[2][3] In 1930, he stayed for five months in Germany (in Berlin and Göttingen) where he worked with Edmund Landau, Carl Ludwig Siegel, and David Hilbert.
In 1931 he started teaching as a Professor at the Moscow State University and worked there until the last day of his life.
In 1939, he was elected a Corresponding member of the Academy of Sciences of the Soviet Union for his works in the field of Cryptography.
According to Vladimir Arnold, during World War II Gelfond was the Chief Cryptographer of the Soviet Navy.
[4] Gelfond obtained important results in several mathematical domains including number theory, analytic functions, integral equations, and the history of mathematics, but his most famous result is his eponymous theorem: This is the famous 7th Hilbert's problem.