The Unification of Fluid Dynamics: A Mathematical Breakthrough
The equations that govern fluids can be tricky to handle
Vladimir Veljanovski / Alamy
In 1900, renowned mathematician David Hilbert presented a list of problems that he believed encapsulated the essence of mathematics at that time and hinted at its future trajectory. Fast forward 125 years, Zaher Hani and his team at the University of Michigan have achieved a significant milestone by solving one of Hilbert’s longstanding problems, thereby uniting several fundamental laws of physics in the process.
Hilbert’s sixth problem challenged mathematicians to derive the laws governing fluid dynamics from basic mathematical axioms. Prior to 2025, physicists had distinct frameworks for describing fluids at different scales – microscopic, mesoscopic, and macroscopic. While efforts had been made to establish connections between these scales, a seamless integration was lacking until Hani and his colleagues bridged the gap.
The breakthrough was made possible by leveraging a diagram-based technique developed by physicist Richard Feynman for quantum field theory. This innovative approach, honed over a multi-year endeavor, has garnered recognition from leaders in the field and is set to be published in a prestigious mathematics journal.
Aside from its mathematical significance, this achievement holds promise for enhancing our understanding of complex fluid behaviors in natural systems like the atmosphere and oceans. The team is now delving into the quantum realm of the problem, where peculiar particle behaviors add a new layer of complexity to the study.
Topics: Fluid Dynamics, Mathematics, Physics
