|
Résumé |
I will describe how one can use modern AI methods to attack open problems in
mathematics, specifically in group theory. I will show how in this setting ideas
from AI, pure math, integrability, string theory, and quantum information meet in
a concrete and computational way. I will focus on widely studied combinatorial
objects known as Cayley graphs, which encode key properties of finite groups but
are often very hard to explore due to their enormous size. I will describe how a
modern ML approach overcomes this challenge and provides efficient pathfinding on
these huge graphs. The outcome is a large set of new results and conjectures that
in particular significantly sharpen famous bounds on the geometry of these graphs.
Surprisingly, these results suggest the existence of a novel, discrete string-like
duality for this setting. It provides a direct realisation of the paradigm
"complexity = volume" from AdS/CFT holography, and could potentially be applicable
to a wider range of AI tasks. Based on arXiv:2509.19162, 2603.22195. |
