Blog of Daniel Litt, about math and other things
I'm currently returning to Toronto from a summit on the future of mathematics, at OpenAI. Sebastian Bubeck asked me to talk a bit about the future we'd all like to avoid, where humans are mathematically disempowered. Jacob Tsimerman advised us to try to prioritize detail over correctness, and I have no doubt that I succeeded in deprioritizing correctness. I tried to find a title that wasn't too…
Announcing a new project: problemsilike.com , a website collecting open problems that I, personally, like, with comments on their context, difficulty, and interest. The goal is to track progress on mathematical questions that I think are important, and to measure human understanding of these questions, as well as the usefulness of AI tools in helping to resolve them. It is also a step for me…
Mathematics isn't only about saying true things. It's about asking the right questions, being confused, stumbling about, getting distracted, being wrong, recognizing when you're wrong, being stuck. Mostly being stuck. It's about clinging to a giant edifice and feeling it out until you understand some tiny piece of it. It's about finding meaning in and intuition for the texture of an object which,…
Since June 15, 2025 there have been 8 papers posted to arXiv with the phrase “Hodge conjecture” in the title or abstract. By my count 6 of them (75%!) are LLM-generated nonsense, replete with hallucinated references; as you might imagine the amount of correct mathematical content they contain is near-zero. I worry this issue will only get worse with time.
The idea for this (very short, and somewhat silly) story popped into my head a couple of weeks ago. Please enjoy. Toast , or, The Golems “It’s just not so simple as that,” the toaster replied. “You say you want your toast ‘medium brown,’ but the very notion of ‘medium’ presupposes a one-dimensional spectrum of toastedness that is, frankly, too idealized to be useful. Of course color is relevant,…
I try to make a habit of posting my grant proposals here after the application period has passed, both because I hope people might find them to be useful models, and because doing so is a good opportunity for a brief postmortem. If you’d like to take a look at my proposal for the NSERC Discovery grant, you can do so here . The proposal was funded, so hopefully it is a reasonably good model. The…
My last post was a little tiling puzzle: you can read it here . In this post I want to quickly give the solution. Represent a red tile by \(1\) and a blue tile by \(-1\); and think of the square in coordinate \((a,b)\) as the monomial \(x^ay^b\). Then the question is equivalent to asking when the polynomial \(p_{N,M}(x,y)=\sum_{a=1}^N\sum_{b=1}^Mx^ay^b\) is in the ideal generated by \((1-x+x^2,…
Here are four magic triominoes: Four magic triominoes Each is made out of three squares, two red and one blue or two blue and one red, alternating in color. These squares have the following property: if you place two squares of the same color on top of each other, they stack. On the other hand, if you place a red square on top of a blue square, they annihilate each other. For example, if you place…
Let \(G\) be a finite group and $$\rho: G\to GL_r(V)$$ a faithful representation, with \(V\) a finite-dimensional complex vector space. The following is well-known: Theorem 1. Let \(\gamma\) be any finite-dimensional irreducible representation of \(G\). Then \(\gamma\) appears as a direct summand of \(V^{\otimes n}\) for some \(n\gg 0\). The usual proof of this uses analysis; today I want to…
Today I want to explain some algebro-geometric manifestations of the Sylow theorems. This blog post is an expansion of a Twitter Thread I wrote a few months ago, which you can find unrolled here . The Sylow Theorems and some examples Let’s start by reminding ourselves what the Sylow theorems say, and think about a few examples. Throughout \(G\) will be a finite group and \(p\) will be a prime.…
Today is the #ShutdownSTEM strike , a day when non-black members of the academy strike in solidarity with the black lives matter movement, and take action to work to improve STEM academia. To quote their website: “ Those of us who are not Black, particularly those of us who are white, play a key role in perpetuating systemic racism. Direct actions are needed to stop this injustice. Unless you…
On Twitter Sarah Griffith made the following wonderful observation: Maybe this doesn't seem strange to anyone else, but I just realized I find it very strange that if you integrate a polynomial over Q between rational bounds you always get a rational number, even though the area under the curve can be quite complicated — Canonically Singular Sarah (@SC_Griffith) April 29, 2020 Indeed, I think this…
I was recently funded by the NSF Algebra and Number Theory grant DMS-2001196. Since other people may find it useful, I figured I would post my proposal here . I don’t claim at all that this is a model proposal, and there are a lot of changes I would make in retrospect, but hopefully it is useful to other people applying for grants.
Two quick announcements. One is that I’ll be hosting department teas for the UGA math department on Zoom, starting next Wednesday. You can find the schedule and Zoom link here ; if you think you should have the password (i.e. if you’re a member of the UGA math department), and you don’t have it, please email me. Second announcement — I’ve now posted a schedule for office hours here , as well as…
This past weekend was the first-ever WAGON conference (Western Algebraic Geometry ONline), which was meant as the online iteration of the Western Algebraic Geometry Symposium (WAGS). Here “Western” refers to the western United States (which is typically the area from which WAGS draws attendees), but the conference ended up attracting participants from all over the world — I think it was plausibly…
For those of you who haven’t yet, you should register for WAGON ! Poster below — it’s going to be great.
Videos are now up for AGONIZE. I’ve committed to organizing another one of these — stay tuned for more info. Since this was one of the first math conferences of our new era, I wanted to write a brief reflection on what worked and what (in my opinion) didn’t work. Technical Aspects The conference was run as a Zoom meeting — UGA’s Zoom license can accommodate meetings of up to 300 people, which…
Since I’ve been working from home for the last couple of weeks, and will continue to do so for the next few months, I’ve felt a bit starved for mathematical contact — I’m sure many of you feel the same way. So I’m starting weekly office hours, from 2-4pm EST on Fridays. Join me at https://zoom.us/j/831448945 . These office hours are primarily for grad students and postdocs in arithmetic geometry…
This post announces the first ever AGONIZE conference ( A rithmetic G eometry is ON line I n Z oom, E veryone)! The conference will take place Wednesday, March 25, from 12pm-5pm EST. For more info and to register, see the conference website and the conference poster below. We have a really great lineup — I couldn’t be more excited.
A couple months ago I went to a fantastic conference on Arithmetic Topology at PIMS . The video from my talk is now up: enjoy ! I spend the first few minutes of the talk joking around about this cartoon: Pictured: Wei Ho, Ravi Vakil, Benson Farb, Jordan Ellenberg, Kirsten Wickelgren, Soren Galatius, Will Sawin, and the Dragon Langlands