On February 12th 2026 Prof. Dr. Sebastian Pokutta gave an interesting lecture entitled “How Machines Explore, Conjecture, and Discover Mathematics.” This Munich AI Lecture was suppported by BAIOSPHERE and our projekt!
In this talk, Prof. Pokutta illustrated this paradigm through a concrete case study: the Hadwiger–Nelson problem, a long-standing open problem in discrete geometry and extremal combinatorics concerning colorings of the plane without monochromatic unit-distance pairs. He showed how neural networks can serve as expressive approximators that transform a mixed discrete–continuous geometric problem with hard constraints into a differentiable optimization problem with a probabilistic loss. This approach enables gradient-based exploration of admissible configurations and has led to the discovery of two novel six-colorings—marking the first improvement in thirty years for the off-diagonal variant of the problem.
Date
12th February, 2026
Location
D 209, LMU Main Building, Geschwister-Scholl-Platz 1
80539 Munich
