Many people see the importance of physics and engineering in everyday life, but few know of the math which supports those innovations. Giuseppe Mingione has devoted his life to studying it, though, and it’s made him one of the most highly cited researchers in the world. He calls it a fourth dimension: Everything in the world can be studied using math, and that means that applying math to more tangible fields can enable much more research than would otherwise be possible.
“This field is pervasive because it’s gone on for centuries and will go on for centuries,” says Mingione, Professor of mathematics at the University of Parma. “Essentially whatever you do is ruled by partial differential equations.”
Partial differential equations and the calculus of variations
Mingione’s field makes physics and engineering research possible. When researchers in these fields come up with questions, one of the first things they do is develop an equation to solve. Mathematicians help develop and solve these equations, enabling further research.
“It’s a field where the unknown is not a number, but a function that appears via its derivatives,” he says. “And essentially you may say that almost every physical phenomenon you can describe is ruled by these equations.” Partial differential equations provide a methodological background and blueprint to solve real-world problems, whether that’s calculating how heat propagates or creating a model for an airplane. Everything can be modeled with math, which makes it a powerful tool.
Mingione hopes that in coming years, his field will begin to develop equations for more and more fields. He especially hopes that it will continue to expand into health research, where equations are already being used to model things like the flow of blood in the body. This would for instance provide noninvasive ways to make predictions about the movement of blood within the body.
