
@littmathi
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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.
Gauss had a personal seal(!) emblazoned with the motto “Pauca sed Matura” ("Few, but Ripe"). Worth remembering as quantity becomes cheaper.
Daniel Litt retweeted
If someone asks you to write a reco letter and you plan to do it with AI, you should disclose it to them first.
It can come across as very lazy and low-effort and will harm the candidate.
If you want your people to succeed, don't do this.
my toddler just asked me to draw her a picture, and then when I was done she hanged it on the fridge
Daniel Litt retweeted
they’re going to automate you. AI will do your job. it’ll be better than you at everything. when you want to smell a flower it’ll smell for you, better than you ever could. it’ll be the flower too.
Daniel Litt retweeted
I’m excited to announce that I will be working at the Mathematical AI Safety Institute (MAISI) full-time as its founding Scientific Director! This means I will not be joining OpenAI as an employee, though I will still be collaborating with them, and I’m happy to announce that OpenAI will be supporting MAISI. They have offered us $10MM in API credits, and access to their latest models for our research use. Moreover, they will be participating in a multi-lab AI safety workshop we are organizing for next year with other frontier AI labs.
As an independent research institute, we are also in conversations with other labs and AI safety orgs about how MAISI can collaborate with them and contribute quickly to AI safety research across the industry. As we’ve seen over the past few weeks, the need for action on AI safety is extremely urgent. Research is an important part of that, and mathematicians have an important role to play!
Daniel Litt retweeted
To the extent that mathematics is getting mogged by AI goodharting, it’s because mathematics goodharted itself into this position by rewarding the solving of conjectures over understanding, exposition, and pretty much everything else.
Q: how should we think about the OpenAI 372 math problem solutions?
A: research mathematics is an abelian sandpile exhibiting self-organized criticality. The OpenAI drop triggered a collapse to sub-criticality.
Q: WTF???
A: explanation here: blog.danromik.com/the-abelia…
Daniel Litt retweeted
first proof third batch results are out! full report here: hexagonmath.org/2610.00244
Daniel Litt retweeted
The ideal outcome for science isn't a couple of labs using proprietary models and millions of dollars to crack trophy problems, it's to have millions of AI-aided human scientists who follow their curiosity and become way more ambitious
Daniel Litt retweeted
The academic hiring practices are changing fast and from what I have been hearing from folks @ Oxford, Cambridge, ETHZ, and NUS the weight of publication record will be far less in measuring competence;
"understanding" is now the rare commodity. Great!
Daniel Litt retweeted
Replying to @SchopenhauerOn
Mathematicians have a wide range of opinions, and the reactions/letters making most of the news may give an incomplete and inaccurate picture of how mathematicians are actually reacting.
Daniel Litt retweeted
Amazingly well-written
Worth a few minutes of your time if you care about these sorts of things
In 1974 Deligne proved the last of the four Weil conjectures—an analogue of the Riemann hypothesis in a world where some prime number has been set to zero. While Deligne’s work was celebrated, his doctoral advisor, Grothendieck, was unhappy. Can solving a problem be bad? I think not, but I want to explain my understanding of the story, which in my view sheds some light on the present moment.
In his memoir, “Récoltes et Semailles” (Reaping and Sowing), Grothendieck explains his approach to problem solving and mathematics more generally: "The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration… the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it... yet it finally surrounds the resistant substance." He compared a precise mathematical question to a nut, which, rather than being cracked open by a chisel, yields at the perfect time to simple hand pressure once it has been soaked in the ocean of mathematical understanding. According to this account of mathematical progress, solutions, though important, are ancillary to the advance of the rising sea of mathematical understanding. At best they measure it to some extent, but the goal is to raise the water level.
Grothendieck had laid out a program to resolve the Weil conjectures: the standard conjectures, which are part of the philosophy of motives. The proof circumvented this program. Deligne characterized Grothendieck's reaction as "he did not care...the proof was a trick" but in fact Grothendieck excoriated Deligne in his memoir, claiming Deligne and others tried to "bury" the theory of motives, and Grothendieck himself. The standard conjectures remain open today.
Deligne's result relied on a lot of work that was not yet well-exposited in the literature, around the theory of étale cohomology. Deligne himself wrote an exposition of this in SGA 4.5, and Illusie contributed additional necessary material in SGA 5. Some have referred to this additional work as "thankless," but it was completed.
While Grothendieck is one of my heroes, and I find his view of mathematics very appealing, I think he was wrong here. Though the standard conjectures are still open, there is an immense amount of work on the theory of motives. People worked very hard to clarify the issues left unclear by Deligne's argument. And crucially, Deligne followed up on his work with a different proof, in "La conjecture de Weil II," that completely revolutionized arithmetic geometry, in many ways going beyond the philosophy of motives as it existed at that time.
I think Grothendieck's view that the first proof Deligne provided was insufficient was, in some sense, correct. But he was wrong about the fact that the theory he so desired, and the attendant quest for understanding, would be abandoned, and that his ideas would be buried. I don't think anything can stop us from trying to understand.
In 1974 Deligne proved the last of the four Weil conjectures—an analogue of the Riemann hypothesis in a world where some prime number has been set to zero. While Deligne’s work was celebrated, his doctoral advisor, Grothendieck, was unhappy. Can solving a problem be bad? I think not, but I want to explain my understanding of the story, which in my view sheds some light on the present moment.
In his memoir, “Récoltes et Semailles” (Reaping and Sowing), Grothendieck explains his approach to problem solving and mathematics more generally: "The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration… the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it... yet it finally surrounds the resistant substance." He compared a precise mathematical question to a nut, which, rather than being cracked open by a chisel, yields at the perfect time to simple hand pressure once it has been soaked in the ocean of mathematical understanding. According to this account of mathematical progress, solutions, though important, are ancillary to the advance of the rising sea of mathematical understanding. At best they measure it to some extent, but the goal is to raise the water level.
Grothendieck had laid out a program to resolve the Weil conjectures: the standard conjectures, which are part of the philosophy of motives. The proof circumvented this program. Deligne characterized Grothendieck's reaction as "he did not care...the proof was a trick" but in fact Grothendieck excoriated Deligne in his memoir, claiming Deligne and others tried to "bury" the theory of motives, and Grothendieck himself. The standard conjectures remain open today.
Deligne's result relied on a lot of work that was not yet well-exposited in the literature, around the theory of étale cohomology. Deligne himself wrote an exposition of this in SGA 4.5, and Illusie contributed additional necessary material in SGA 5. Some have referred to this additional work as "thankless," but it was completed.
While Grothendieck is one of my heroes, and I find his view of mathematics very appealing, I think he was wrong here. Though the standard conjectures are still open, there is an immense amount of work on the theory of motives. People worked very hard to clarify the issues left unclear by Deligne's argument. And crucially, Deligne followed up on his work with a different proof, in "La conjecture de Weil II," that completely revolutionized arithmetic geometry, in many ways going beyond the philosophy of motives as it existed at that time.
I think Grothendieck's view that the first proof Deligne provided was insufficient was, in some sense, correct. But he was wrong about the fact that the theory he so desired, and the attendant quest for understanding, would be abandoned, and that his ideas would be buried. I don't think anything can stop us from trying to understand.
Apart from general awkwardness, mathematicians are at a disadvantage in discourse because the general public (including much of the twitterati) has very little sense of what we do. I like the activity of solving problems/proving theorems but math research is not a problem set.

















