Luis Caffarelli has been awarded the most prestigious prize in mathematics for his work on nonlinear partial differential equations, which have many applications in the real world
By Alex Wilkins
22 March 2023
Luis Caffarelli, winner of the 2023 Abel prize
Nolan Zunk/UT AUSTIN
Luis Caffarelli has won the 2023 Abel prize, unofficially called the Nobel prize for mathematics, for his work on a class of equations that describe many real-world physical systems, from melting ice to jet engines.
Caffarelli was having breakfast with his wife when he found out the news. “The breakfast was better all of a sudden,” he says. “My wife was happy, I was happy — it was an emotional moment.”
Based at the University of Texas at Austin, Caffarelli started work on partial differential equations (PDEs) in the late 1970s and has contributed to hundreds of papers since. He is known for making connections between seemingly distant mathematical concepts, such as how a theory describing the smallest possible areas that surfaces can occupy can be used to describe PDEs in extreme cases.
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PDEs have been studied for hundreds of years and describe almost every sort of physical process, ranging from fluids to combustion engines to financial models. Caffarelli’s most important work concerned nonlinear PDEs, which describe complex relationships between several variables. These equations are more difficult to solve than other PDEs, and often produce solutions that don’t make sense in the physical world.
Caffarelli helped tackle these problems with regularity theory, which sets out how to deal with problematic solutions by borrowing ideas from geometry. His approach carefully elucidated the troublesome parts of the equations, solving a wide range of problems over his more than four-decade career.
“Forty years after these papers appeared, we have digested them and we know how to do some of these things more efficiently,” says Francesco Maggi at the University of Texas at Austin. “But when they appeared back in the day, in the 80s, these were alien mathematics.”