be incapable of non-machine validation due to a lack of mathematicians is a bit silly, since this would happen eventually anyway.

there are hard cognitive limits involving human brains and math. computers will hit them, and keep going. that is a FEATURE.

the objections also strongly presume that computer math is incapable of 'innovation,' and will end up dead-ending 'math' generally into what is currently understood along with some brute-force refinements. this is presented without evidence and feels very much like cope.

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50181001)

I'm not trying to strawman you, but it's really tiresome seeing this repeated over and over as the same response to every single criticism of AI as a technology

It's useless hand-waving that contributes nothing of substance. "Well, these issues that you're bringing up don't matter, because AI will magically Just Do Everything For Us Just The Way We Want." What is the point of mentioning this possible future trajectory at all? Obviously there will be no problems of *any* kind if this is the way that the future plays out. It's not worth discussing or mentioning. It's an artificial conversation-ender and thought-terminator

No one *ever* thinks about the future by assuming the best possible scenario and working backwards from that. Everyone does the opposite: starting from the worst possible scenario and working forwards from it, to figure out how to get the best results with the least risk. Why would AI be any exception? It isn't, but people treat it this way because they are wishcasting for self-serving agendas or straight up delusional fantasies (which are a category of self-serving agenda)

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50181055)

I can't believe that I'm in the position of being the only person ITT to defend mathematicians, a group of people who I normally cannot stand

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50179044)

"first, AI came for will smith's spaghetti, and i was silent because i was not spaghetti"-ahh mathmos

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50179295)

mathematics as a discipline, and mathematicians as people, are valuable to human society because through their efforts, they are able to come up with complex breakthroughs in abstract concepts that enable the creation of new technologies that benefit human society as a whole. mathematicians need patronage and support in order to do their work and to run their micro-society in which they train and bring up the next generations of mathematicians. our most talented mathematical minds will no longer be interested in devoting their lives to mathematics if there is no accompanying status and prestige in doing so

making mathematics the domain of AI bots goodhart'ing problems, and reducing mathematicians to checkers and interpreters of these context-less proofs, makes it impossible for the micro-society of mathematics to function properly and do its pro-social job. these LLM "proofs" do not produce useful new concepts or understanding. all they are doing is grinding out counter-examples that do not advance conceptual understanding of mathematics in ways that can make a practical difference for humans

the danger of encouraging this kind of AI takeover of math is that it will "kill the golden goose" of the human discipline of mathematics. it's the same danger that always comes with goodhart'ing domains, but it's a much more grave concern when it comes to math, since math is the foundation and driver of all human scientific and technological progress

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50179347)

https://kirwinhampshire.substack.com/p/the-dark-night-of-mathematics

People just need to accept they are meat computers and move on and stop thinking the work they are doing is all that important or meaningful

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50179115)

Throw it all in the oven.

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50179152)

lmao this guy is ngmi

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50179284)

https://x.com/hsu_steve/status/2108364887605018884?s=46

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50179713)

But here's the thing, you keep telling me I'm not a mathematician. Fine! I'm not a mathematician! I'm a glorified autocomplete! Whatever makes you happy!

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50179872)

The commentary from various Thought Leaders and public figures about how mathematicians are "stupid" and "selfish" for objecting to mass-produced AI slop math "proofs" is a real Le 56% America Current Year moment

It doesn't seem like it's motivated by self-interest or even polemics. These people just genuinely do not understand the principled and sound objections, and appear to not be capable of it either, nor interested in spending 2 minutes thinking about the topic to figure it out

It reminds me of watching broadcasted presidential debates from the 1990s. The audience questions from Americans and the candidate responses were pertinent, thoughtful, and laid out in good faith from the perspective of a common good. That America is gone now and is never coming back

There's a certain "irony" in people desperately hoping that "ASI" will emerge as a benevolent dictator and mandate a common good and functional structure upon our society. Since "we" are no longer capable of doing it ourselves. "We can't. We don't know how."

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50180432)

I can't tell if you're trolling in this thread or what. It's either shitty, boring, lame trolling about an otherwise interesting and important topic, or you're just not very smart

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50180468)

To me the number 1 thing they should have brought up is that it isn't fair that they don't have access to these gated tools. I would actually sympathize with that. When the lab has access to tools significantly more powerful that haven't been released and with a huge compute budget, it makes it unfair and assymetrical to the mathematicians.

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50180492)

It's okay if understanding the topic is over your head. Just don't respond, then

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50180513)

But most regular people's response when they learned that AI had solved some "millennium prize" problem they'd never heard of was "sounds pretty stupid and gay, like the kind of emperor's-new-clothes thing where you have to tell me why it's impressive and then expect me to drop my jaw after the fact like I was actually immediately impressed."

The pro-hype response to the ho-humming ultimately boiled down to "mathematicians and other [TRUST THE] EXPERTS **say** that it's super important and impressive and game-changing, so what do YOU know by failing to be impressed, you philistine POGUE!"

But if in fact the mathematicians are saying it's fraudulent and evil and no one should be impressed, well I'm just left with my initial reaction, which was that it was stupid and gay. And now instead of eminent mathematicians telling me I'm wrong, I have loser xo poasters who make $212K/year telling me I'm wrong.

EDIT: I should clarify that none of this precludes the highly likely possibility that mathematicians are ALSO being butthurt little faggots. I very much assumed this was true, even prior to this whole kerfuffle.

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50180474)

E.g., I sure as fuck assume that chatGPT really did "solve" their little rubik's cube.

But let's also not act like this was something that all of humanity, and the full power and might of our markets, was struggling with for a century. The number of professional mathematicians out there is probably in the 4-digits, and I assume <0.001% of their collective brain power was being devoted to solving this particular piece of stupid shit. But to be honest I don't know and certainly don't care, and the previous argument was that I should get in line and trust the experts (the very experts whose outmaneuvering by AI was supposed to be the impressive thing here).

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50180493)

For me, that's law, and in law, I gotta tell you, all of the benchmark improvements from like 2023 to early 2026 only produced a marginally better product. Whatever has happened in the past couple months, though, has reflected the greatest improvement since these chatbots came out. That may not be true generally, but it is in law, and *I'm* the one (me and my profession) who gets to decide that.

This is a very results-oriented mindset that leads me to be (1) unimpressed with highly abstract "accomplishments" like solving a tricky math puzzle; and (2) tending to defer to domain professionals when I cannot tell something (so this is different from a cancer drug or some shit who's value is undeniable and does not require any expertise to appreciate).

Obviously you run into people -- and law is rife with them, believe me -- who let the fact that they're quite-reasonably threatened by the tech bias their evaluation of it. (Btw, this is a rational, healthy response that every other technology, and people, have to overcome IRL, so it's good that we're not artificially protecting AI from the the same biases that everyone/think else has to deal with and overcome.) But fucking Grow Up if you don't think that, at the end of the day, we don't have the capacity in every major domain to sit people down and soberly evaluate the thing's ability to do work in the domain. If math fags truly coalesce around the position that this development was Bad & Wrong, or Stupid & Gay, Not an Achievement, or whatever, and persist in that position... bro they're probably right.

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50180567)

https://x.com/andrewcurran_/status/2108992955382210632?s=46

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50184000)

Queering Mathematics

Posted on November 20, 2020 by Brian Katz

First: Trans people are people who deserve to have their identities respected and validated and to live without fear. On this Trans Day of Remembrance #TDoR2020, we mourn those who have died from transphobic violence. As a broader queer community, we remember that this violence disproportionately impacts trans women of color, a group who have also led many of the efforts to secure human rights for us all.

I am proud to have participated with Ron Buckmire, Emily Riehl, Juliette Bruce, Anthony Bonato, and Robin Gaudreau in LGBTQ+Math Day (virtually) at the Fields Institute this week. An event like this contributes to the visibility of queer people and our accomplices/allies, and a major theme of our conversation was the fact that each of us, by virtue of existing, queered spaces by being in them, from the rugby pitch to mathematics conferences. But for this post, I’d like to reflect on the ways that I saw our queer identities influencing our mathematics.

Ron Buckmire kicked off the event with a talk entitled “Different Differences”. He started by telling us about some of his identities, which developed into an observation that our community treats some identities like race and gender as “standard” differences and often ignores others, like his gay and Caribbean identities. Ron reminded us that the data about representation in the higher education mathematics are sparse (and shameful) for the “standard” differences and often completely absent for the “different” differences. But Ron’s title also applies to the overview he gave of his research. Using calculus-based methods, we describe continuous change using a limit of an average rate of change, and this process can be discretized in multiple ways. Discretizing the most famous definition of a derivative leads to what is often called a forward difference, but those of who have taught calculus will be familiar with versions that could be called backward or center differences, corresponding to various ways to draw secant lines to continuous curves near a point.

Ron’s observation was that these three approaches all implicitly assume that the width of the approximations, h, will approach 0 linearly. In what I saw as the first example of queering mathematics in the session, Ron demonstrated how we can reject this assumption (i) by replacing the role of h with more interesting functions that still approach zero on the order of h to get “non-standard differences, which he would like to name Mickems differences, after Ron Mickems, and (ii) by taking non-local discretizations, which felt to me like a radical reorganization of an approach to discrete difference modeling.

Next, Emily Riehl talked about “Contractibility as Uniqueness”, which she explicitly framed as “queering uniqueness”. Emily’s work is in category theory, a subfield that I see as overtly working to reconsider and rebuild the foundations of mathematics, and this talk showed how we might think of that agenda as a queer one. Emily started from the idea of the first fundamental group of a topological space, which is a group made of all loops at a base point in the space with the (associative) operation of composition (or concatenation). If we loosen the restriction that the paths be loops, allowing them to start and end at different points, we lose the ability to compose an arbitrary pair elements, so Emily’s core question became: when it is possible to compose them, how unique is that composition? Is it unique enough for associativity? She built a tetrahedron representing a homotopy that answers this question affirmatively, but she wanted to step back even further. Uniqueness can be quantified as: there exists an x such that, for all y, x=y. Interpreting this from a categorical perspective, this became the sum over all x of the product of all y of the set of proofs that x=y, where sum and product are adjoints of the pull-back, and uniqueness because the observation that this is a contractible space, which can be proved without referencing the base topological space. I am personally drawn in powerfully by this kind of work in category theory, which reimagines the foundations of what had seemed necessary in mathematics and logic in ways that feel analogous to the work of reimagining the messages of what had seemed necessary in society for gender and sexuality.

Third, Juliette Bruce told us about “Computing Syzygies”. This is a classical subfield that owes a lot to Emmy Noether, but Juliette’s overview showed how there is still so much we don’t know about the relationships between monomials! In light of the themes of queering mathematics above, one particular move by Juliette stood out to me. Her research has made progress in understanding syzygies by bringing tools from applied mathematics for computing with enormous matrices to bear on what had previously been viewed as a classical, abstract problem. While it might be a bit of a stretch from the talk, I see this as Juliette rejecting the false binary of abstract and applied mathematics. I was pulled into algebraic geometry as a graduate student because I like the double vision of seeing objects from both algebraic and geometric perspectives, and I’ve long felt that the most exciting mathematics brings this kind of binary-rejecting double vision to approach problems from new directions. And while we didn’t get to hear about Robin’s work during this event, in a later communication they offered a sketch of a similar interpretation of some of their work in virtual knot theory in which some functions require or break a binary.

The final presenter, Anthony Bonato, told us about “Out, Proud, and Combinatorial: A gay mathematician’s journey”. He told us about his efforts to be an out, proud, mathematician as well as the challenging ways environments have resisted these efforts. In his overview of his work, he described efforts that overlap abstract and applied mathematics, similar to Juliette, in complex network analysis. He studies the hidden geometry behind complex networks, such as social networks, showing how complex social networks often reduce to a small number of characteristics (the dimensions in this hidden geometry). I might be reaching to claim this as queering the mathematics, but this hidden geometry certainly reminds me of Ron’s different differences and my own experiences learning to see implicit social structures that my non-queer peers could safely ignore. Anthony also turned the connection I’m making in reverse, perhaps mathing queerness, stating his axioms for mathematics and diversity/equity/inclusion work that remind me of Federico Ardila’s axioms. In both situations, mathematicians are using the disciplinary concept of an axiom to structure their approach to justice.

My own work is also inspired by my experiences as a queer person. I never fit into the implicit expectations for gender or sexuality as a young person, and that misalignment made me hyper aware of the systems that guided and structured human activity in general. In mathematics, this awareness served me well: I spent my time asking why we did what we were doing and how we knew the things we claimed to know. More recently, I have come to see that I was lucky to happen into those habits in mathematics, buttressed by my other privileges. I see how students, especially students of color, who ask similar kinds of critical questions are often driven out of mathematics when people assert that there is nothing to ask, that mathematics is just “pure” truth that they must accept. And even those who aren’t driven away are forced to experience mathematics as a form of authoritarianism. As a teacher educator, I work on helping teachers to critique, perhaps to queer, mathematics so that they in turn can build classrooms that don’t recreate this history of violence in the name of mathematics. In response to a comment I made on the panel, a participant offered the amalgamated word inqueery, on which I’m going to keep reflecting.

Queerness has been my entryway into understanding exclusion, but queering mathematics will not be enough, just as spaces dominated by cisgender gay men can sometimes be racist and toxic in other ways. The game historically called “cops and robbers” is an example of how dangerous ideas related to white supremacy and the police can subtly pervade even queer mathematics spaces.

Thank you for coming with me as I reflected on the ways that Ron asked us to queer our assumptions, Emily to queer our foundations, Juliette to queer our methods, and Anthony to queer our results. These talks will appear shortly on the Fields Institute’s YouTube channel, and I hope watching them through this lens encourages you to help further queer mathematics.

(http://www.autoadmit.com/thread.php?thread_id=5910854&forum_id=2#50184269)