Commentary

The inverse Galois problem asks whether every finite group occurs as the Galois group of some finite Galois extension of ℚ. The program to realize the sporadic finite simple groups as Galois groups over ℚ began in 1984. Over the following years, every case except M_23 was solved, leaving M_23 as the last open case for nearly four decades. Our recent preprint, joint with Xiaoyu Huang, Blake Jackson, Kyu-Hwan Lee, Bjorn Poonen, and Rachel Pries, resolves this fi