Paata Ivanisvili
@PI010101
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Professor of Mathematics @ UCI. Former postdoc @ Princeton. Exploring what AI can (and can’t) do in math.
Irvine, CA
Joined October 2019
I find this amazing. Imagine how long it would take a human to do the same! The problem of finding the optimal constant C^d is still open.
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Today I asked Grok Expert to carefully read the paper and improve the constant (2.69076)^d using only the techniques in the paper. After 11 minutes, Grok produced (2.408845)^d and pinpointed exactly where the improvement occurs: https://t.co/jGVhxICMMC 6/n
grok.com
In https://arxiv.org/pdf/1902.02406 we show that the second moment of degree $d$ polynomial on $\{-1
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After publication, we later realized that our method actually gives (2.41)^d. The improvement comes from optimizing a single unpleasant function -- but we never revised the paper. 5/n
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Our proof uses conformal maps, Hahn–Banach, Riesz representation, complex hypercontractivity. I also posted an outline here: https://t.co/gdAX4wQiry 4/n
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This improved the long-standing bound e^d; see Theorem 9.22 in Ryan O’Donnell’s wonderful book ( https://t.co/ZEozOLvkCn) or Remark 5.13 in Janson’s *Gaussian Hilbert Spaces*. 3/n
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In one of my papers with A. Eskenazis ( https://t.co/VIXvvvOkGw) we proved that for any degree-d polynomial f on the Hamming cube {-1,1}^n, its L^2 norm is bounded by its L^1 norm times (2.69076)^d, a reverse Hölder inequality 2/n
arxiv.org
Let $(X,\|\cdot\|_X)$ be a Banach space. The purpose of this article is to systematically investigate dimension independent properties of vector valued functions $f:\{-1,1\}^n\to X$ on the Hamming...
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Pick any paper and ask your favorite AI to improve one of its results (even using only the techniques in the paper). There is a nontrivial chance it might actually succeed. 1/n
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Sounds correct. This integral representation for CDF of binomial distribution is a nice thing to know.
Haven’t checked the proof of Telgarsky conjecture, but think it should be amenable to the approach in my linked answer to @aryehazan
https://t.co/aHE5hJuZTR Just expand the difference of the two sides as power series in 1/m and check the sign of the leading coefficient.
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If you keep testing Erdős problems with LLMs, it’s very likely you’ll eventually solve one of the open ones. Experts aren’t doing this (for obvious reasons). Non-experts assume the experts are doing it. They’re not.
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Install Aristotle. Get API key. Run it from your terminal. Pick any open problem in math and input in aristotle (in its natural language!). After several hours it will either produce full formal lean proof or may fail. 👏
We are on the cusp of a profound change in the field of mathematics. Vibe proving is here. Aristotle from @HarmonicMath just proved Erdos Problem #124 in @leanprover, all by itself. This problem has been open for nearly 30 years since conjectured in the paper “Complete sequences
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The first open source model reaching gold medal on IMO 2025. https://t.co/n7Ure8FmQZ
github.com
Contribute to deepseek-ai/DeepSeek-Math-V2 development by creating an account on GitHub.
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This is quite possibly what the future of mathematical work will look like.
A novel and beautiful AI generated mathematical proof. This is now happening on a daily basis.
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Grok refutes conjectures on Almost-orthogonality in the Schatten-von Neumann Classes (see page 6) https://t.co/FNnJNhiZi3 I am impressed with its rate of progress, I think it is extremely powerful model. Full chat conversation. https://t.co/4oVz4z7Vnx Summary of the
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The Department of Mathematics at the University of California, Irvine invites applications from outstanding candidates for the Edward and Vivian Thorp Endowed Chair. The Thorp Chair is provided to recruit a world-renowned mathematician who can bring eminence, visibility, and
recruit.ap.uci.edu
University of California, Irvine is hiring. Apply now!
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Back in 2008, in a class I was taking with Anatoly Vershik, he said that big-money math prizes are “show business”—the worst traits of mass culture seeping into mathematics. At that time I absolutely disagreed with him. Now, since time has passed, I completely agree: they create
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