Sheaf herder. I believe in you 🔥
Joined October 2013
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12 Dec 2025
I worked with UVA undergraduate Seth Bernstein on this fun project in homotopical combinatorics: arxiv.org/abs/2511.02982
He'll be presenting a poster on it at the JMM this year! meetings.ams.org/math/jmm202…
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I remember when calls to Pause AI started becoming popularish in my slice of the internet (feb '25?)
Tbh at the time I thought "nah maybe later, I'd like more capabilities first"
Today I'm quite happy with capabilities! They're unbelievable! So, I find myself becoming ⏸️-pilled
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There's a classic (invalid) proof by induction that all horses are the same color: the inductive step P(n) ⇒ P(n 1) fails only at n=1.
Is there a fun non-theorem that would be true by a nice inductive argument, except that the inductive step fails only for n=7, or something?
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E.g. some argument that implicitly assumes in the inductive step that every automorphism of S_n is inner? Would fail only at the P(6) ⇒ P(7) step
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The new arXiv policy is obviously v good for papers in math, where a paper has your name on it if and only if it is your work. The new policy enforces the very low bar that you read your own paper before you submit it!
Of course, this is not how authorship works in other fields.
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For comparison, imagine someone in your lab writes a paper which is completely fraudulent -- they just totally fabricated the data or whatever. All of the authors should suffer some consequence, even if they did not actually write the paper or contribute to it in any way!
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If you're going to have a culture where you get academia points for having your name on good papers you didn't contribute to, you need to also receive negative points when the papers are bad / have serious problems. Not reading your own paper is a serious problem.
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More generally: when 0≤k≤n, the binomial coefficient (n choose k) is equal to the coefficient of x^k in the polynomial (1 x)^n.
For k,n arbitrary integers with k≥0, one should extend this by defining (n choose k) to be the coefficient of x^k in the formal power series (1 x)^n
Apr 28
I’ve made an important mathematical discovery; apparently -1 choose 0 is equal to 1, since there’s one way to put zero indistinguishable items in zero bins
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For example, (-1 choose 0) is the coefficient of x⁰ in
(1 x)⁻¹ = 1 - x x² - x³ ...,
which is indeed 1!
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Missing from mathematical english:
"Maximal" is to "Maximality"
as
"Maximum" is to ????
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Resolved. Goes to show... nah, I've got nothing
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The semi-orthogonality thesis says that improved alignment of LLMs will not make them better at understanding triangulated categories.
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Gemini 3.1 Pro has contributed a useful example to an upcoming paper! Was very nice to work with.
ChatGPT (from my institution's Edu plan) did a terrible job with the same prompt.
19 Jul 2025
I had my second genuinely positive experience with AI-assisted math research recently.
I asked Gemini 2.5 pro to prove a theorem, and it failed (gave an invalid argument with obvious handwaving at the gap) BUT in the process it correctly proved a lemma that was useful to me!
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It's an example in commutative algebra, which I think a domain expert would have found pretty easily, and I think I could've found with enough time to think about it. This kind of thing seems like a very good use case for LLMs in pure math research.
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Well done y'all
Do you think the Sora app will actually be successful? i.e. relevant one year from now
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A tool specifically for vibe-writing papers? Worrying
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Ben Spitz (63/100 improv meals) retweeted
Jan 27
[Galvin 1995]. Let E be an infinite set. Given a subgroup H of Sym(E), TFAE:
(1) H is countable.
(2) H ≤ ⟨f,g⟩ for some f,g∈Sym(E).
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I continue to be worried about how much the average person trusts LLMs
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Here's a translation of the relevant paper by Euler: arxiv.org/pdf/math/0501118
He just says
"... for I have observed after thinking about this for many days that this number can be divided by 641, which can be seen at once by anyone who cares to check."
🐐
Jan 11
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I've arrived in DC for JMM!
DM me if you're around, I'd love to grab coffee etc :)
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