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
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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.
Daniel Litt retweeted
I'm calling for an immediate and total ban on mathematicians writing words until we figure out what the hell is going on here
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)"
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."
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.
Daniel Litt retweeted
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)
Daniel Litt retweeted
I have read the reaction of @marcusgnt and @ValerioCapraro to @ElliotGlazer astounding announcement. I strongly disagree with them and for practical reasons.
I’m working on understanding and rewriting the OpenAI H10 paper: very far from done. But bringing Glazer’s work into the mix was actually helpful. It has shed light on some of the rewritings that a collaborator and I are trying to make. I’m still digesting things, and I’m not claiming to have verified his proposed proof, though I definitely hope eventually to understand it as well.
I disagree with the idea that “slop on slop” is somehow additive. The effect need not be cumulative in the negative direction. There can be a nonlinearity here, where an attempt at a harder result can shed light on an earlier undigested argument. That is actually exactly what I’m seeing empirically in this case. Making more raw material available can actually help.
It is the responsibility of the mathematical leadership to design new incentives that promote understanding. Asking people not to produce more raw material seems just not empirically useful and not an adequate response from academic leadership.
Regarding Capraro's outrage. "The argument looks plausible, and plausibility takes the place of verification." Who said that this is so? The mathematical community will have to digest and verify these arguments of course. However the plausibility here is valuable for this process: this is more raw data that has a strong chance to be correct and be actually profitably used by the humans thinking about the proof. And I am not talking in generalities: this is exactly what is happening here.
Daniel Litt retweeted
Looking forward to tomorrow's TCS+AI Workshop at FOCS. @littmath will give a keynote, followed by a panel discussion with Dan Spielman, @littmath, @praveshkkothari, @B1ar2n3a, and Nikhil Srivastava. I'll moderate. Come with all of your questions, anxieties, and hopes!
Daniel Litt retweeted
hello there ℤ is Diophantine in ℚ, thanx to my close friends Astra and Claude
The polynomial characterizing ℤ isn’t quite Tweet-sized; it has m=292,890,231,905 variables, is of degree d < 2^^7, and all its coefficients have absolute value < 2^^8.
Daniel Litt retweeted
I’ve worked through the circuit of skepticism, denial, grief, and have landed on quite a bit of excitement about AI in math. Current AI proofs feel like clever technical tricks without fundamentally new ideas, but compare to where they were 6 months ago. I expect that further developments over the coming year will lead us to metaphorical new continents and planets that we could never have reached with just pencil and paper. Then the opportunities for exploration will open up much faster than they close down.
Maybe a better metaphor is aliens. Even if there are alien civilizations out there, humans could never make the interstellar travel required to physically meet them. But in mathematics we will encounter a kind of alien intelligence, and only mathematicians will be able to directly see and appreciate what it is saying. Anybody curious to learn alien insights should invest in human mathematicians.
Daniel Litt retweeted
New "Futures of Maths" platform: as a research mathematician you can rate your agreement to statements on current+future practices in AI-assisted math & see how others answered. Strangely addictive, can recommend! Curious to see their final results.
proofsandprompts.com/2026/11…
Daniel Litt retweeted
Fantastic essay by Frank Calegari – forward looking and positive. I think I completely agree with everything that Frank says. He is also one of my absolute favourite math writers.
terrytao.wordpress.com/2026/…
Daniel Litt retweeted
For the record, my feeling is that the answer to this question is “yes” for research overall. Perhaps I’m overly skeptical but my impression is still that LLMs, in the current paradigm, lack the diversity of thought which is fundamental in collective human research. For most of my research career, I have felt like I was the only person in the world thinking about the particular question/approach I was working on. Of course this is not universally the case for mathematicians, but it is a lot more common than people might imagine. So my mental model of mathematics research is sparse exploration of an infinite universe, rather than a lot of people trying to solve the same problem (as might be the case in other sciences). This isn’t “solved” even if you have oracle-level LLMs, because the questions are continuously discovered in the course of exploration. Oracles can only accelerate the exploration, making it more valuable.
Now in order to develop this diversity of inquiry, people need to cultivate their own unique experiences and thoughts. This doesn’t happen if everybody is just pushing buttons on the same chatbot. Therefore it is necessary not to outsource too much thinking to LLMs, and for this reason I think AI-eschewing organizations like AHM also play an important role in the ecosystem.
Daniel Litt retweeted
What do we really need LLMs for in mathematics?
Not necessarily for writing those relatively short papers built around insightful ideas that can have an enormous impact on mathematics. And perhaps not even for the technical work we can already do ourselves, although it’s certainly nice to get a speed boost and avoid spending too much time proving side lemmas.
Where this technology is making a qualitative difference is on problems whose solutions require extraordinarily complex proofs, potentially beyond what individual mathematicians, or even teams of mathematicians, could reasonably produce.
But there is a problem. Current LLMs still struggle to translate very long formal proofs from Lean into understandable mathematical arguments. Better training will presumably improve that.
Even so, suppose you have a proof of the Riemann Hypothesis, but no training in number theory. What exactly is that proof good for you?
You can certainly ask an LLM to explain its significance and perhaps get a reasonably accurate explanation of bits and pieces of it. But that doesn’t give you the mathematical understanding needed to work with the result, extract its ideas, connect them to other areas, or develop something new from it.
Mathematical knowledge is not just a collection of verified theorems. It is a body of ideas, concepts, methods, and connections, continuously developed and reorganized by a community of researchers.
I really don’t see how these technologies, which are amazing, are removing mathematicians from the picture. If anything, we may need more of them.
What I understand even less is why a company pursuing a trillion-dollar valuation has spent the past two months quarreling with a bunch of mathematicians.
The entire NSF Division of Mathematical Sciences has historically operated on a budget of roughly $250 million a year. Are we seriously supposed to believe that these multibillion-dollar investments are being made to prove theorems? Or are we seriously still at the proof-of-concept stage?
Of course, mathematical breakthroughs are also a way of demonstrating the capabilities of these models. But the commercial significance of those demonstrations and their scientific significance are two very different things.
I think we have become stuck in OpenAI’s PR campaign, discussing the future of mathematics on terms set by a company whose economic objectives extend far beyond mathematics.
And there will be plenty of confusion until the conversation moves beyond the spectacle and toward what these technologies can actually do for science and society.
Hopefully, investors will soon bring us there…
