Aleksandr Osipovich Gelfond

Aleksandr Gelfond taught mathematics at the Moscow Technological College (1929-30) and then from 1931 at Moscow State University where he held chairs of analysis, theory of numbers and the history of mathematics.

In addition to his important work in the number theory of transcendental numbers (that is, numbers that are not the solution of an algebraic equation with rational coefficients) Gelfond made significant contributions to the theory of interpolation and the approximation of functions of a complex variable.

In 1929 he conjectured that:-

If a_n and b_n for 1 < m < n are algebraic numbers such that {ln a_n, 1 < m < n} are linearly independent over Q, then
b₁ln a₁+ b₂ln a₂+ ... + b_nln a_n 0.

In 1934 Gelfond proved a special case of his conjecture namely that a^b is transcendental if a is algebraic (a 0, 1) and b is an irrational algebraic number. This result is now known as Gelfond's theorem and solved Problem 7 of the list of Hilbert 23 problems. It was solved independently by Schneider.

In 1966 A Baker proved Gelfond's Conjecture in general.

Gelfond's major contributions to transcendental numbers are in Transtendentnye i algebraicheskie chisla (1952) and to approximation and interpolation theories are in Ischislenie konechnykh raznostey (1952).