Mathematicians and AI crack a long-open problem on symmetries hidden in polynomial solutions

Scientific American reports that mathematicians combining their own insight with AI have solved a decades-old problem about the symmetries in the solutions of polynomial equations. The effort grew out of a sprint in May, when the American Institute of Mathematics gathered mathematicians at the California Institute of Technology. The institute asked for problems suited to AI's ability to search possibilities at a scale beyond human capacity. Rachel Pries, a mathematician at Colorado State University, presented one of the strongest candidates. It concerned the deep connections between polynomial equations, such as 4x² − 1 = 0, and the symmetries buried in their solutions. "This problem had been open for a very, very long time," she said. The magazine reports that within a few months of the meeting, the problem was solved by combining human insight with AI. In a separate effort, amateurs and mathematicians raced to find all 25,000 cases of one "inverse Galois problem," which asks which symmetry groups can arise from polynomial equations. The work is a documented example of AI used as a search tool inside a human-led research program, not as an autonomous prover. It adds to a period in which AI's role in mathematical discovery is under close scrutiny.