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Computer-Assisted Proofs Take on Fluid Flow

By Don Monroe
Communications of the ACM, August 2023, Vol. 66 No. 8, Pages 12-14
10.1145/3603745
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ball balanced on a stalagmite under a graph, illustration — Credit: Photoneye

Researchers have long been numerically solving the partial differential equations that govern important fluid phenomena such as weather, fusion plasmas, and aerodynamics. Of course, the accuracy of the results is always limited by the finite precision and spatial resolution of computer representations of the equations.

Computers have also become a powerful tool for exact, rigorous mathematics. Proof assistants, for example, instill confidence a logical argument is sound and all cases have been considered. Programs can tirelessly examine superhumanly large libraries of combinations, such as those underlying the four-color map theorem proof in 1976.

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