François Charton

AI for mathematics and theoretical physics
Tomorrow's problems on yesterday's machines
Axiom - École nationale des ponts et chaussées

[François Charton @f_charton]

Using our own prover to discover new mathematics!

[Axiom @axiommathai]

1/ Since February, 8 papers across algebraic geometry, representation theory, number theory, combinatorics have been quietly appearing on arXiv.

Proofs by AxiomProver.

5 papers are now accepted at solid peer-reviewed math journals. To our knowledge, a first for the literature.

[François Charton @f_charton]

@Fabien_Mikol @yanndubs Ca reste capricieux. En raisonnement, après un certain temps, les modèles de RL s’effondrent, en produisant des chaînes de plus en plus courtes. Ça n’est pas très documenté: les petites équipes ne le voient pas, les grosses ne s’en vantent pas. Mais c’est bien réel.

[Gary Shiu @gary_shiu]

It's my pleasure giving the opening talk of the Strings and Geometry Conference: https://t.co/ri2tYXMmpP where I presented joint work with Jacky Yip and Alessandro Mininno @UWMadPhysics and collaborators @arnal_charles @Meta @f_charton @axiommathai

[François Charton @f_charton]

@Simi_2210_ 170: 160+10 (sum of digits of previous number)
25 = 20 +1+4
47=40+2+5
91=80+4+7
170=160+9+1

[François Charton @f_charton]

@rvleroux On le voyait en première, mais le réflexe de l’utiliser venait plutôt en terminale ou en prepa

[François Charton @f_charton]

Axplorer: an open source library for constructing interesting mathematical objects (and attacking really hard problems).

Have fun!

[Axiom @axiommathai]

We open-sourced Axplorer.

Axplorer builds on PatternBoost; it discovers outlier math constructions to attack open problems.

On Turán 4-Cycles, No 5 Points on Sphere, and Isosceles-Free Sets, Axplorer matched SOTA w/ a fraction of compute cost and time.

It's now in your hands.

[François Charton @f_charton]

Announcing our series A, and a great video!

[Axiom @axiommathai]

Axiom launched six months ago with one conviction: mathematics is the right foundation for building systems that reason.

Today we announce Axiom's Series A.

We raised $200M at a $1.6B+ valuation, led by @MenloVentures, to extend our lead in formal mathematics into Verified AI.

[François Charton @f_charton]

Verified mathematical discovery. An impressive first !

[Axiom @axiommathai]

1/ AxiomProver has solved Fel’s open conjecture on syzygies of numerical semigroups, autonomously generating a formal proof in Lean with zero human guidance.

This is the first time an AI system has settled an unsolved research problem in theory-building math and self verifies.

[François Charton @f_charton]

Lyapunov follow up

[François Charton @f_charton]

@FranNunesEcon @axiommathai @albe_alfa @antimath3 It is in AIAS, please visit us

[François Charton @f_charton]

The Lyapunov team reunited in Aarhus

[François Charton @f_charton]

In Aarhus for the AI and math workshop, our regular meeting of the AI for math discovery community (after Seoul last July and Oberwolfach last September). Can’t attend? The talks will be recorded and broadcast on the Youtube channel of Aarhus University.

[Axiom @axiommathai]

1/ We’re proud to announce the Aarhus Math&AI Workshop, sponsored and co-organized by Axiom.

Speakers include Fields Medalists Terence Tao and Maryna Viazovska✨

From Axiom: Francois Charton @f_charton, Alberto Alfarano @albe_alfa, Seewoo Lee @antimath3

See you in Denmark! ❄️

[François Charton @f_charton]

@jdlichtman @thomasfbloom Three years ago (five, even), it was already pretty obvious for most practitioners of AI for maths.

[François Charton @f_charton]

@antimath3 See you there!

[François Charton @f_charton]

@RomainPete98794 I don’t think there is a continuity. They are different parts of a mathematician’s job. But they are not completely unrelated either: a new idea, a conjecture, must eventually be derived or proved, with techniques similar to those one uses to solve Putnam problems.

[François Charton @f_charton]

Our results on the latest Putnam challenge, together with the proofs and a discussion.

[Axiom @axiommathai]

1/ AxiomProver got 12/12 of Putnam 2025. Today we release the Lean proofs AxiomProver generated autonomously.

We also provide our take of the problems, proof visualizations, and compare how humans vs AI approach differently. Tons of fun math and Lean!

Our findings in thread.

[Axiom @axiommathai]

For more info, here's a video of Francois @f_charton speaking at the renowned Kavli Institute for Theoretical Physics (Collatz starts 40'49''):
https://t.co/INKsSOxw6n

The talk also covers other discovery work: Lyapunov functions, PatternBoost, generating Calabi-Yau manifolds.

[François Charton @f_charton]

@zavaindar Pivot to AI for Maths: it a lot more fun!

[François Charton @f_charton]

Curious about AI discovering new maths? Come join us!

[Axiom @axiommathai]

9/ Axiom's discovery team @f_charton @albe_alfa @KenOno691 is currently looking for a highly selected group of PhD interns.

We are searching for candidates with advanced mathematics and strong machine learning backgrounds.

Apply: https://t.co/HFolsmmVnV
📧 [email protected]

[François Charton @f_charton]

A blog post about our recent Collatz paper
https://t.co/IwboAUvWAh

[Axiom @axiommathai]

1/ The Collatz conjecture has humbled mathematicians for near 90 years. Paul Erdös said "mathematics is not yet ready for such problems." 🧵

So we handed it to transformers. What they learned stunned us!

New research from Axiom's math discovery team, blog live this morning.