Argentine mathematician Luis Caffarelli has won the 2023 Abel Prize for making natural phenomena more understandable and eliminating dreaded “infinities” from a calculation
Mathematics is the language that lets us describe the universe. Galileo Galilei was already convinced of that in the 16th century. But even everyday phenomena such as the melting of an ice cube in a glass of water can lead to equations that are so complex that they overwhelm those with high levels of mathematical expertise. That has not stopped Argentine mathematician Luis Caffarelli from devoting himself to precisely such problems during his research career, however.
Differential equations are formulas that contain derivatives, which describe properties such as the rate of change in a physical system. Although all this sounds complicated and abstract, it is these kinds of equations that describe the constant physical flux of the world around us. Differential equations explain how certain variables change over time and space. They allow us to glimpse into the future because they predict how a system will change temporally and spatially.
One of the most important questions when considering this problem is the size of the surface of the region where the bubble and the obstacle touch. Intuitively one would say that the bubble’s contact surface has a smooth boundary without corners or edges. But proving this mathematically is quite difficult because you have to calculate the resulting minimum area for all kinds of obstacles that requires solving an extremely large number of extremely complicated differential equations.
Until the 1970s it was unclear whether they could provide abstract solutions that were divorced from the real world. The equations could predict an ice cube shape resembling a fractal, which has never been observed in nature. This was much more difficult to investigate than just looking at soap skins. The melting of ice cubes contains a temporal and spatial component.
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Mathematician wins Abel Prize for ‘smooth’ physicsLuis Caffarelli’s work includes equations underpinning physical phenomena, such as melting ice and flowing liquids.
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Mathematician wins Abel prize for solving equations with geometryLuis 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
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