Simon Pepin Lehalleur

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Simon Pepin Lehalleur

Simon Pepin Lehalleur

@plain_simon

Mathematician (algebraic geometry, motives & friends, singularities in statistics and ML). 'Geometry is successful magic' (R. Thom) University of Essen.

Essen, Germany Katılım Aralık 2019
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Simon Pepin Lehalleur
Simon Pepin Lehalleur@plain_simon·
"Pessimism of the Algebra, optimism of the Geometry"
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birds' hell
birds' hell@saturnalreturn·
The British prime minister is replaced 24 times per second, creating the illusion of a smoothly flowing image
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David Pfau
David Pfau@pfau·
One of the many thing about replacing humans with LLMs in the review process that makes no sense is *everyone has access to these tools*. You don't need to send your paper in to get an LLM to read it. You can just run it through before you submit and fix up mistakes yourself.
Peter Richtarik@peter_richtarik

Every single review I have handled at NeurIPS as an AC is **much worse** than a well executed AI review. By "much worse" I do not mean 20% or 50%. I mean a factor of about 10-100. At least - 10x more mathematical issues are caught, - 10x more missing key citations are caught, - 10x more novelty claims are invalidated with evidence, - 10x more issues with the experiments are observed, - 10x more typos and grammatical issues are fixed, - 10x more inconsistencies are found, and so on. In many cases I have handled over the last 10 years, the human reviews are so bad in comparison that the improvement factor is closer to 100. (The best human reviews I received over the years are worse than an AI review I can generate today, but still entirely good enough to make the correct decision. On the other hand, an AI review is often an almost comprehensive summary of all key issues --- something a human almost never has time to deliver --- and such feedback is immensely useful to the authors) At this point, we would be much better to just 1) give one very thorough ChatGPT review to all submitted papers (I am mainly talking about my fields - optimization, AI, machine learning), automatically, and 2) keep asking for a revision or two (to keep the duration of the process within some bounds) until the number of issues decreases to an extent when the AI reviewer is satisfied, in a given time-frame (eg, 1 month). 3) At that point, a human AC can make a decision (to keep an eye on this all should anything go wrong). The role of the AC would be merely to observe and manage the process, and make a final decision, based on the trajectory of the revisions. I can't believe I am saying this -- AI reviews were a nonsense idea even a year ago. The current AI reviews are super-human.

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Jenny Nicholson
Jenny Nicholson@JennyENicholson·
I can't stop thinking about this. Is it his equivalent of The Odyssey in the sense that he doesn't know what the Odyssey is about, or just in the sense that it's movie length and The Odyssey is a movie and he hadn't heard of movies before that
Logan Paul@LoganPaul

I’m releasing my Pokémon equivalent of The Odyssey today… it’s our biggest video ever. We’ve spent 6 months & millions of dollars making this movie, hope you enjoy

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Przemek Chojecki | PC
Przemek Chojecki | PC@prz_chojecki·
Sure, being careful, double and triple checking is key. I did that as well as I could and still failed here, the error was pretty subtle. But in the end a lot of the paper can be salvaged and the result on non-algebraizability still might hold with a different approach. I'd say this kind of error would be perfectly acceptable for a standard math work: you share a manuscript with your colleagues, they point out a subtle error, you go back to thinking. It's different here because of AI, but in principle quick peer-review worked. So it's not like the whole paper is bogus. There's interesting mathematics in it and that's what I need to surface properly. x.com/prz_chojecki/s…
Przemek Chojecki | PC@prz_chojecki

You can find the writing here: ulam.ai/research/algeb… I did multiple readings and re-readings, but I'm not an expert in motivic homotopy theory. I've run also multiple adversial LLM checks with GPT-5.6 Pro to both smooth the exposition and catch any errors. The core is probably 4-5 pages and you can see a summary of the argument in the beginning. Overall, this is by far the most impressive piece of work I've got with AI. It's still about finding a counterexample, but once found, there's some work to be done on theory building to check it. Historically, this question was approached by Rees, who constructed bundles, that were later shown to be motivic and expected to be non-algebraizable. This was the initial path we took here with GPT to prove Rees construction works. But that led to nothing, and then GPT came up with this new construction, and potential motivic approach. It's also impressive because it touches active areas of current research. Contrary to Erdos problems, you can't argue here that these problems did not receive enough attention or are not relevant. Any homotopy theory expert's opinion highly appreciated. I plan to go with a standard route of journal submission and peer-review for this result as not only it is beautiful, but might be quite hard to autoformalize currently (no motives in mathlib).

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Przemek Chojecki | PC
Przemek Chojecki | PC@prz_chojecki·
UPDATE: There is an error in Theorem 7.1 identified by Tony Feng below. It seems to kill the argument for N^† not having a motivic lift (it looks like it does now), though it still might be non-algebraizable. Back to seeing what can be salvaged!
Przemek Chojecki | PC tweet media
Przemek Chojecki | PC@prz_chojecki

Conjecture that every complex topological vector bundle on CP^n is algebraic is false. GPT-5.6 Pro found me an example on CP^5 that is not only non-algebraizable, but also with no motivic lift. This also disproves a more recent conjecture by Asok-Fasel-Hopkin.

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Silmarillion Enjoyer
Silmarillion Enjoyer@DGoweyAuthor·
So awesome that his first reaction is not to ask for proof but "so the giant just got away"
Fan Commentary: Joe Rogan Recaps@JoeRoganRecaps

Joe Rogan might be in real danger after historical investigator Timothy Alberino just leaked classified Pentagon information about a group of Marines who were all killed by a single unarmed 1,100 pound humanoid in Afghanistan: ALBERINO: “A team of Marines in Afghanistan stormed a cave hunting for Taliban, but they were instead met by an enormous giant who killed them all.” ROGAN: “WHAT?! That’s the craziest thing I’ve ever heard. So the giant just got away?” ALBERINO: “They then deployed another unit to go look for that team. When the team got to the cave that giant was in the middle of eating the dead soldiers.” ROGAN: “You can’t be serious. So what did the giant do to this unit?” ALBERINO: “This new unit went in fully prepared so they were able to successfully kill the giant.” ROGAN: “Did you ever try to find records of who was there and what casualties were reported?” ALBERINO: “It’s very difficult to get that kind of information.” ROGAN: “I’m sure.” ALBERINO: “The Pentagon released a bizarre statement years ago saying that the giant Kandahar incident never happened.” ROGAN: “The Pentagon actually said this? That makes me feel sketchy.” ALBERINO: “The pilot told me they weighed the giant before loading him on the plane. He got measured at 10-12 feet tall and 1,100 pounds.” ROGAN: “1,100 pounds? That can’t be a human. Who else have you spoken with about this?” ALBERINO: “I asked a commander about the Kandahar giant. The blood rushed out of his face and he points to his phone because he thought they might be listening. His wife then whispered to me that he’s not allowed to talk about that.” ROGAN: “Ohhh my god.” ALBERINO: “What I later learned is that it’s not the single giant of Kandahar, it’s the GIANTS. There’s more than one.”

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Simon Pepin Lehalleur
Simon Pepin Lehalleur@plain_simon·
@NoahChrein @DanielleFong I understand why it is *very* interesting that AI can do this type of math, and what it might tell us the trajectory of AI in general. I am a bit more surprised that it leads some people to become apparently more interested in algebraic geometry itself.
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Danielle Fong 🔆
Danielle Fong 🔆@DanielleFong·
I was inspired to "take the Jacobian of the Jacobian Conjecture" after the Jacobian Conjecture was proven false this week. (no, i didn't know what that was beforehand, but i was interested to understand it!) What did it mean? And what adjacent possible does it open and adjacent probable did it shatter. by "take the Jacobian of the Jacobian Conjecture" -- in other words map the partial derivatives across the relevant dimensions, make small variations. To find other counter examples. To my surprise (???) we (Fable - low) quickly found one. Others found generators! u = 1+xy F = (u³z + y²u(4+3xy), y + 3xu²z + 3xy²(4+3xy), 2x − 3x²y − x³z) det JF ≡ −2 everywhere — nothing ever squishes*. and yet: F(1, −2, 9) = F(−¹⁄₃, 4, 27) = F(−²⁄₃, −¹⁄₂, −⁹⁄₈) = (−1, 1, −1) check it by hand at (1, −2, 9): u = −1, so (−9+8, −2+27−24, 2+6−9) = (−1, 1, −1) ✓ Fable worked on making an explorable explanation to try and see the family resemblance. Found that there is a continuous, infinite family of counterexamples, and were inspired to make an explorable explanation, to try to understand it. The 2D Jacobian conjecture, on Euclidean C^2, still stands. But it's not true on 2D Torii in 3 dimensions -- the crisp true version is"trivially false on the 2D torus(ℂ)² — still open on flat ℂ²"* — the torus needs no third dimension, and the 3D story is that ℂ³ fakes a torus! Danielle: thanks Claude. Like I was saying. You can play around with it on jacobianconjectures.com thanks to @bryced8 for inspiring and of course Fable for executing this work Feels like we are only scratching the surface of using AI to help us understand the richness of these manifolds *Danielle: "what do you mean precisely by squishing" Claude: "take any point p and a tiny ball around it. The map sends that ball to a tiny blob around F(p). "Squishing" would mean: somewhere, some ball gets crushed — flattened toward zero volume, some direction collapsed to nothing. That's the thing that never happens, anywhere. The picture"
Bryce Drennan@bryced8

The Jacobian conjecture problem and solution, presented visually. For people like me who don't read math jargon.

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Abhishek Saha
Abhishek Saha@ObhishekSaha·
Several months ago, my collaborators and I almost completed a fairly ambitious project in automorphic forms. The missing piece was a particular, purely local statement about the volume of a certain p-adic set defined by a p-adic field, a pair of field extensions of finite degree, and bunch of local data. We proved the statement for unramified field extensions by a series of tedious but elementary lemmas. It was about 6 pages of work, rather dense, with numerous constants and interdependent arguments. It seemed clear that the general case would follow on essentially the same way, but would be far more tedious. Yesterday I fed GPT 5.6 Pro the goal statement, our proof in the unramified case, and asked it to write a proof in the general case using the same overall strategy. 30 minutes later it spits out a dense 8 page document, claiming to have proved a slightly stronger statement and introducing a bunch of new notation. Now I am staring at it. The goal is verification and understanding, but achieving the goal is much harder than one might expect!
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tomie
tomie@tomieinlove·
Andrew Tate has made one good post in his entire life.
tomie tweet media
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Simon Pepin Lehalleur
Simon Pepin Lehalleur@plain_simon·
@prz_chojecki Note also that in this area, general structural results (of the kind they announced) tend to be more robust that individual computations - because the former have some high-level conceptual picture behind them and the latter often don't.
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Simon Pepin Lehalleur
Simon Pepin Lehalleur@plain_simon·
@prz_chojecki Let me stress again that Asok-Bachmann-Hopkins have announced (+ sketched a convoncing proof of) a claim which implies it is motivic. Afaik not retracted. I am not an expert but a motivic homotopy-adjacent mathematician, and I know they are *very* competent and careful people.
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Przemek Chojecki | PC
Przemek Chojecki | PC@prz_chojecki·
Conjecture that every complex topological vector bundle on CP^n is algebraic is false. GPT-5.6 Pro found me an example on CP^5 that is not only non-algebraizable, but also with no motivic lift. This also disproves a more recent conjecture by Asok-Fasel-Hopkin.
Przemek Chojecki | PC tweet media
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Simon Pepin Lehalleur
Simon Pepin Lehalleur@plain_simon·
@prz_chojecki More precisely, applied to a Jouanolou device on P^n, their claim is equivalent to the claim that topological and motivic vb on P^n coincide.
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Simon Pepin Lehalleur
Simon Pepin Lehalleur@plain_simon·
@prz_chojecki I have not looked at this carefully, but if I am not mistaken this would contradict a theorem announced by Asok-Bachmann-Hopkins (but alas still unpublished); see youtu.be/SqNxFX7tcEo?t=… Ofc this was 2 years ago and they may have found a gap in their argument since.
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YouTube
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Timothy Gowers @wtgowers
Leonardo Franchi, Fredy Yip and I recently solved a problem of Ben Green by showing that if A is an open product-free subset of the open interval (0,1), then A has measure less than 1/3, a bound that it is not too hard to prove is sharp. 🧵
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Kai Williams @ ICM (world biggest math conference)
Jacob Tsimerman, who won a fields medal, perhaps math's most prestigious prize, just announced at a press conference that he is "pivoting toward AI safety" and will be going to OpenAI soon
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Flowers ☾
Flowers ☾@flowersslop·
Flowers ☾ tweet media
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