Doc Octagon

@the_good_matty @RecrInsomnia I believe he has a very different perspective on the purpose of math research, social responsibilities of mathematicians, ideal role of tech institutions, etc. than e.g. you or I; there is some ideological/political difference

@RecrInsomnia frankly that's what's the most upsetting; this type of polyannaness is impossible for a smart guy who is actually involved in thinking about this stuff

i've absolutely lost my patience for this nonsense, what the fuck is this??

@littmath Controversial perspective!

@DocOctagonical I mean, insofar as they’re spending money resolving some conjectures, they are doing so.

I’m kind of a fan of OpenAI’s decision to devote some resources to math. Obviously there’s a PR aspect but I much prefer a pdf signed “OpenAI” to the new trend of signing one’s name to short arxiv preprints to which one didn’t contribute anything meaningful.

@littmath You mean perhaps OpenAI will fund math research?

Also just nice to have a large institution with some people who care about math making decisions. Perhaps OAI will fill some of the vacuum left by the NSF here.

@AcerFur @Creative_Math_ This is a good example since every piece of math in the Adam paper is wrong; see Reddi, Kale, and Kumar (2018) and David Martínez Rubio's 2017 master's thesis at Oxford. My takeaway is that the math in most of these ML papers is just completely irrelevant

@Creative_Math_ Sure, the models can still have agents running code experiment training loops to see what is working well. But e.g. the end of Adam paper does have quite a bit maths going into it.

An experiment I’ve wanted to work on is if a current frontier model can develop a paper on the level of the Adam/MuonClip, MLA, PPO/AlphaZero/MuZero papers. I think they’re now at the mathematical level to do something like this, but the safe guards probably nerf them to not.

@TaliaRinger Not a huge issue but it's very weird to me that they keep talking about "textbooks" but they only mean lecture notes

A case study in why it is still wildly important for expert humans to check autoformalized theorems and definitions, which AI tools still frequently get wrong in ways that can mislead a novice easily

@BjarturTomas "Scott Aaronson finds [X] to have literary significance" is a useful signal of anything for you?

Scott Aaronson finds a GPT 5.5 story to have literary significance. I don't trust myself to judge such things fairly, so a useful signal. One thing that accords with my very short timelines is this feeling that every high-level skill is falling at once.

@lyndalovon @AndyMasley @dearmadisonblue Completely agreed. I've seen it for years espoused as an article of faith by certain kinds of 'rationalists.' I might have even believed some form of it when I was younger, but then I got degrees in math and physics!

@DocOctagonical @AndyMasley @dearmadisonblue He’s basing it on deep ignorance of physics. Very few things in the universe can be described by closed algebraic algorithms or mathematical formulas. Crazy. I would delete it as soon as possible. It’s so ridiculous. I’m embarrassed for him.

I'm becoming really doomer on the average public intellectual's interest in actually thinking about philosophy of mind at all. This quoted passage is so goofy.

@arnal_charles @AIatMeta I'm a bit confused - when you refer to "textbooks" you exclusively mean lecture notes on ocw.mit.edu?

Our team at @AIatMeta is excited to announce ATLAS: one of the largest automated formalization efforts to date. ATLAS contains Lean 4 formalizations of both statements and proofs from 25+ mathematics textbooks, spanning dozens of domains, for a total of 500k lines of code. We are also releasing a flexible formalization harness and a companion paper. External contributions are welcome! Joint work spearheaded by our amazing PhD student Ahmad Rammal (@Ahmad3Rammal), together with Niket Patel (@niketnpatel ), Fabian Gloeckle (@FabianGloeckle), Amaury Hayat (@Amaury_Hayat), Remi Munos (@MunosRemi), Julia Kempe (@KempeLab), Vivien Cabannes, and myself from @AIatMeta, @NYUDataScience , and Ecole des Ponts. This is an ongoing effort; more details in the thread below. (1/9)

@AndyMasley @dearmadisonblue "Literally everything in the universe can be described by mathematical formulas." What are you basing this on?

@dearmadisonblue Literally everything in the universe can be described by mathematical formulas. The fact that a system can be stated as a specific formula you can plug numbers into tells you literally nothing about whether it can or can't do things other things in the universe can

@littmath Of course, there are many broader dangers as well, e.g. adoption of certain tools also promotes certain companies & thereby certain individuals, e.g. environmental dangers (which I don't understand well)... the balance of benefit and cost is not at all clear to me

@DocOctagonical Right. We can produce a huge amount of text, some of which is interesting. And then…?

STEM academia serves two closely intertwined purposes: the production of high quality science and the production of human capital. These two purposes feed into each other. The obvious direction is that we develop human capital by paying people to produce science. What is perhaps less obvious is that the very fact that human labor is used to produce science has historically been an important input to its quality. The goal of science is not simply to produce papers, but rather to produce good work--that a person is willing to spend months working on a paper is a (weak) witness to the fact that it has some minimum quality. If someone has a record of producing high quality work, that they wrote a paper is a stronger witness, since it was worth the opportunity cost to write it. If many people engage with it substantially, that is even stronger evidence. This is not to say that there isn't lots of low-quality work--there is, in fact a huge amount--but we have strong sorting mechanisms, admittedly using imperfect proxies (all depending on costly human labor!), to find high-quality stuff. Arguably the paper itself is not the primary product here; in many cases the primary product is actually the expertise developed over the course of producing it, which can then be applied to other questions. If you believe, as I do, that producing high quality science should be one of our fundamental goals, I think you’re obligated to embrace new tools that help one do so. Refusing to is a declaration that these outputs are not important. But I worry that we are not on track to automate the production of good work; rather, we are on track to automate the production of papers. We need new mechanisms to ensure that we are also producing good work, and to ensure that we are developing the human capital to engage with it.

@scottnarmstrong @datbrownnigga Interesting, I thought you would have meant the kind of stuff Gomez-Serrano has been talking about.

@DocOctagonical @datbrownnigga "Ask GPT to help me solve it" is exactly what I have in mind.

Indeed. While combinatorics is an important and central part of mathematics, it is also a very small subset of mathematics. A very small subset which is apparently easier for AIs. Before we get too excited: let's see them solve a central PDE problem open for 80+ years.

@scottnarmstrong @datbrownnigga But surely the AI use you have in mind with this (PINNs, numerical solvers) has pretty much no overlap with 'ask GPT to solve it for you / help you solve it'?

@datbrownnigga I expect initially to hear about human-AI interaction leading to some breakthroughs. This may first arrive in the form of counterexamples. My timeline is “some time this summer” Singular solutions of fluids is an obvious guess since so much attention is there currently

@scottnarmstrong e.g. the unit distance problem was a central problem in its field AND the proof is two pages long AND (at least as per @tonylfeng) doesn't contain any conceptual breakthrough. Reductive to only single out part of it

@scottnarmstrong Sure, but even if you prompt it with an idea, it's not presently able to generate 100 pages to flesh it out and apply it... my point is just that there are obvious limits to present capabilities, beyond the domain-specific

@wtgowers If they solved 9 of 353 attempts and each cost that much, don't you think it's more accurate to say it's several thousand dollars per problem? On the slot machines at the casino you wouldn't only consider your profit on the winning rounds ...

The paper also discusses the cost of solving these problems, describing it as a few hundred dollars per problem, but exactly what that means is complicated -- more details can be found in Section 5.

Let A be the set of positive integers with just 0s and 1s in their ternary expansion. Let B be the set with just 0s and 1s in their base-4 expansion. Let N be a large integer. Must at least 1% of the numbers from 1 to N be expressible as a+b with a in A and b in B?

@scottnarmstrong It also seems much closer to the interests of the mathematicians who have been employed at OpenAI, designing the systems. Not obvious to me whether this is a coincidence ...

Why does GPT 5.X seem to be much better at combinatorics/number theory than other areas of math? Is this: - a reflection of the interests of the prompters? - because these areas lend themselves to millions of simple to state problems? Other areas of math are more theory-heavy?

@ChrSzegedy What are you basing that on?

@WKCosmo But "things like this" have themselves been evolving. The early results claimed as breakthroughs *were* actually low-hanging fruit or problems nobody cared about!

It has been interesting watching the response from the community to things like this evolve over time, especially from early dismissals of machine proofs as trivial demonstrations of low-hanging fruit that humans just hadn't bothered to get around to yet.