Daniel Litt

New paper with Josh Lam, about which I'm really excited! I want to try to briefly explain what the point is in this thread.

@davikrehalt @PiotrPePo I’m probably overstating the case; I’m mostly annoyed at the flurry of short, obviously AI-written, one-shottable results on arxiv recently. I think this is a tell the humans contributed little. IMO always fine to put up a paper but should be clear what you contributed.

@littmath @PiotrPePo Ah you mean they should just not put it out at all. I guess I strongly disagree with this take.

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.

@davikrehalt @PiotrPePo IMO people should not be writing or signing their names to such papers!

@littmath @PiotrPePo Surely this cannot be the only criteria as soon (if not now) the models will be able to one-shot many main results of papers which are completely human written

(On vacation at the moment so may be a few weeks before I really have a chance to invest significant time to digest it, but I'm pretty excited.)

Still thinking through the details but I think this is likely correct!

@beezressee It's just that the solution is a few lines from previous work, of which the people who thought about this problem were not aware.

@littmath "I would say the construction is in some sense implicit in the literature..." I see comments of this flavour often when mathematicians write about LLM proofs. Is it for the purpose of identifying source of reasoning or is it a deflation or something else?

Also, very exciting news! Another math problem (potentially) solved, this time, one posed by @littmath! Last wednesday in a last try with GPT-5.5 pro before 5.6 pro came out, I got an interesting partial on this problem. This prompted me the next day to use GPT 5.6 sol pro, which essentially autonomously worked through the remaining parts and managed to complete the solution by drawing on somewhat obscure techniques. I messaged Daniel with my findings and thoughts, particularly on the exposition and digestability to make sure this proof contributes something genuinely meaningful to the world. And, I believe this task is quite succesful. Though the main crux of the argument relies on these Raynaud bundles, nonetheless the connection is nontrivial and new in this specific application! The remaining work is now to digest the proof. As the subject expert Daniel had some great insights and feedback which I have tried hardest to include. It's my belief that this proof taught us about a new and exciting tool and angle to handle such problems! Particularly suprising to me is that with sufficient steering, the output of GPT-5.6 sol pro is remarkably incredible, and upon further inquiries, it seems to genuinely be able to present the underlying geometry of the problem and abstract from it to reason through the complete construction. Exciting times! I definitely see a very very clear improvement from GPT-5.5 pro in math, and it seems 10 times more trustworthy in its output, and its exposition in these proofs also improved a ton. #post-50" target="_blank" rel="nofollow noopener">problemsilike.com/forum/thread/1…

@PiotrPePo (How do I know? Because the models can oneshot the main results.)

@PiotrPePo I didn’t say the papers do not deliver anything significant. But I think a lot of recent papers are people signing their names to work to which they made little to no intellectual contribution.

@good2thinkwith @burny_tech I have a lot of thoughts on this but on vacation so probably won’t have time to put them together for a bit. Of course it’s the stuff that’s harder to measure!

@littmath @burny_tech Daniel, what’s your take on what the current models are missing to do even more with math? If we can precisely identify what they can’t do, better benchmarks can be made and they can train to improve it.

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

@littmath You mean perhaps OpenAI will fund math research?

@littmath Agreed! I'm also encouraged by the fact that they have very good human mathematicians in house, who (based on the unit distances, I assume also with double cycle) take a careful look at proofs now before making a public announcement.

A very nice proof! A thread with a couple of comments:

@doomslide There are worse uses of marketing budgets!

OAI's PR strategy being mass sweeps on decades of combinatorics literature wasn't on my bingo card. That marketing budget doing serious work!

@ViewToATweet @polynoamial Looks cool! I don’t know anything about this conjecture but it looks like people have spent time thinking about it.

@polynoamial I need @littmath to tell me what to think

More test-time compute leads to greater intelligence. But as we push ttc from seconds to weeks, latency becomes a bottleneck. GPT-5.6 Sol Ultra scales parallel ttc. The time taken to generate a proof to a 50-year-old problem drops from perhaps a whole day to a single hour.

toddler, who has started sprinting in a random direction any time I blink: daddy, the high chair protects me, from running away!

For the majority of the population, access to information is not the moat to learning—education is not the textbook.

@haider1 tldr of an 8 line post?

Nvidia principal engineer's review of GPT-5.6 Sol: tldr; - more depth-first, which means it sticks with harder ideas - more failures, but i see that as good if it's testing harder paths - less code, which usually means cleaner reasoning - simpler C++, another positive sign if it still targets the right optimization

@RefinedLurk Yes, I think this is wrong!

@littmath I don’t know what direction you’re emphasizing. I can think of some pretty fundamental papers post 1970s. But my suggestion is that’s a smaller part of math every decade. Do you think that’s wrong?

Kind of funny to read all the QTs and replies saying “this isn’t true of my field!” FWIW I find it very plausible that average paper quality has decreased over the last 50 years in math, but my sense is that the best papers have more or less continuously gotten better.