A “Feature” article in Nature (21 May 2026) and a long article in the New York Time (June 8, 2026) are both covering the sudden intrusion of AIs in proving or disproving mathematical conjectures… Genuine, hard, conjectures likes Erdös problems. Specialised AIs like Alethia, Math Inc., AlphaProof are hacking at existing open problems and a benchmark collection of problems whose solutions are not available (yet) called First Proof has been recently gathered, solved by OpenAI, and is soon to be extended. In an earlier interview with Nature (27 April 2026), Terry Tao acknowledges the tectonic shift represented by this intrusion and how a mathematician’s skill need evolve. (This is also the starting point of the NYT story. ) A side issue of this is that reviewing the proofs thus produced by an AI may prove inhumane if it reaches hundreds of pages, which also relates to the un-academic (?) tendency of AIs companies to over-blow the results produced by their machines. For the times they are a-Changin…
Archive for computer-based proof
AIs rushing to the proofs
Posted in Books, Kids, University life with tags AIs, Alethia, AlphaProof, Bob Dylan, computer-based proof, conjecture, Erdös problems, Fields medal, Math Inc., mathematics, Nature, NTY, OpenAI, Terry Tao, The New York Times on June 23, 2026 by xi'anNature snapshots
Posted in Books, Kids, pictures, Statistics, University life with tags AI, Bank of Sweden, computer-based proof, conjecture, cows, Daniel Kahneman, Emmanuel Macron, French politics, mathematics, Nature, Paris-Saclay campus, Pink Floyd, religious persecutions, SARS-CoV-2, Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, Vichy régime, WW II on July 13, 2024 by xi'an
- One of the editorials is about AI-assisted design of mathematical conjectures. Reminding me of grant panels I took part in where candidates in pure maths were often focussing on solving one or many conjectures, as opposed to more applied branches (like statistics).
- Two entries about France, one about Macron’s idea of a European DARPA, unlikely to convince European partners after his calling most unnecessarily an election and bringing the extreme-right to its apex since the Vichy régime. Another one about the super mega campus Paris-Saclay unable to settle on a form of leadership and hence elect a president. Federalist versus centralised… Once again, thanks to Macron’s reckless gamble, his current Ministry for Higher Education may be in need of a position next month and could return to heading the campus.
- Worrying coverage of bird flu in US cows (not yet pigs on the wing but worrying enough) and of zombie cells that should have died and that new treatments can fight way better.
- A reflection on coming up with a treaty against AI weapons with autonomous kill decisions but isn’t it too late?!
- Building design that would avoid total collapse of a failing building, as in South Florida four years ago. But solely for new ones, unfortunately. (And the connection with lizards escapes me, except for managing to escape by loosing a tail…)
- A biography of Daniel Kahneman, decision-theorist, 2002 Nobel economics (aka Bank of Sweden) Prize, author of Thinking, Slow and Fast, and spending the WW II in occupied France hiding from round-ups by the Vichy police.
séminaire P de S
Posted in Books, pictures, Statistics, University life with tags Biometrika, computer-based proof, extreme value theory, Institut Henri Poincaré, neural network, Paris, probabilistic numerics, séminaire, seminar, stochastic gradient descent on February 18, 2020 by xi'an
As I was in Paris and free for the occasion (!), I attended the Paris Statistics seminar this afternoon, in the Latin Quarter. With a first talk by Kweku Abraham on Bayesian inverse problems set a prior on the quantity of interest, γ, rather than its transform G(γ), observed with noise. Always perturbed by the juggling of different distances, like L² versus Kullback-Leibler, in non-parametric frameworks. Reminding me of probabilistic numerics, at least in the framework, since the crux of the talk was 100% about convergence. And a second talk by Leanaïc Chizat on convex neural networks corresponding to an infinite number of neurons, with surprising properties, including implicit bias. And a third talk by Anne Sabourin on PCA for extremes. Which assumed very little on the model but more on the geometry of the distribution, like extremes being concentrated on a subspace. As I was rather tired from an intense week at Warwick, and after a weekend of reading grant applications and Biometrika submissions (!), my foggy brain kept switching to these proposals, trying to make connections with the talks, not completely inappropriately in two cases out of three. (I am afraid the same may happen tomorrow at our probability seminar on computer-based proofs!)
