Nizhny Novgorod Scientist Solves 'Eternal' Mathematical Problem

A mathematician from the Nizhny Novgorod branch of HSE University, Ivan Remizov, has made a conceptual breakthrough in the theory of differential equations by deriving a universal formula for solving problems that have been considered unsolvable analytically for over 190 years.

Remizov explained, «Imagine that the desired solution to an equation is a large picture. It»s very difficult to see it all at once. But mathematics excels at describing processes that develop over time. The result of the work is a theorem that allows «slicing» this process into many small, simple frames, and then using the Laplace transform to assemble these frames into a single static picture—the solution to a complex equation, i.e., the resolvent. Simply put, instead of guessing what the picture looks like, the theorem allows restoring its appearance by quickly «scrolling through the film reel» of its creation.«

The second-order differential equations for which a solution has been found are used for modeling real physical processes. They underlie the special Mathieu and Hill functions, which are critically important for calculating satellite orbits or proton motion in the Large Hadron Collider.

Previously, Ivan Remizov has already participated in solving another «eternal» problem. In 1968, American mathematician Paul Chernoff proposed a method for approximating operator semigroups, but the question of its convergence rate remained open for over 50 years until it was solved by Nizhny Novgorod scientists.