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. In 1943 he became a Corresponding Member of the USSR Academy of Sciences. He got his first Stalin Prize in 1946 for his works on aircraft auto-oscillations. In 1943 he also became a full member of the Academy and the Director of NII-1 (Research Institute number 1) of the Department of the Aviation Industry. He also headed the Department of Applied Mechanics of the Steklov Institute of Mathematics. In 1966 the department was named after him to become the Keldysh Institute of Applied Mathematics.