**Gelfond** developed basic techniques in the study of transcendental numbers.

- Gelfond entered Faculty of Physics and Mathematics at Moscow State University in 1924 and completed his undergraduate studies in 1927.
- He then began research under the supervision of Aleksandr Khinchin and Vyacheslaw Stepanov and completed his postgraduate studies in 1930.
- The second of these 1929 papers contained the lecture which Gelfond gave to the First All-Union Mathematics Congress held in Kharkov in 1930.
- These papers by Gelfond represent a major step forward in the study of transcendental numbers.
- In the second of the 1929 papers Gelfond applied this result to prove that certain numbers are transcendental, so solving a special case of Hilbert's Seventh Problem.
- After his return to Russia, Gelfond taught mathematics from 1931 at Moscow State University where he held chairs of analysis, theory of numbers and the history of mathematics.
- Gelfond developed basic techniques in the study of transcendental numbers, that is numbers that are not the solution of an algebraic equation with rational coefficients.
- In addition to his important work in the number theory of transcendental numbers, Gelfond made significant contributions to the theory of interpolation and the approximation of functions of a complex variable.
- This result is now known as Gelfond's theorem and solved Problem 7 of the list of Hilbert problems.
- (In 1966 Alan Baker proved Gelfond's Conjecture in general.) Gelfond's papers in 1933 and 1934, which include his remarkable achievement, are: Gram determinants for stationary series (written jointly with Khinchin) (1933); A necessary and sufficient criterion for the transcendence of a number (1933); Functions that take integer values at the points of a geometric progression (1933); On the seventh problem of D Hilbert (1934); and On the seventh problem of Hilbert (1934).
- Gelfond addressed the Second All-Union Mathematics Congress in Leningrad in 1934) on Transcendental numbers.
- We now look briefly at a number of books which Gelfond wrote.
- This was based on a text of the same title which Gelfond originally published in 1936.
- Also in 1952 Gelfond published the low level Solving equations in integers which was translated into English in 1960.
- In 1962 Gelfond published the book Elementary methods in the analytic theory of numbers written jointly with Linnik.
- A further text by Gelfond is Residues and their applications (1966).
- Many eminent mathematicians think roughly along the same lines as less eminent ones, though more rapidly and in a more organised way; Gelfond always thought in his own way, one that was unconventional and quite original.

Born 24 October 1906, St Petersburg, Russia. Died 7 November 1968, Moscow, Russia.

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Origin Russia

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive