"In applying the theory of optimal transport to physical and chemical phenomena, the equation plays an important role," Figalli explains. "In many cases
the concept of minimal 'cost'
refers to energy, because nature minimises energy."

Aside from clouds, Figalli has also looked at changes in the shape of soap bubbles and crystals. Both bubbles and crystals strive for a shape that keeps their surface energy as low as possible. The types of energy are different at a physical level, but mathematically the equations are very similar. The theory of optimal transport can be applied to both phenomena to describe how their shapes change when energy is supplied. After that, it's possible to study how the particles are transported from the configuration with minimal energy to the one with increased energy.

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Original thinker and problem-solver

Some mathematicians develop new techniques destined to open doors to entirely new fields of research: this was the case when Isaac Newton (1642-1726) and Gottfried Wilhelm Leibniz (1646-1716) introduced differential calculus. Alessio Figalli is not one of them. Rather than design new theories and models, he concentrates on developing solutions to existing problems – preferably those that mathematicians have been studying for a long time.

In this competition, anyone aspiring to be the first to solve a problem and support it with bullet-proof evidence requires a great deal of creativity and originality in addition to profound knowledge. This includes accepting dashed expectations: "It's a long way from the idea to the rigorous proof. I've failed many times, but I've always learned something from it," says Figalli. He was fortunate enough to have amongst his teachers some of the most original and innovative mathematicians: Luigi Ambrosio in Pisa, Italy, Cédric Villani in Lyon, France (Fields Medal holder in 2010), and Luis Angel Caffarelli in Austin, Texas/USA.