I was contributor to the Project Numina and FrontierMath projects.
Join to our Mathematics and AI Zulip organisation!
ProofCouncil: https://arxiv.org/abs/2607.09474
ProofCouncil is an agentic harness we developed for a submission to the second batch of FirstProof, a challenge consisting of 10 real-world mathematical problems that agents must solve autonomously. Its submissions for 6 of the 10 problems were judged by the referees to be correct up to at most minor revisions, showing the best performance among participating teams.
Two Google DeepMind papers on AI and mathematics
Two Google DeepMind papers related to AI-assisted mathematical research are now available.
I am a co-author of DeepMind's new AlphaProof Nexus paper
I was also among early mathematicians who tested and gave feedback on DeepMind's AI Co-Mathematician system.
These works raise many important questions for the mathematics community about collaboration with AI systems, verification, access to computation, and the future practice of mathematical research.
Two preprints on AI-assisted algebraic geometry
(with Y-H Kiem) Real-rootedness of the Poincaré polynomial of moduli of curves: an AI-assisted proof. https://arxiv.org/abs/2605.29151
This is a really charming, emerging story in AI-assisted algebraic geometry. Combining DeepMind's AlphaEvolve and Co-Mathematician systems with human insight, we managed to prove a conjecture of Aluffi--Chen--Marcolli on the real-rootedness of the Poincaré polynomial of the Deligne--Mumford moduli space of genus zero curves with n marked points. The AI system found a two-dimensional deformation of the Poincaré polynomial with real root branches, and topology of these branches provides the key argument. In a follow-up paper we will give full topological description of the coefficients of this deformation, and generalize the result to other moduli spaces.
(with László Fehér) Positivity in classical enumerative geometry: a case study in synchronized AI-assisted mathematics. https://arxiv.org/abs/2605.25271
We designed an exciting workflow which combines various AI systems to prove classical positivity conjectures in algebraic geometry. We tested the strengths and limits of these tools. We provided a detailed overview of how this AI-assisted approach lead to progress, highlighting the parts where human mathematical verification remained essential.
My AlphaEvolve experiments series: This series of papers grows out of my experiments with AlphaEvolve, an evolutionary search model by DeepMind. My choice of problems is deliberate: I focus on deep questions that require substantial mathematical and engineering work, precisely to see how the model behaves when things are genuinely hard. Using AlphaEvolve in these problems is far from straightforward and it requires careful design and a fair amount of mathematical insight. I am a geometer who has been working with machine learning and reinforcement learning in recent years, and I see this project as a hands-on attempt to probe classical problems using experimental, AI-driven tools.
Paper 1: Evolving Ranking Functions for Canonical Blow-Ups in Positive Characteristic, arxiv.2602.06553
Paper 2: Evolving Local Corrections for Global Constructions in Combinatorics, arXiv:2603.06692
IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation
(with J. Schmitt, J. Dekoninck, J. Feusi, T. Gehrunger, et al****.)
preprint, NeurIPS Math-AI Workshop, 2025
Flow-based Extremal Mathematical Structure Discovery, arXiv.2601.18005, Oberwolfach talk, github repo
In this joint project with Jonas Klüver (Aarhus) and Baran Hashemi (MPI Leipzig), we introduce FlowBoost, a flow-based evolutionary search model. We aim to extend the PatternBoost method to continuous optimization problems. We are developing a pipeline to address the following general question: given a bounded domain in R^d and a target function f(x_1, ..., x_n) defined on n points in R^d, how can we find the optimal arrangement of these points in the domain that minimizes or maximizes the target function? Examples include classical packing problems, such as sphere packings in cubes, the Heilbronn problem and finding points sets with minimal star discrepancy.
Resolution of singularities: Github repo , ICML 2023 paper: arXiv:2307.00252
In this joint project with Honglu Fan (Geneva) and Mingcong Zeng (Bonn) we search for optimal resolutions of singularities using reinforcement learning, through the Hironaka game. In 1964 Hironaka proved that it was possible to resolve singularities of varieties over fields of characteristic 0 by repeatedly blowing up along non-singular subvarieties, using a very complicated argument by induction on the dimension.
The process can be translated into various versions of a 2-player game, the so-called Hironaka game, and a winning strategy for the first player provides a solution to the resolution problem. In this paper we introduce a new approach to the Hironaka game that uses reinforcement learning agents to find optimal resolutions of singularities.
As application, we derive new formulas for Thom polynomials and integrals over Hilbert scheme of points on manifolds based on blow-up trees generated from different versions of the Hironaka resolution game.
Stanley-Stembridge chromatic positivity conjecture, Github repo, preprint arXiv:2410.19189 , Proceedings of the Harvard Mathematics and Machine Learning Program, 2024
Joint project with Jonas Klüver. We develop an ML assisted proof to a central problem in combinatorics, the Stanley positivity conjecture on chromatic polynomials of graphs. Based on recent work of Szenes, Paunov and Rok we develop a graph reinforcement learning agent to find combinatorial interpretation of the coefficients of the chromatic symmetric function.
Small Percolating Sets on Hypercubes via Generative AI , preprint arXiv:2411.19734
Joint project with Adam Zsolt Wagner (Worcester/DeepMind) We apply a generative AI pattern-recognition technique called PatternBoost to study bootstrap percolation on hypercubes. With this, we improve the best existing upper bound for the size of percolating subsets of the hypercube.
Voice cloning: Github repo
Joint project with Jonas Klüver (Aarhus). We use MFCC technology and PixtoPix deep network for voice adapting.
Regularization via complete collineations, preprint arXiv:2311.03329
In this joint work with with E. Hamilton, P. Reichenbach and A. Seigal we uncover connections between maximum likelihood estimation in Gaussian graphical models described by directed acyclic graphs and GIT stability properties of sample points. As a result we develop a new regularization method in ML and statistics, extending Tikhonov regularization.