Adam Zsolt Wagner

About me

I am a research scientist at Google DeepMind, working on using AI for mathematical reasoning. Until recently, I was an assistant professor of mathematics at Worcester Polytechnic Institute.

While I still mostly consider myself a mathematician, in recent years the focus of my work has heavily shifted towards finding new and fun ways to use computers in mathematics research. This includes using reinforcement learning methods so programs can learn disprove open conjectures by themselves, exploring how generative ML methods can be used to attack open problems, and other ways machine learning can be used to guide our intuition.

My full CV.

Publications: Scholar, arXiv

Email: azwagner@google.com

Math-AI Publications

Proceedings of the London Mathematical Society, 2025	Advancing Geometry with AI: Multi-agent Generation of Polytopes Grzegorz Swirszcz, Adam Zsolt Wagner, Geordie Williamson, Sam Blackwell, Bogdan Georgiev, Alex Davies, Ali Eslami, Sebastien Racaniere, Theophane Weber and Pushmeet Kohli [arXiv]
arXiv 2024	PatternBoost: Constructions in Mathematics with a Little Help from AI Francois Charton, Jordan Ellenberg, Adam Zsolt Wagner and Geordie Williamson [arXiv]
NeurIPS Math-AI 2023	Finding Increasingly Large Extremal Graphs with AlphaZero and Tabu Search Abbas Mehrabian, Ankit Anand, Hyunjik Kim, Nicolas Sonnerat, Matej Balog, Gheorghe Comanici, Tudor Berariu, Andrew Lee, Anian Ruoss, Anna Bulanova, Daniel Toyama, Sam Blackwell, Bernardino Romera Paredes, Petar Veličković, Laurent Orseau, Joonkyung Lee, Anurag Murty Naredla, Doina Precup and Adam Zsolt Wagner [arXiv]
arXiv 2021	Constructions in combinatorics via neural networks Adam Zsolt Wagner [arXiv] Quanta article

Selected math-AI talks with videos

Finding interesting mathematical objects with ML (NeurIPS Math-AI workshop, 2024)

We have seen that we can achieve good results in mathematics by using some very simple ML tools. In this talk, I will show you how adding just a little bit of complexity to our setups can drastically improve our results. With every extra idea we introduce, the door to the possibilities of what kinds of problems we can successfully tackle will open rapidly. By the end of the talk, we will have reached the algorithm that has successfully solved a genuinely important open problem in mathematics and complexity theory.

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Finding counterexamples to conjectures via reinforcement learning (IPAM, 2023)

We use a simple reinforcement learning setup to find explicit constructions and counterexamples to several open conjectures in extremal combinatorics and graph theory. Amongst the conjectures we refute are a question of Brualdi and Cao about maximizing permanents of pattern avoiding matrices, and several problems related to the adjacency and distance eigenvalues of graphs. You do not need to know much about machine learning or maths to be able to follow this talk, I explain everything from the basics!

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Math Publications

Proceedings of the AMS 2024+	The extremal number of Venn diagrams Peter Keevash, Imre Leader, Jason Long and Adam Zsolt Wagner [arXiv]
JCTB 2024	Intersecting families of sets are typically trivial Jozsef Balogh, Ramon I. Garcia, Lina Li and Adam Zsolt Wagner [arXiv]
Electronic Journal of Combinatorics 2023	Balanced edge-colorings avoiding rainbow cliques of size four Felix Clemen and Adam Zsolt Wagner [arXiv]
JCTA 2022	Infinite Sperner's theorem Benny Sudakov, Istvan Tomon and Adam Zsolt Wagner [arXiv]
Random Structures & Algorithms 2022	Uniform chain decompositions and applications Benny Sudakov, Istvan Tomon and Adam Zsolt Wagner [arXiv]
Electronic Journal of Combinatorics 2020	Bounded Degree Spanners of the Hypercube Rajko Nenadov, Mehtaab Sawhney, Benny Sudakov and Adam Zsolt Wagner [arXiv]
Israel Journal of Mathematics 2020	Nearly-linear monotone paths in edge-ordered graphs Matija Bucic, Matthew Kwan, Alexey Pokrovskiy, Benny Sudakov, Tuan Tran and Adam Zsolt Wagner [arXiv]
JCTA 2020	Refuting conjectures in extremal combinatorics via linear programming Adam Zsolt Wagner [arXiv]
JCTB 2020	Completion and deficiency problems Rajko Nenadov, Benny Sudakov and Adam Zsolt Wagner [arXiv]
Electronic Journal of Combinatorics 2020	The Ramsey Number of Fano Plane Versus Tight Path Jozsef Balogh, Felix Klemen, Jozef Skokan and Adam Zsolt Wagner [arXiv]
Journal of Graph Theory 2020	Families in posets minimizing the number of comparable pairs Jozsef Balogh, Sarka Petrickova and Adam Zsolt Wagner [arXiv]
arXiv 2019	The performance guarantee of randomized perfect voting trees Jason Long and Adam Zsolt Wagner [arXiv]
European Journal of Combinatorics 2019	The largest projective cube-free subsets of Z_{2^n} Jason Long and Adam Zsolt Wagner [arXiv]
JCTA 2019	Partition problems in high dimensional boxes Matija Bucic, Bernard Lidicky, Jason Long and Adam Zsolt Wagner [arXiv]
Discrete Mathematics 2019	Turan numbers for Berge-hypergraphs and related extremal problems Cory Palmer, Michael Tait, Craig Timmons and Adam Zsolt Wagner [arXiv]
arXiv 2019	A note on some conjectures about combinatorial models for RNA secondary structures Adam Zsolt Wagner [arXiv]
Electronic Journal of Combinatorics 2019	Monochromatic Hilbert cubes and arithmetic progressions Jozsef Balogh, Mikhail Lavrov, George Shakan and Adam Zsolt Wagner [arXiv]
Combinatorics, Probability and Computing 2018	Tilings in randomly perturbed dense graphs Jozsef Balogh, Andrew Treglown and Adam Zsolt Wagner [arXiv]
Advances in Mathematics 2018	Kleitman's conjecture about families of given size minimizing the number of k-chains Jozsef Balogh and Adam Zsolt Wagner [arXiv]
Discrete Applied Mathematics 2018	Two results about the hypercube Jozsef Balogh, Tamas Meszaros and Adam Zsolt Wagner [arXiv]
Bul. of the London Math. Soc. 2017	An improved lower bound for Folkman's Theorem Jozsef Balogh, Sean Eberhard, Bhargav Narayanan, Andrew Treglown and Adam Zsolt Wagner [arXiv]
Journal of Graph Theory 2017	Large subgraphs in rainbow-triangle free colorings Adam Zsolt Wagner [arXiv]
Israel Journal of Mathematics 2017	On the number of union-free families Jozsef Balogh and Adam Zsolt Wagner [arXiv]
Random Structures & Algorithms 2016	Applications of Graph Containers in the Boolean Lattice Jozsef Balogh, Andrew Treglown and Adam Zsolt Wagner [arXiv]
Recent Trends in Combinatorics 2016	Further applications of the Container Method Jozsef Balogh and Adam Zsolt Wagner [arXiv]
Discrete Mathematics 2015	Cops and Robbers on diameter two graphs Adam Zsolt Wagner [arXiv]
-	Pursuit on Graphs (Master's thesis) Adam Zsolt Wagner [pdf]

Selected math talks with videos

The largest projective cube-free subsets of $Z_{2^n}$ (IBS, 2020)

What is the largest subset of $Z_{2^n}$ that doesn’t contain a projective $d$-cube? In the Boolean lattice, Sperner’s, Erdos’s, Kleitman’s and Samotij’s theorems state that families that do not contain many chains must have a very specific layered structure. We show that if instead of $Z_{2^n}$ we work in $Z_{2^n}$, analogous statements hold if one replaces the word $k$-chain by projective cube of dimension $2^{k-1}$. The largest $d$-cube-free subset of $Z_{2^n}$, if $d$ is not a power of two, exhibits a much more interesting behaviour.

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