So much crap, and non-crap, so little time. I have a half-dozen posts that had to be done last week but have been so busy acting locally, and being sick, that I have had no time or energy to post on my global thoughts. This one is a quick placeholder, albeit it may be holding a place for nothing.
I have been paying attention to the AI and mathematics thing, of course, and people have been throwing articles at me. I had been reluctant to write anything about it while feeling some obligation to do so, since I am fully aware that people do not know what to think about things until I weigh in. It is a heavy burden I bear.
Yesterday, a very good mathematician friend, Mr. Big, suggested/encouraged me to write on it all, which I found pretty funny. Why bother with the thoughts of a washed-up fourth rate mathematician1 when Terry Tao is writing long and carefully every day? Still, Mr. Big had some concerns about mathematicians’ responses to it all and thought that it may be worthwhile contributing the left-field perspective I sometimes bring to things. I’m not sure, and I’ll think more and talk more with Mr. Big. In the meantime, it seems worthwhile making a few quick points, providing a few links and providing a post where regular readers can weigh in and ask questions.
The first point to make is that the AI leaders are bona fide psychopaths. They are genuinely terrible, terrible people. And they are incredibly dangerous people. One could go on long on this but it is all obvious. I hate them with every fibre of my being.
The second point is that AI is here and, even if the psychopaths are somehow shackled to be less psychopathic, we have to work hard to figure out what it means, for everyone and everything.
The third point is that this non-post is not about AI and mathematics education. I have written about a couple clowns advocating AI in schools but it is such an absurd notion, I am not sure that even the standard educational nitwittery will push for it. In any case, the issue of AI for mathematics education is much different from that for mathematics research and the mathematician community.2
The fourth point is that anybody who did not see this coming from Day One was simply ostriching. I remember people laughing at ChatGPT’s first, feeble attempts at doing mathematics, but I didn’t join them and I didn’t believe them. That laughter was fear, and justified fear.
The fifth, personal, point is that I find this all heartbreaking. I understand the great power and benefit that AI can bring to mathematics research. Mathematicians that I respect have embraced this power. AI need not and will not kill mathematics research, but it will change research in a way that depresses me beyond description.3 I was a poor mathematics researcher,4 it was a struggle for me. But it was a struggle that I also loved, and it was absolutely magical when that struggle resulted in the rare successes. It was incomparable to anything else.5 I cannot see that that magic will be part of mathematics research in the future.
Those are my few thoughts. Here are a few links.6
Matt Baker’s Late-Night Thoughts
Baker’s is the best one-off post I have seen on it all.
Quanta on the Navier-Stokes controversy
I’m not sure this is the best summary, or is even accurate, but it will have to do until readers weigh in with better sources.
Terry Tao’s Blog and Mathstodon Posting
I think it is fair to say Tao was bitten by the AI psychopaths, that he trusted them way too much to be remotely human. But Tao is still the guy to read generally on this.
The Fields Medallists’ J’Accuse
As if it will do any good.
Tristan Buckmaster’s statement on Open AI’s snakery
I’m not going to bother linking Open AI’s faux denials.
1) This is not false modesty. Most mathematicians are fifth rate or sixth rate.
2) Commenters will of course take any discussion where they wish, and they are free to ponder here on AI and maths ed. Or, if Terry Mills puts his mind to it, we can all ponder why “llama” is spelled with two “L”s.
3) This we becoming a factor even before AI. The advancement of computing power and systems such as Mathematica was transforming at least some areas of mathematics into more of an experimental science, in a way that I totally understood but in a way that I found joyless.
4) See footnote 1.
5) It’s kind of like kicking the perfect torpedo punt, but, at least at that moment, you’re the only one who can kick it.
6) I have not been reading diligently, and figured it better to not add too many derivate meh-links. Readers should feel free to suggest other sources, and I will be grateful for any suggestions. In particular, I have not read carefully on the Navier-Stokes business and do not know the best one-off summaries of who proved or didn’t prove what. I’ll check anything that people suggest, on N-S or anything, and add it if I think it’s worth it.
OpenAI supposedly solved the Navier -Stokes equations. I didn’t plan to write this post. However, I have no objection to the rich man winning. I have an objection to the rich man not saying what he aimed at.
Both teams in the Navier–Stokes story used AI. Tristan Buckmaster and Levent Alpöge spent nearly a year on the forced Euler equations using Claude and Codex, with the Lean formalisation written by Claude under Alpöge’s direction. This was never humans versus machines. It was humans with machines and two different budgets.
OpenAI’s budget was larger by orders of magnitude. Roughly 10,000 concurrent agents, a result in about 88 hours, some 130 billion output tokens. Fine. That is what a frontier lab is for.
The effort began on 1 September, after word reached OpenAI that a rival was close. Sam Altman’s own account: they were curious whether their models could do it too. In mathematics, knowing a result exists is not a small piece of information. It tells you which branch to attack and it tells you the attack terminates.
None of that is theft. All of it is worth stating plainly at the moment of announcement, rather than after somebody objects.
What actually happened: an initial denial that the pair’s work shaped the effort, then, within days, a published page crediting both men for concurrent work on forced Euler and offering to recognise their priority jointly. Firms that consider an allegation baseless do not usually respond with a priority offer that fast.
Nobody accuses physics of building CERN. Big physics solved this decades ago, with thousand-author collaborations and explicit contribution records. Mathematics has the spending now and none of the discipline.
In February, Google DeepMind published a framework for exactly this: levels of autonomy, a novelty scale, and “human–AI interaction cards” documenting what the model did and what the humans did. They wrote it after consulting working mathematicians, who told them that transparency about the AI’s role was their dominant concern.
On 11 September, twenty-five Fields Medallists signed a declaration warning that AI-assisted results are announced in a rush, without proper write-ups and without citing the relevant previous work of others.
Terence Tao, who published it, notes that they skipped the consultative process the earlier Leiden Declaration had, because the situation felt urgent.
I am not scoring points. A document written in a week, by people with no commercial incentive, complaining about rushed work that omits prior art, also omitted the prior art. That is how hard this problem is. The labs have the compute and no norms. The profession has the standing and no mechanism. The one concrete proposal on the table came from a lab, and the profession walked past it.
If you separate your paragraphs I’ll try to read it.
(People, please check your comments are formatted correctly once posted.)
Screw it, I did it for you. But kind of ironic for a guy whining about “rushed work”.
Your comment is multi-absurd, and you are most definitely scoring points, but I cannot be bothered with it now.
Thanks for formatting it, Marty. I’ll make sure to format it properly next time.
My “multi absurd” points are actually quite simple and sane: a declaration by 25 Fields Medalists is an important instrument to waste on expressing their mood—especially when one of the labs offered a constructive solution seven months ago.
Big labs and big money have existed in physics for quite some time, and the ways of acknowledging and dealing with that have been established for decades. Against this background, the Fields Medalists’ outcry looks even more ridiculous. I hope you read their statement.
The solutions are already there; all they have to do is suggest them and push for their adoption. These people have enough influence to bring a workable solution into a much wider discussion and potentially get it adopted.
Instead, all they have produced is a declaration of their mood.
You’ve picked on one aspect that pisses you off. Your comment was ridiculous.
Those who are interested may read “Towards Autonomous Mathematics Research” on arXiv by Google’s DeepMind
> OpenAI supposedly solved the Navier -Stokes equations.
They didn’t “solve” the Navier-Stokes equations. What they claim to have done is shown that there exists a counterexample to the N-S “existence and smoothness” conjecture.
Yes, an important point, although a bit of a gotcha, and my concerns with Dr. Mike’s post are much more fundamental.
Most people either know enough to know that “solve” refers to the problem(s) associated with N-S, or know little enough that the distinction does not matter.
Indeed, the differences are fundamental. Where I agree with you: Altman doesn’t strike me as an honest man, that much is certain. But discussing him is a waste of time.
The idea of mathematics without “equipment” is an illusion, and has been since at least the days of the abacus. Appel and Haken’s 1976 work on the Four-Colour Theorem consumed roughly 1,200 hours of mainframe time; genuinely scarce equipment at the time, available to people at the right institutions and to virtually nobody else.
And the reaction then rhymes with what we are seeing now. Tymoczko’s objection was not that the result was wrong, but that no human could survey the proof in its entirety, and that it therefore was not a proof in the sense the profession had traditionally understood the term. The community argued for years about whether a result that ultimately had to be taken on the machine’s word belonged in the canon.
Yes, LLMs are the new mainframe, the new computer, the new abacus, if you like.
Seven months ago DeepMind published “Towards Autonomous Mathematics Research”, introducing an agent for research-level mathematics. The mathematical community largely ignored it.
…and here we go: twenty-five Fields Medalists expressing concern 🙂
Mike, do you realise you’re being a dick?
By insulting me, you may establish status, but it doesn’t establish truth.
So the answer is “No”.
I don’t know enough to comment on AI in maths research. However I think it’s worth a separate post on what might be appropriate uses of AI in education. Craig Barton has an excellent series on AI in education, with contributions from a very diverse set of people. Of course, AI development is going so fast, any evaluation may be outdated quickly.
The first principle would have to be that articulated by Tony Gardiner – MAKE HASTE SLOWLY – we have methods that have worked for centuries, let’s not jump to the latest fad. Of course listening to him would have avoided mass adoption of computers in maths, Powerpoint and the incredible lunacy of inquiry and other forms of weird and fashionable ideas – but that’s what much of this blog is about!
The uses I have so far found worthwhile is that once I’ve pondered a problem and can’t solve it, I can put it into Claude and see the solution. I’ve also used it to identify flaws in my thinking and to offer alternative explanations of concepts so I can teach them. A specialist I saw recently used AI in such a manner – he supplemented his decades of experience with an AI query. That’s the sort of use I understand.
Thanks, JJ. I understand the use of AI for pedestrian mental tasks, even if it means a lot of material is even greyer than usual. I’m not sure that aspect interests me, but I’ll consider it.
Here’s me from my non-mathematical perspective commenting on (glad I finally remembered your blog name again). I’ve been following the Buckmaster/OpenAI story from a distance. It’s truly despicable what OpenAI did to him and his colleague, and what they tried to get away with. (Threatening his career and trying to write Apôlge out of the story altogether). They need to be thoroughly regulated, if not closed down altogether, but they exist under the Trump administration. So that’s not going to happen.
(And I don’t think I’m the only one who finds that Sam Altman seems to be turning more and more into a goblin in each public appearance. Or is it his demonic self finding itself more comfortable appearing in public now? But that’s just by the by.)
One needs no mathematics to recognise the loathsomeness of Altman and his fellow sleazebags.