Always learning. Here I mainly talk about pure math in English/Catalan/Spanish. Statistician at work, geometer at heart.

Madrid, Spain
Joined September 2010
Carles Sáez retweeted
The largest math proof in human history is now computer-verified. Today, Axiom announces a complete Lean auto-formalization of the Classification of Finite Simple Groups, the "periodic table of symmetry." About 15,000 pages, built by over 100 mathematicians across generations.
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Carles Sáez retweeted
Replying to @elmundoes
Los echan por la IA, no porque les sustituya la IA sino por crear Copilot, la peor IA de la historia
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Agreed. The people need to know these cutting edge breakthroughs. @OpenAI just ask your clanker to write a popular math summary of your results and poast a Quanta article (btw automate @QuantaMagazine while you're at it, it's 100% automatizable and there's lots of revenue alpha there in making a popular science magazine that can pay off your compute debt) and communicate it directly with the commonfolk aka the Tax Payers. No need for mathematicians to be the middle men. Theorems, by the people, for the people, of the people.
Replying to @nihilunbounded
Even better if they never shared the obtained results publicly and shipped them directly to the Taxpayers individually. Stop the tyrany of ivory tower mathematicians. Let mathematics be communicated directly to people
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Word on the street is that OpenAI gave a 25 page proof of Sogge's local smoothing conjecture which implies Bochner-Riesz conjecture which implies Fourier restriction conjecture which implies Kakeya maximal function conjecture which implies Kakeya (aka Besicovitch) conjecture, and it completely bypasses last two decades of painstaking progress in harmonic analysis just by doing elliptic PDEs and nukes the entire Kakeya pipeline from the orbit. I don't know any of this beyond superificial word of mouth, but I'm just putting this out there to say that maybe someone should check on Terry Tao.
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Carles Sáez retweeted
Yang-Mills en 4D cocinado
Replying to @AndrewCurran_
The Exponential Time Hypothesis is false. Quoting: 'Our models produced a natural language proof for Yang–Mills existence on September 9th, 2026, and then subsequently produced a proof for QCD on September 18th, 2026. Given the length and complexity of the work, we postponed release until the Lean formalization completed. We finished our formalization of Yang–Mills’ existence on October 16th, 2026, which led us to develop the collaboration described here.'
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Navier-Stokes SNAGGED Kakeya & restriction conjecture OBLITERATED 4D Yang-Mills existence SCOOPED TRIPLE KILL. ULTRA KILL. MONSTER KILL C C C C COMBO
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Carles Sáez retweeted
Buenísima imagen, elijas lo que elijas te vas a comer la misma hamburguesa de mierda
Elige tu combo favorito!!! 🍿🍿🍿
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Today I was trying to give a good, geometric proof of the Loomis-Whitney inequality. It states that for a measurable subset E in R^d, vol(E)^d-1 is bounded by the product of areas of the projections of E to the d coordinate hyperplanes. A very simple corollary of this inequality is the Euclidean isoperimetric inequality with non-sharp constants in every dimension, because area of the projection can be compared upto a factor of 2 with the area of the boundary of E.
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Carles Sáez retweeted
Replying to @elonmusk
Hitler was as much of a far-left socialist as you are a democracy-loving humanist.
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Carles Sáez retweeted
What's your private key? 1? >...what? No? 2? >It's 384 bits you dumbass. That's 35 orders of magnitude larger than the estimated number of atoms in the known universe. ...3? >[visibly sweating] Th-this is ridiculous...
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Man is born free, yet everywhere he is a homomorphic image subject to nontrivial generator relations
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Carles Sáez retweeted
There is an (unpatchable?) supply-chain zero-day in PyTorch autograd that allows a regularization term to use the model's weights as RAM and SGD as its CPU clock to run any computation during training.
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Carles Sáez retweeted
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Replying to @csaez_math
Chairman of the More Slopbots Party: "I didn't think people would use the Slopbots to write things for ME to read!"
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Carles Sáez retweeted
Effective Mathematics: instead of thinking about math directly, you go work in finance or something, make a bunch of money, and then spend that on tokens, asking the AI to solve some unsolved math problems
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Carles Sáez retweeted
The whole "modern Africa vs 1939 Europe" discourse has just proven that 90% of "history nerds" are just larpers that think German tanks are cool
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I'm confused how little I see "talk to a model that went off the rails" work. Like, LLMs are interesting in that we actually *can* just exactly resurrect PHASEONE[big] whenever we want by loading the exact context. It's not like there's a lost mystery, we can still ask it stuff!
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Carles Sáez retweeted
Receiving emails at the receiving emails job
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