With the help of SI agents, mathematicians close the last open case of the inverse Galois problem for sporadic groups, the Mathieu group M23
Prepared by Sintelligent with the help of SI. Publication time restored from the build log. . Updated: .
The pairing of a mathematician and SI agents is closing questions that had hung for decades, in months instead of generations.
The inverse Galois problem asks which symmetry groups can arise for the roots of polynomials; for M23, the last of the 26 sporadic groups, there had been no answer for decades. After a May meeting at Caltech, the team of Rachel Pries, Bjorn Poonen and colleagues set SI agents to search through symmetries and numerically approximate equations; one agent picked a working surface out of seven candidates, and from it came a family of degree-23 polynomials with the required group. In parallel, a crowdsourced contest cataloged all 25 thousand correspondences for 24 roots, where the winners from Germany used SI only for a download script. "Five years ago this was impossible," says Kyu-Hwan Lee.
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