Watershed Moment for AI–Human Collaboration in Math

When Ukrainian mathematician Maryna Viazovska received a Fields Medal—widely regarded as the Nobel Prize for mathematics—in July 2022, it was big news. Not only was she the second woman to accept the honor in the award’s 86-year history, but she collected the medal just months after her country had been invaded by Russia. Nearly four years later, Viazovska is making waves again. Today, in a collaboration between humans and AI, Viazovska’s proofs have been formerly verified, signaling rapid progress in AI’s abilities to assist with mathematical research. “These new results seem very, very impressive, and definitely signal some rapid progress in this direction,” says AI-reasoning expert and Princeton University postdoc Liam Fowl, who was not involved in the work.In her Fields Medal–winning research, Viazovska had tackled two versions of the sphere-packing problem, which asks: How densely can identical circles, spheres, et cetera, be packed in n-dimensional space? In two