The SAIR Foundation’s international Inverse Galois Problem (IGP24) competition took place from June 16 to August 15, 2026.
The goal was to construct number fields of degree 24 over the rational numbers for every possible pairing of Galois group of the Galois closure and signature. Part of the challenge lay in the fact that there are 25,000 distinct transitive permutation groups of degree 24, resulting in a total of 165,836 possible signatures.
140 teams from around the world participated in the competition, partly with heavy use of AI tools. Jürgen Klüners (Paderborn) and Gunter Malle won the challenge by a wide margin, having found 143,364 fields.
Crucial to this success were the Oscar programs for constructing relatively cyclic extensions of number fields — originally written by Carlo Sircana during his doctoral studies supervised by Claus Fieker within project B2 of SFB/TRR 195 — which were further expanded, adapted, and improved for the competition. Furthermore, the extensive polynomial database created and maintained by Klüners and Malle was utilized so intensively — and not just by the winning team — that access to it was temporarily unavailable. An interview on this topic with Jürgen Klüners and Gunter Malle can be found here.