Mathematical Breakthrough: Proof Establishes Regularity for Important Class of Differential Equations

The trajectory of a storm, the evolution of stock prices, the spread of disease — mathematicians can describe any phenomenon that changes in time or space using what are known as partial differential equations.

Mathematicians instead rely on a clever workaround. They might not know how to compute the exact solution to a given equation, but they can try to show that this solution must be 'regular,' or well-behaved in a certain sense — that its values won't suddenly jump in a physically impossible way.

Mathematicians finally understand the behavior of an important class of differential equations that describe everything from water pressure to oxygen levels in human tissues.