On October 27th, 2026 I will give a talk in the Mathematical Colloquium of the Ludwig-Maximilians-Universität in Munich.

The boundaries of mathematics - from Gödel to the study of large infinities

After proving that not all statements in mathematics can be proven or disproven from the accepted ZFC axioms, Gödel raised the question whether natural statements, such as Cantor’s continuum hypothesis, can be decided via extending the axiomatic framework by axioms of large infinities. While this question has been answered in the negative for large infinities, the problem of finding good axioms that decide natural mathematical statements remains open. There are several compelling candidates that we will motivate and describe, together with strong evidence for them provided by recent advances in set theory as well as their impact on other areas of mathematics.