In 1950, Bakhvalov entered the Faculty of Mechanics and Mathematics at Moscow State University.

Bakhvalov authored over 150 papers, several books, and a popular textbook on numerical methods.

He had made major pioneering contributions to many areas of mathematics and mechanics.

Starting early in his career, Bakhvalov formulated and proved important results on the optimization of numerical algorithms.

In 1959, he determined the complexity of the integration problem in the worst-case setting for integrands of smoothness.