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Mathematics

Mathematicians solve 125-year-old problem to unite key laws of physics

Can one single mathematical framework describe the motion of a fluid and the individual particles within it? This question, first asked in 1900, now has a solution that could help us understand the complex behaviour of the atmosphere and oceans.

By Karmela Padavic-Callaghan

14 March 2025

Understanding fluids requires mathematical tools that operate at different scales

KARL GAFF / SCIENCE PHOTO LIBRARY

Mathematicians have finally succeeded in unifying the laws of physics that govern the motions of particles at different scales. Their efforts resolve a question set by mathematician David Hilbert in 1900 as part of an ambitious programme for all mathematicians of the 20th century 鈥 and could deepen our understanding of the complex behaviour of fluids in the atmosphere and oceans.

鈥淭his is a major result in my view. I thought it was completely beyond reach,鈥 says at the University of Lyon…

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