The history of Galerkin's method and its role in M. V. Keldysh's work

The paper analyses the history of creation, development and justification of the widely known numerical Bubnov–Galerkin method. It gives some background about the prominent Russian engineers I. G. Bubnov and B. G. Galerkin. It shows how after using the method in researching the flutter problem, M. V. Keldysh studied the issue of the method's convergence. This work subsequently led to his famous research in nonself-adjoint operators and tauberian theorems. The paper is illustrated with photographs of exhibits from the Academician M. V. Keldysh Memorial Museum.