Moving dirt to build fortifications during the French Revolution more than 200 years ago, has led leading mathematicians ever since to study the concept of optimal transport theory, which explains how things can be moved in the best possible way.
But it was a major breakthrough by Professor Alessio Figalli led to greater interest in this theory from the mathematics community.
Over the centuries, mathematicians have realised that the mathematics behind optimal transport is useful for more than moving dirt, and that whenever you want to compare two shapes (which mathematicians want to do), there is something to be learned by thinking about the most efficient, or optimal, way of converting one shape into the other.
Prof Figalli demonstrated that certain changes in the shape of clouds, which are of great importance for meteorology, can be calculated using optimal transport. For his contribution, he won the Fields Medal in 2018, which is to mathematics what the Nobel Prize is to the natural sciences. The Medal is awarded by the International Mathematical Union every four years and is the most prestigious in the field of mathematics.
“Mathematics is all around us,” says the Italian mathematician. He described how each time someone uses a technological tool, there is maths behind it. It can be as simple as taking a photograph or having a discussion on Zoom video conference, and that such tools are based on mathematical calculations and thus have an impact on society.
One current area of research he is pursuing is to study physical processes, like the melting of ice, by using mathematical equations. This allows scientists to gain a better understanding of the development, which can then be replicated in a simulation. Scientists can use the simulation to improve their prediction of how the process will occur over time.
Winning the Fields Medal award impacted his life in many ways, he said. “The recognition meant that the scientific community value what I am doing. It also gave me the energy and motivation to keep going”. He has become a role model, invited to give talks to high school students on the significance of mathematics.
Figalli says that, “Mathematics is in a golden era. Society is realising its importance and governments and organisations are willing to invest and support research.” He describes how mathematics graduates are being hired by big tech companies like Google, Facebook, and Microsoft to do pure research. While the outcome of the research cannot be predicted, he believes mathematics will improve the way artificial intelligence and machine learning models work.
A plenary speaker at the Global YoungScientists Summit 2021, Prof Figalli will share his thoughts on the transport theory, its emergence more than 200 years ago, the current focus areas, and the reason mathematics is relevant in machine learning.
Prof Figalli is FIM Director and Professor of Mathematics at ETH Zurich, Switzerland. He has won numerous awards in addition to the Fields Medal 2018, including the Falling Walls Award in Engineering and Technology, 2020.