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Une infinité d'autres mondes sont possibles, et dans aucun l'ordre ne règne! images.math.cnrs.fr/+Un-autr…
Pierre Colmez 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.
Forbidding papers not written in American English seems to have improved the level of submissions to @arxiv considerably:
arxiv.org/abs/2209.01890
A clever use of ChatGPT to desloppify its output (see p.4).
hexagonmath.org/pdf/2610.002…
Pierre Colmez retweeted
How often do ArXiv papers contain errors in the main theorems they claim to prove? Using GPT-6.1 Sol to identify such mistakes, it finds:
- 6% of papers before 08/2026 contain main theorems that are false.
- Only 1.5% contain similar mistakes in the last two months.
That was quick !
hexagonmath.org/2610.00200v1
It seems that the standards for mathematical writing have been drastically lowered since then...
Almost as demanding as writing a math paper.
xitter.cf/XiaoJi0403/status/2050…
Pierre Colmez retweeted
Here is a Short Proof of the Quasi-Riemann Hypothesis.
My goal here is to substantially simplify OpenAI’s proof and focus only on proving the Quasi-Riemann Hypothesis for some 1-c, without worrying about maximizing the value of the c.
I obtained a much shorter proof for c=1/48. This proof is easy to understand and it can be taught in math courses in one lecture.
It is self-contained. It is only 21 pages including abstract, proof overview, all proof details and references.
Paper is on my homepage: shivakintali.github.io
PDF file: shivakintali.github.io/paper…
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We’re releasing a broad range of new mathematical results produced by an internal frontier model.
We’ve been consulting with the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study, and we have drawn on their advice and public recommendations to inform how we release these results.
github.com/openai/math
"the most significant moment in mathematical history" like "being bombed was the most significant moment in the history of Hiroshima"
Big, big, big, big props for quasiriemann and no Siegel zeroes (with many other beauties in there), I’m kicking myself for talking all over about it being within reach but not actually having pushed.
There are some sad stories related to their users getting scooped / conflicts of interest (kakeya maximal comes to mind), and obviously we had some of the problems (without commenting on precise rumours).
We should put that aside for today though. It’s obviously the most significant moment in mathematical history.
Pierre Colmez retweeted
TIL in 1830 half the students at Yale were expelled because they didn't want to use new tech -- the blackboard -- for math exams
Pierre Colmez retweeted
ChatGPT has now a big problem.
Researchers at Oxford and Cambridge exposed a massive threat to large language models.”
They call it “model collapse."
Internet ecosystem is rapidly changing, and generative AI will soon contribute much of the text found online. This forces us to consider what happens to future iterations like gpt-n when they are trained on data scraped from the web that was already generated by an llm.
According to the research, indiscriminately using model-generated content in training causes "irreversible defects" in the resulting ai. the model loses the "tails of the original content distribution." in other words, it begins to forget the creative, fringe, and unique nuances of actual human writing, collapsing into a repetitive echo chamber.
This isn't just a chatgpt issue.. the researchers built theoretical intuition showing this collapse is ubiquitous across learned generative models, occurring in large language models as well as in variational autoencoders and gaussian mixture models.
Tech companies rely on scraping the internet for large-scale data to build smarter models. However, the paper warns that if we want to sustain the benefits of training on web data, model collapse must be taken seriously.
Ultimate takeaway? data collected from genuine human interactions is going to become increasingly valuable in a web filled with ai content.
ChatGPT, just 6 months ago...
xitter.cf/ColmezPierre/status/20…
I thought that banning submissions not written in american english was supposed to fix this problem...
We are seeing a new trend in submissions to @arxiv (and presumably to conferences and journals): Authors submitting papers whose contents they likely do not understand. 1/
Pierre Colmez retweeted
Without commenting on the correctness of this claim, I want to briefly say a few words about what it would mean in practice.
Chess is supportable as a hobby in part because one can pick up the rules of chess in an afternoon. While one can't quickly play at a high level, it is relatively easy to appreciate the game, and have fun at it.
Research math is not like this. Over the last decades we have made incredible progress understanding basic concepts (number, shape, etc.) but the edifice we have built to do so requires an incredible time investment. Learning the ideas that go into proving, or understanding the proof of, basic statements like Fermat's last theorem requires years of institutional support.
It's possible that soon, AI will be able to do work at this level; despite recent successes, this isn't the case yet. But even if it can do this, why would it? Without people who care about these deep but fundamental ideas, who will ask it to? Perhaps it might on its own, or a person asking it to "do some cool math" might elicit a similarly deep idea, but who would understand it, if doing so requires years of unsupported work?
In practice, turning pure math into a hobby means the end of pure math, and the end of people who understand basic mathematical concepts at a deep level. Whether this is something we want is something we'll have to decide together.
First time that I receive an offer, by a graduate student, to collaborate on an AI-assisted project to solve a problem for which I have no particular competency (or appetite)...
If I were to bet, I would bet that they did not make any progress towards BSD. Maybe they can prove that BSD is true for 100% of elliptic curves (asymptotically), but this would not bring us 1mm closer to a proof of BSD.
I am told the Hodge Conjecture is very close to being verified by OpenAI, and that one of OpenAI or Anthropic are also close to solving Birch-Swinnerton-Dyer. The race to be 'next' behind the scenes is unlike anything I've had described to me before
If true - and it may not be, given the scale of the rumour mill right now - it could mean 3 Millennium Problems fall in the space of a month. Crazy times





















