Mathematicians unified key laws of physics in 2025
It took 125 years, but in 2025 a team of mathematicians discovered the solution to a long-puzzling problem about the equations that govern the behaviour of particles in a fluid
Mathematics
It took 125 years, but in 2025 a team of mathematicians discovered the solution to a long-puzzling problem about the equations that govern the behaviour of particles in a fluid
29 December 2025
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The equations that govern fluids can be tricky to handle
Vladimir Veljanovski / Alamy
In 1900, mathematician David Hilbert presented his colleagues with a list of problems he believed both captured the present state of mathematics and the shape of its future. This year, 125 years later, Zaher Hani at the University of Michigan and his colleagues solved one of Hilbert’s problems – and unified several laws of physics in the process.
Hilbert was a proponent of deriving all laws of physics from mathematical axioms – statements that mathematicians take to be basic truths. The sixth problem on his list was to derive laws of physics that dictate the behaviour of fluids from such axioms.
Until 2025, physicists actually had three distinct ways of describing fluids, depending on their scale. Different rules governed the microscopic scale of single particles, the mesoscopic world populated by collections of particles and the macroscopic realm filled with fully fledged fluids like water flowing in a sink. Researchers had made strides in finding links between them, but the three were never stitched together seamlessly until Hani and his colleagues figured out how.