Distasteful?
On October 6th, OpenAI released hundreds of manuscripts with proofs that were mostly unreadable and in some cases false. […]
In August, OpenAI claimed that such a dump would be ‘distasteful’, that their ‘main focus is shipping great models so everyone can use them to make discoveries of their own’.
This passage surprised me. Buckmaster is making a strong accusation here: that OpenAI said one thing in August and did the opposite in October. It also rests on a judgement of his own, that the openai/math release, which I wrote about in The flood, released responsibly?, is “such a dump”. I’m not sure I agree with him.
The two links are on X, and the word “distasteful” is not in either tweet. So I went back to who said what, and when.
Timeline
Tweet times are in UTC, from the tweets themselves.
1 August: ten open problems
OpenAI publishes Ten advances in mathematics and theoretical computer science, by an internal version of Astra. Noam Brown tweets it at 08:17:
An internal version of Astra, @OpenAI’s next major model family, solved 10 major open problems in mathematics, quantum complexity, and theoretical computer science.
We believe it will be a major step for scientific reasoning.
15 and 22 August: Alpöge and Buckmaster
According to Buckmaster’s statement, he and Levent Alpöge obtained blowup with smooth forcing for Boussinesq and Euler on 15 August, and verified it in Lean on 22 August.
Before 28 August: a letter to Bubeck
Sébastien Bubeck is a researcher at OpenAI, who moved there from Microsoft in October 2024, where he was VP of generative AI research. He is also the one on the other side of the calls in Buckmaster’s account of the Navier–Stokes credit dispute.
After the ten problems, Bubeck reached out to a mathematician who posts on X under a pseudonym. The reply, which is undated, was later published as a screenshot (see 8 October):
Dear Sebastien,
Thank you for reaching out.
I think the project your company has embarked on is fundamentally antithetical to mathematics as a discipline. From private communications with a handful of high-profile mathematicians, I have heard that they were extremely angry at the way the 10 problems were marketed (as a public example, see the footnotes in Fournier-Facio’s writeup, his interview, and try to read between the lines), and the fact that there were discrepancies between the Lean formalization and prose proofs and that the prose proofs were extremely hard to read. I do not expect these to slow you down because I understand this is part of the marketing gimmick of OAI.
However, if you want some suggestions:
- On the positive end I would recommend presenting these “proofs” really as “findings”, as an astronomer does by looking at the Hubble telescope, without a confident claim to correctness and “settling an old problem”. Most important you can emphasize that maybe there are ways to generalize these findings to discover not isolated examples but conceptual phenomena, which is the ultimate goal of mathematics in my view. This way you can take the mathematical community along as you speed headfirst into the nebulous “progress” into human science that your company envisions, instead of leaving behind humans and gunning for a future where none of these theorems have any value because no one is looking at them. It might help to read, and re-read, Thurston’s “On proof and progress in mathematics” over and over before playing the slot machine with infinite compute on these new technologies of the future.
- However as a cynical alternative you can just keep dumping your findings at an even faster rate and larger volume without any heed to what I expect is 50% of the mathematical community that are opposing this new culture, without looking for the detractor’s approval, completely crush them all at once, dissolve and declare academic mathematics as an exercise in antiquity so that we (the 50%) can get out faster from this furnace and just become a religion; because no matter what, even if superintellience [sic] arrives and has the capacity to solve all of math, some of us will do math “the old way”. We just want to do mathematics instead of being endlessly trapped in this artificial discourse.
Anyway these are all my opinion and it’s a common sentiment among people I talk to but I am under no pretense of being a representative of some broader math research community. I hope these are of some use. I’m a little baffled by having to be put in the position to suggest policy for OAI given my obvious and open distaste for the corporation, and its influence in my field, and more importantly how I’m quite literally a nobody. But I have nevertheless tried to collect some thoughts and I present them to you as such.
28 August: Bubeck’s reply, Brown’s tweet, and a new model
Bubeck replies in direct messages on X. The screenshot is headed “Fri, 28 Aug at 9:40 am”, in whatever time zone the recipient’s phone was in:
I really like your angle of claiming “findings” rather than “proofs to old conjectures”!
but actually, I think I really failed in explaining myself into why we did a few (< 20) Erdos problems earlier this year, then unit distance, then the 10 astra problems
it’s truly to update the community that these capacities are real, and the reasoning is real. It is to put behind the sterile debate of “are they really reasoning” and give an opportunity to the community to get a heads up on what’s coming
We will NOT continue to release proofs. That would be distateful [sic] and against the principles that we want these tools to empower existing communities
we might do one here and there, if it’s like interesting in some ways, but you can rest reassured that we will NEVER do a play on “volume” and try to flood the zone with a ton of proofs that nobody cares about. That would kill the field.
Is that a better outcome in your mind? Or still falling short?
At 21:30 the same day, Brown, quoting his 1 August tweet:
Today I was asked why we haven’t announced more math results from Astra since these problems.
At @OpenAI we aim to devote time to finding and announcing math results from internal models only when they would meaningfully change people’s understanding of the pace of AI progress. Our main focus is shipping great models so everyone can use them to make discoveries of their own.
And, by OpenAI’s later account in its Navier–Stokes post, this is the day it started training a new model:
Since August 28 we have been training a new internal model that has exhibited unprecedented performance in our benchmarks, including mathematics.
6 October: hundreds of manuscripts
OpenAI announces “a broad range of new mathematical results produced by an internal frontier model”, after consulting the Advisory Group on Mathematics and Artificial Intelligence. The repository says the model was posed approximately 4,000 problems, and the catalogue now holds 719 manuscripts in 372 families, after three withdrawals the next day.
8 October: the screenshots
At 03:23, David J. Webb, replying to @gro_tsen:
OpenAI should just say “we have some results, they may be slop, but we think of them as ‘raw data’” - then at least the disorganization would make sense.
But they insist on a veneer of respectability while putting out slop - worst of both worlds!
At 03:49, Daniel Litt, quoting Webb:
I do think these are clearly something like “research findings” or “raw data” at this point. Very unusual situation in math.
At 06:37, the pseudonymous account, quoting Litt, posts the letter and Bubeck’s reply above as three screenshots:
This is the exact word I had suggested to my friend Sebastien Bubeck when he reached out to me after the 10 problems by Astra. I imagine this was not a popular idea internally in OAI, because all they want to do is maximize marketing. I’ve attached Seb’s thoughtful views as well:
The exact word here is “findings”. “Distasteful” is only in the screenshot of Bubeck’s reply.
19 and 21 October: Buckmaster
Buckmaster gives a talk at the Institute for Advanced Study on 19 October, and expands on its ending in the guest post quoted above.
In their shoes
I am an amateur Bible scholar myself. I study the original biblical languages, and know a thing or two about exegesis, the critical interpretation of a text, especially of the Bible. One fundamental principle of interpreting the original language is to think about what the original speaker intended it to mean, and what the original audience could reasonably be expected to understand by it. This is the historical-grammatical method. Putting a modern perspective into the text is taking it out of its context.
As yet another analogy, I’m an amateur musician too, and one fundamental principle in playing a piece is to convey what the composer intended it to sound like. The differences are different interpretations, but all should be faithful, within the room for interpretation. Für Elise is one famous example: it is so easy to play, yet so easy to play it “so romantically”, especially by amateurs, changing the dynamics and tempo so much throughout the piece that it becomes unrecognizable, so to speak. Reviewing a Decca disc of piano encores, Christopher Howell puts it this way, of Vladimir Ashkenazy’s recording:
A much more likely encore is “Für Elise”, a piece that every young pianist has slaughtered, here played with a serene composure which suggests that Ashkenazy loves it and really feels a mission to let us hear it properly. (Howell 2002)
Simple is faithful. Don’t play it like a virtuoso piece, because it is not.
It seems to me that Buckmaster is over-interpreting what they said. You can’t understand their words by what you think their words mean. You need to put yourself in their shoes and think about what they intended them to mean. Unfortunately, he is a person too close to the events to be deemed objective in the matter: he was on the other end of the Navier–Stokes calls with Bubeck.
And as a human being, I’d advocate starting by giving people the benefit of the doubt: assume they are not guilty first. In this case, assume they are self-consistent first, then ask: can you find a contradiction? If not, you don’t have enough evidence to say they aren’t. This principle holds well when studying the Bible too. Oh, you think it is so obviously false? It is actually much less obvious if you start from this principle: assume the Bible is self-consistent, what would it mean? Can you find inconsistencies? And for those apparent inconsistencies, can you find an honest interpretation in which it is still self-consistent? This is part of the art of exegesis, and how one can explain many difficulties in the Bible.
So let me try that with OpenAI.
OpenAI is not a person
“In August, OpenAI claimed” puts two people’s words into one mouth. “Distasteful” is Bubeck’s, in a private message to one person, which we only see because that person posted a screenshot of it. “Main focus is shipping great models” is Brown’s, in public. We can assign a personality to OpenAI, as corporate psychology would do, but I don’t think it helps to read too much into it, as if OpenAI has a consistent mind of its own.
And whatever Bubeck and Brown had in mind on 28 August, it was probably not the model that produced these results. OpenAI only calls that “an internal frontier model”, but the new model behind Navier–Stokes started training on the day they wrote, and the Millennium Prize hunt started four days later, on a rumour. Brown was even asked specifically about results “from Astra since these problems”. A promise made before a step change in the model, about a model it then superseded, can turn out wrong without anyone lying.
Pace of AI progress, not of math
Look again at Brown’s criterion: announce results “only when they would meaningfully change people’s understanding of the pace of AI progress.” That is a statement about understanding the pace of AI progress, not about understanding mathematics. Bubeck says the same about the earlier releases, that they are “to update the community that these capacities are real”. And the Navier–Stokes post says “Our goal in releasing this result is to report on the substantial progress of our AI models.”
I think Buckmaster is dwelling on what mathematicians value in mathematics, and loses sight of why these AI researchers might be saying something consistent. Their values might disagree with a mathematician’s. But if we put ourselves in their shoes, are they internally consistent? Hundreds of results, at an average of three hours of ChatGPT Pro each, are certainly meant to change our understanding of the pace of AI progress, whatever we think of them as mathematics. Buckmaster seems to be accusing them of not being consistent, but I still can’t see where.
A flood?
The line that looks hardest to square with the release is this:
we might do one here and there, if it’s like interesting in some ways, but you can rest reassured that we will NEVER do a play on “volume” and try to flood the zone with a ton of proofs that nobody cares about. That would kill the field.
Hundreds of manuscripts is not one proof here and there. But “one here and there” could just as well mean one release here and there, and the openai/math release happened to contain hundreds of proofs. If what this release demonstrates is the breadth of the model’s capability, then a single release of hundreds, where the hundreds are the demonstration, makes sense. And the ten open problems were already one release of ten proofs. So if Bubeck meant one proof per release, he was already wrong, by their own history, when he wrote it.
And can we read openai/math as not trying to flood the zone? I think, from the point of view of AI researchers, it absolutely can. They posed about 4,000 problems, and released the 719 manuscripts they judged significant, once. They did not keep running their model every day and release new discoveries every day. That would be the flood. Hundreds at once and then stop seems consistent with what they think they should be doing: release only to demonstrate AI progress, not to flood the field.
Flood as defined by whom, though? I said AGMAI’s “large number of significant results” sounds more like a flood to me, in What if the button came with the understanding?, and I still think it is one, in the sense of the flood Gowers predicted. But we can interpret that, in Bubeck’s mind, it isn’t a flood.
And if they release again, I don’t think that would be inconsistent either. Their announcement already talks about “future releases”, and as I guessed in The economy of AI math, for mathematicians, there is always a frontier model in training, one generation ahead of the public one, so they’ll be back. Each release would be demonstrating the progress of a new model, which is exactly what Brown said they announce results for, and still not running the model every day to flood the field.
Not aligned, and why would they be?
I often side with mathematicians in my posts. But not on this statement, at least: that OpenAI said in August that such a dump would be “distasteful”, then did it in October.
Later in the same post, Buckmaster says:
We cannot assume the interests of Academia and the AI companies are aligned.
I agree, and I’d go further: why would we ever think they are? They care about AI research, through and through, and not math research. We are different communities with different incentives, but each of us, in our own shoes, is trying to do good. Not only to maximize shareholder value (maybe they do! But can we blame them?), but to make the world a better place, from their own perspective.
Only if we can see that can we start to have a constructive conversation. Asking them to align with us won’t help, and treating them as our enemy won’t help either (think of a conflict between two countries). Realizing that we both need to compromise and reach something mutually beneficial is the beginning of building a better world, together. That is the vision of progressive disclosure: it should be mutually beneficial. And as I argued in The economy of AI math, for mathematicians, that is also what OpenAI is asking of AGMAI: a win-win, given math as a benchmark.1
References
Footnotes
There is a start. On 15 October, OpenAI updated its announcement to say it is contributing $5 million to a Simons Foundation initiative “to help mathematicians examine, understand, and build on results produced by AI”, close to what I asked of AI labs at the end of the progressive disclosure post.↩︎