Daniel Litt (@littmath) header
Daniel Litt (@littmath) profile picture

Assistant professor (of mathematics) at the University of Toronto, visiting Harvard Fall 2026. Forever confused. Algebraic geometry, number theory, etc. He/him.

Toronto, Ontario
Joined August 2010
Photo by Daniel Litt (@littmath)Photo by Daniel Litt (@littmath)Photo by Daniel Litt (@littmath)Photo by Daniel Litt (@littmath)Photo by Daniel Litt (@littmath)Photo by Daniel Litt (@littmath)Photo by Daniel Litt (@littmath)Photo by Daniel Litt (@littmath)Photo by Daniel Litt (@littmath)Photo by Daniel Litt (@littmath)
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.
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I now assign some non-zero probability to the timeline where coding gets solved, solved swiftly, utterly, superexponentially, to the point that <30B models in Q2 2027 can zero-shot build operating systems – and then there's no "RSI" or singularity. basically Chollet's take
One of the biggest misconceptions people have about intelligence is seeing it as some kind of unbounded scalar stat, like height. "Future AI will have 10,000 IQ", that sort of thing. Intelligence is a conversion ratio, with an optimality bound. Increasing intelligence is not so much like "making the tower taller", it's more like "making the ball rounder". At some point it's already pretty damn spherical and any improvement is marginal. Now of course smart humans aren't quite at the optimal bound yet on an individual level, and machines will have many advantages besides intelligence -- mostly the removal of biological bottlenecks: greater processing speed, unlimited working memory, unlimited memory with perfect recall... but these are mostly things humans can also access through externalized cognitive tools.
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I understand that you don't want mathematicians associated with this inegalitarian idea. My impression came from engagement with a few who kept drawing unjustifiable (from my PoV, as I'm not one) qualitative boundaries ("heh proof X was trivial… but LLMs will NEVER do Y")
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FWIW I was also skeptical in 2025 that LLMs would be able to do high quality research math in the near term, but this was more due to broad skepticism of claims about the rate of progress than thinking that math was special, I think. 🤷
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Replying to @littmath @sebkrier
Some mathematicians. Think Penrose for a caricature, perhaps. There is a strain of thought that Real Novel Reasoning, which mathematicians are capable of, represents a qualitatively different process from what LLMs (and, given current evidence, most white collar workers) do.
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It’s true that for any given belief, particularly beliefs flattering to mathematicians, you can probably find a mathematician who holds it.
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he's writing abstracts for math talks
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Daniel Litt retweeted
Replying to @littmath
I'm calling for an immediate and total ban on mathematicians writing words until we figure out what the hell is going on here
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Replying to @littmath @sebkrier
Correct. Note that the above isn’t my main model, I can just entertain it being true. You can appreciate that so far, ML didn’t take disruptive paradigm shifts, so I don’t by default expect that we will sorely need one before ASI.
Replying to @doomslide
My biggest reason for skepticism about any remaining hard barriers is the intellectual history of ML itself leading to this moment, history which fractally resembles its output. Recall Rosenblatt? Hinton, Sutskever, Kingma, Vaswani? Mordvintsev's DeepDream, my personal "aha" moment? He's ResNet lol? What in all of that was a great paradigmatic leap? The King's road was just ironing out the logistics for connectionism, It's been continuous relaxation, iterative problem-solving, with some natural science analogies and combinations of tools of applied math available to above-average erudite scientists, and indeed pruning of too clever by half branches; and spectacular crashes of programs of those luminaries who grew too intellectually ambitious, like LeCun. Hinton himself assumed that his invention is a dead end facsimile, half-clever research prototype that can't measure up to the brain's actual algorithm; and his confidence in that was shattered by a joke from a model we'd only laugh at in pity today. At no point did we stall in need of some profoundly new mafs or a breaking conceptual insight – and yet we're here, where networks have learned to competently operate with human concepts, with the entire repertoire of reasoning motifs available to a frozen human mind (no I do not agree that the best models are wholly incapable of abduction, which you brought up before; they are grasping at it in long sessions, they try to condense their representations into compact hypotheses and come up with research arms to test them). Something is missing, partially clearly due to lack of demand, partially for reasons I don't understand. Indeed, I think the best public models can't even write this post unless provided with massive authored input, nor your rebuttals. But is that necessary? They are fast and cheap. From now on they will do hundreds of times as much qualitatively comparable iterative work as had been done to create them, as much as we can afford to pay. And incredibly, obscenely much had been paid upfront already. Where does this lead? Naive induction provides the answer. They will gradually do better and better ML research, developing better and better models. That is what is called "RSI". Its exact exponent is subject to debate and market incentives. When continual learning is adequately solved (with actual parametric learning on small batches), whether under human guidance or not, it will accelerate. I think it will be solved. I can abstractly imagine being wrong, I've written on that xitter.twitterapi.xyz/teortaxesTex/status/18…, but do not actually believe that we have any solid reason to believe this ride stops or meaningfully slows down. That would be hubris, and unearned hubris in my case, and I – perhaps narcissistically – believe it'd still be hubris on part of those who have earned the right to it. The journey from perceptron to Astra was longer than from Astra to some Scholze. Humans differ a lot but they are not qualitatively different species, for all that mathematicians like to imagine themselves as such. If LLMs stop after conquering the level of mathematicians' parents, that'd be a big anthropological discovery before it is a finding about LLMs, and we're not exactly doing anthropology here, I think.
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Yep I basically agree with the quoted tweet (though I'm not sure the claim about what mathematicians believe is right)!
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This tweet is "this tweet is" twice, first without quotes then with quotes, followed by (twice, first without quotes, then with quotes) "twice, first without quotes then with quotes, followed by (twice, first without quotes, then with quotes)"
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I think the combinations of possibilities are much richer than Runaway Sci-Fi that allows you to edit consciousness and minor GDP boost. For a start, even though true RSI is possible and enabled by ten thousand AIs with well-rounded Einstein-like general intellectual abilities with much stronger raw computation abilities, working memories, and stamina, perhaps it will turn out that the underlying substrate of our universe is arranged in such a way that achieving any true next-level scientific understanding and engineering is still out of reach. Perhaps the next meaningful AI architecture improvement will require one million pages of Navier-Stokes blowup-like raw brute force construction (brute force might be inaccurate, but I don't know what else to use here).
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Yeah, I agree there are a lot of open questions about the nature of progress itself.
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OpenAI is so generous they constructed *infinitely many* pure Yang-Mils theories one for every possible way of approaching the IR limit and each with potentially infinitely many vacuua!
The YM repository has just been made visible 30 minutes ago. I was skimming the assessment document, and to my untrained eye I found the fact that OAI does not establish an answer to Question 1 really fascinating. Usually this is an integral part of establishing scaling/infinite volume limits going from discrete probabilistic models to a continuum one (eg, SLEs).
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Oh I am sure they tried very very hard to prove uniqueness
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I do think it’s a bit funny that “tried very hard” is a euphemism for “here’s 20 million dollars. make no mistakes.”
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I think "risky" here makes some assumptions about how credit will be apportioned down the line, but if true this is obviously bad for scientific progress. I don't think the mechanism behind progress is as simple as "smart machine hence better science."
Even sharing a paper with a partial result is risky -- someone with more compute and access to internal models can finish it and post the full solution before you do, and your contribution disappears. You either release a sharp result or you post nothing.
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Is the endpoint of this line of thinking that most of the science will end up being done inside of the frontier labs? They'll hire staff scientists to work on problems that will make them a profit
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One point about basic research is that it's very hard to tell in advance what directions will make you a profit. I think it's always been the case that obviously profitable stuff has been pursued in industry, but there seems to be broad agreement that less immediately profitable stuff has value too.
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Daniel Litt retweeted
I keep seeing people claiming that "grad students only work 5 hours a week" and then clicking on their profile and they're in some tea-leaf reading field like econ or analytic philosophy. You're telling on yourselves! Some of us are doing real things like reading sonnets.
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Had fun at the FOCS TCS+AI workshop yesterday. @littmath gave a spectacular keynote, followed by a great panel with @Knikct, Dan Spielman, @B1ar2n3a and @praveshkkothari. Big audience; no recording, but hopefully the event was useful to attendees. photo cred @thegautamkamath
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Classic conference photo: 50% with plaid button-downs
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Looks like it's actually levelling off?
papers posted to math arXiv per week in 2025-2026
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Seems like everybody got the low hanging fruit out of their system and is now having an existential crisis wondering what the meaning of a preprint even is.
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Too soon to say. I suspect there will be more “jumps” with new model releases at least.
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Front row seats for a #FOCS2026 panel on the future of TCS&AI. After keynote by Daniel Litt (@littmath), he joins an all-star panel w Nikhil Srivastava (@Knikct), Dan Spielman, Barna Saha (@B1ar2n3a), Pravesh Kothari (@praveshkkothari). Organized & hosted by Aaron Roth (@Aaroth)
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papers posted to math arXiv per week in 2025-2026
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Is the implication here that slop is being posted? Or that a lot of good mathematics is happening faster?
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There’s no implication!
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Most of the massive growth is coming from distinct authors, not more papers per author. We are in the toddler days of how good the systems will be. Every jump in AI capabilities will massively expand the pool of people who can produce interesting publishable results. So I don't see anyway in which it doesn't continue to skyrocket from that source of growth. And if the 2-paper cap was taken away, it would just unlock another source of growth from power users.
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I think this is likely but not certain. Of course you can just say "codex write me a paper" but currently the fact that non-experts can generate something interesting to experts relies on the existence of lots of open conjectures certified as interesting to experts.
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Replying to @littmath
wait how are you seeing the hep-th increase, looks like it's not one of the categories?
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I (well, Codex) made another graph which I didn't post!
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Replying to @BrunsJulian1541
Not sure, will think if there's a good way to see this.
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It looks like a combination of more people submitting and more submissions per person (this could be sort of the same phenomenon, e.g. people who haven't posted a paper in a few years suddenly posting one), not just a few hyperproductive people.
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