A Mathematician Who Makes the Best of Things

Alessio Figalli studies optimal transport, a field of math that ranges from the movements of clouds to the workings of chatbots.

The words “optimal” and “optimize” derive from the Latin “optimus,” or “best,” as in “make the best of things.” Alessio Figalli, a mathematician at the university ETH Zurich, studies optimal transport: the most efficient allocation of starting points to end points. The scope of investigation is wide, including clouds, crystals, bubbles and chatbots.

Dr. Figalli, who was awarded the Fields Medal in 2018, likes math that is motivated by concrete problems found in nature. He also likes the discipline’s “sense of eternity,” he said in a recent interview. “It is something that will be here forever.” (Nothing is forever, he conceded, but math will be around for “long enough.”) “I like the fact that if you prove a theorem, you prove it,” he said. “There’s no ambiguity, it’s true or false. In a hundred years, you can rely on it, no matter what.”

The study of optimal transport was introduced almost 250 years ago by Gaspard Monge, a French mathematician and politician who was motivated by problems in military engineering. His ideas found broader application solving logistical problems during the Napoleonic Era — for instance, identifying the most efficient way to build fortifications, in order to minimize the costs of transporting materials across Europe.

In 1975, the Russian mathematician Leonid Kantorovich shared the Nobel in economic science for refining a rigorous mathematical theory for the optimum allocation of resources. “He had an example with bakeries and coffee shops,” Dr. Figalli said. The optimization goal in this case was to ensure that on a daily basis every bakery delivered all its croissants, and every coffee shop got all the croissants desired.

“It’s called a global wellness optimization problem in the sense that there is no competition between bakeries, no competition between coffee shops,” he said. “It’s not like optimizing the utility of one player. It is optimizing the global utility of the population. And that’s why it’s so complex: because if one bakery or one coffee shop does something different, this will influence everyone else.”

The following conversation with Dr. Figalli — conducted at an event in New York City organized by the Simons Laufer Mathematical Sciences Institute and in interviews before and after — has been condensed and edited for clarity.