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.
Becoming highly cited
Mingione makes a distinction between purely technically advanced research and more fundamental and original research, and says that understanding the difference between the two is key to becoming highly cited. In order to be highly cited, researchers must be original and timely, coming up with creative ideas and looking at things in new ways. They should also follow their own passions and ideas.
“It’s like when you invest in stocks, if you want to earn a lot, then there are very little stocks that are underrated,” he says. “If you buy the stocks that are already big, the probability of high gain is very low. The most valuable ones are those which are low.”
He credits his success to his career-long attempts to do this, even when ideas haven’t been easy to come up with. He has had low points, where ideas have been hard to find, but he says that those points come with new knowledge. New knowledge leads to new ideas, so these are part of the creative process. The key is to find or create emerging fields whose potential hasn’t been recognized yet.
Many young researchers might find this daunting when the job market is competitive and there is pressure to publish as much as you can, but Mingione says that giving into these pressures leads to modest outcomes. High risks come with high gains, and researchers should work to develop creative and innovative work while following their own interests. Dramatic and innovative results are often risky, and rarely fast, but they have been his goal throughout his career, and it’s paid off.
“Too many people expect fast success, but research is about doing a lot of silent work,” Mingione emphasizes. “For a long time, you don’t see anything, but then you see the bubbles coming up.”