AI for mathematics and theoretical physics Tomorrow's problems on yesterday's machines Axiom - École nationale des ponts et chaussées
France
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I have little to contribute on the AI and maths debate, everything is too confused and fast-moving. Yet, I keep noticing that the arguments put forth by mathematicians critical of AI are always more interesting than their counters from AI fans..
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Number theorists, applied mathematicians, AxiomProver, a lot of compute, and a world record. Human-AI collaboration at its best!
1/ ✨ World record today on bounded gaps between primes, one of number theory’s oldest open conjectures.
We show that infinitely many pairs of prime numbers are separated by 212 or less.
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Using our own prover to discover new mathematics!
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.
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François Charton retweeted
It's my pleasure giving the opening talk of the Strings and Geometry Conference: indico.uu.se/event/1912/ where I presented joint work with Jacky Yip and Alessandro Mininno @UWMadPhysics and collaborators @arnal_charles @Meta @f_charton @axiommathai
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Axplorer: an open source library for constructing interesting mathematical objects (and attacking really hard problems).
Have fun!
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.
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Announcing our series A, and a great video!
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.
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Verified mathematical discovery. An impressive first !
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.
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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.
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! ❄️
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Our results on the latest Putnam challenge, together with the proofs and a discussion.
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.
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François Charton retweeted
For more info, here's a video of Francois @f_charton speaking at the renowned Kavli Institute for Theoretical Physics (Collatz starts 40'49''):
online.kitp.ucsb.edu/online/…
The talk also covers other discovery work: Lyapunov functions, PatternBoost, generating Calabi-Yau manifolds.
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.
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Curious about AI discovering new maths? Come join us!
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: axiommath.ai/join-us
📧 careers@axiommath.ai
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A blog post about our recent Collatz paper
axiommath.ai/territory/learn…
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.
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And here we go !!
Putnam, the world's hardest undergrad math contest, ended 4pm PT yesterday.
By 3:58pm, AxiomProver @axiommathai autonomously solved 8/12 of Putnam2025 in Lean, a 100% verifiable language.
Last year, our score would've been #4 of ~4000 and a Putnam Fellow (top 10 in recent yrs)
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François Charton retweeted
I've spent my career thinking about hard math problems.
I am excited to share that I've joined Axiom @axiommathai as Founding Mathematician working with my former student @CarinaLHong.
AI for mathematical discovery in WSJ today.
AxiomProver keeps getting stronger.
And @axiommathai keeps growing.
I'm excited to share that Prof. Ken Ono @KenOno691 has joined Axiom as Founding Mathematician and FTE #15.
He left his tenured position as STEM Advisor to Provost at UVA to build an AI mathematician with us.
Here's Ken's story. (1)
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Very excited to have @KenOno691 in Axiom! Looking forward to many collaborations.
AxiomProver keeps getting stronger.
And @axiommathai keeps growing.
I'm excited to share that Prof. Ken Ono @KenOno691 has joined Axiom as Founding Mathematician and FTE #15.
He left his tenured position as STEM Advisor to Provost at UVA to build an AI mathematician with us.
Here's Ken's story. (1)
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