Alexander Engel – SPP 2026

AI achieves silver-medal at IMO

Google developed AI models that achieved on this year’s IMO questions a silver-medal (with only one point away from a gold-medal). You can read more about it in this blog post of Google: link. The for me most interesting thing in this news is not that it achieves a silver-medal, but how the system works, … Continue reading

All triangulations have a common stellar subdivision

Already in April a paper was put on the arXiv (2404.05930) by Karim Adiprasito and Igor Pak proving the following result: Every two triangulations of a geometric complex in Euclidean space have a common stellar subdivision. At first I was a bit confused, because my mind connected this to the Hauptvermutung, which was disproven a … Continue reading

Cantor-Medaille 2024 für Felix Otto

Felix Otto bekommt die Cantor-Medaille der Deutschen Mathematiker-Vereinigung (DMV) für herausragende wissenschaftliche Leistungen […] von außergewöhnlicher Tiefe und höchstem Einfluss für das Gebiet der Analysis und die Partiellen Differentialgleichungen (Pressemitteilung).

Sergei Novikov 1938 – 2024

A week ago Sergei Novikov passed away. He was a notable mathematician working in topology. The conjecture he posed in 1965 about the homotopy invariance of higher signatures of manifolds is one of the most important unsolved problem about the topology of manifolds. An obituary (in Russian) may be found here: link.

Kervaira invariant one problem

Last month a solution to the Kervaire invariant one problem in the final remaining dimension 126 was announced (link to a mathstodon post). I have already mentioned this problem in an earlier post here: link (2nd paragraph about the 2-line).

Shaw Prize 2024

The Shaw Prize in Mathematical Sciences 2024 is awarded to Peter Sarnak for his development of the arithmetic theory of thin groups and the affine sieve, by bringing together number theory, analysis, combinatorics, dynamics, geometry and spectral theory.

Jim Simons 1938 – 2024

Three days ago Jim Simons passed away. He was a great mathematician (the Chern-Simons form is named after him together with Shiing-Shen Chern) and the most successful hedge fund manager of all time (citation from wikipedia). Together with his wife he founded the Simons Foundation whose mission is to advance the frontiers of research in … Continue reading

Blaschke’s Inclusion Theorem

An extremely classical theorem from planar geometry is the following one: If \(B_1\) and \(B_2\) are two strictly convex, compact planar domains with smooth boundaries touching at some point \(p \in \partial B_1 \cap \partial B_2\) with common inner normal, then \(B_1 \subset B_2\) provided that the curvatures \(k_i(\nu)\) of the boundaries satisfy \(k_1(\nu) \ge … Continue reading