Keldysh's maternal grandfather, Alexander Nikolayevich Skvortsov, was a General of Infantry, and fought in the Caucasian War.

It was a part of the campaign of collecting gold from the population, but after Keldysh's father brought all the jewelry the family had, the unsatisfied NKVD officer returned "all this garbage" back.

[4] Keldysh's brother Mikhail, a historian who specialized in Medieval Germany, was arrested in 1936 and executed in 1937 on suspicion of being a German spy.

Alexander was spared because of the slight liberalization of the repressions during the transfer of the NKVD leadership from Nikolai Yezhov to Lavrentiy Beria, and was acquitted in the court.

In 1937 Keldysh became Doctor of Science with his dissertation entitled Complex Variable and Harmonic Functions Representation by Polynomial Series, and was appointed a Professor of Moscow State University.

During the 1940s Keldysh became the leader of a group of applied mathematicians involved in almost all large scientific projects of the Soviet Union.

Keldysh created the Calculation Bureau that carried most of the mathematical problems related to the development of nuclear weapons.

In 1954 Keldysh, Sergei Korolev and Mikhail Tikhonravov submitted a letter to the Soviet Government proposing development of an artificial satellite to orbit the Earth.

The letter was rejected, and the group filed exaggerated Soviet newspaper articles which influenced American authorities to start satellite programs.

This in turn began the effort that culminated in the world's first satellite, Sputnik 1 in October 1957, which marked the beginning of mankind's Space Age.

In 1961 he received a second Hеrо of Socialist Labour award for his contribution to Yuri Gagarin's flight into space, the first person to orbit the Earth.

[9] A street (Akadēmiķa Mstislava Keldiša iela) was named after Keldysh in the district of Pļavnieki in his native Riga, Latvia.