Alexander Gelfond

Alexander Osipovich Gelfond (Russian: Александр Осипович Гелфонд; October 24, 1906 - November 7, 1968) was a Russian mathematician, author of the Gelfond's theorem. October 24 is the 297th day of the year (298th in leap years) in the Gregorian Calendar, with 68 days remaining. ... 1906 (MCMVI) was a common year starting on Monday (see link for calendar). ... November 7 is the 311th day of the year (312th in leap years) in the Gregorian Calendar, with 54 days remaining. ... 1968 (MCMLXVIII) was a leap year starting on Monday (the link is to a full 1968 calendar). ... In mathematics, the Gelfond-Schneider theorem is the following statement, originally proved by Aleksandr Gelfond: If is an algebraic number (with and ), and is an irrational algebraic number, then is a transcendental number. ...

Biography

Alexander Gelfond was born in Petrograd (currently Saint-Petersbug) in a family of a professional physician and an amateur philosopher Osip Isaakovich Gelfond. He entered the Moscow State University in 1924, started his postgraduate studies there in 1927 and obtained his Ph.D in 1930. His advisers were Alexander Khinchin and Vyacheslav Stepanov. Saint Petersburg  listen (Russian: Санкт-Петербу́рг, English transliteration: Sankt-Peterburg), colloquially known as Питер (transliterated Piter), formerly known as Leningrad (Ленингра́д, 1924–1991) and Petrograd (Петрогра́д, 1914–1924), is a city located in Northwestern Russia on the delta of the river Neva at the east end of the Gulf of... Physician examining a child A physician is a person who practices medicine. ... A philosopher is a person who thinks deeply regarding people, society, the world, and/or the universe. ... Moscow State University campus M.V. Lomonosov Moscow State University (Russian: Московский Государственный Университет имени Ðœ.Ð’.Ломоносова, often abbreviated МГУ, MSU, MGU) is the largest and oldest university in Russia, founded in 1755. ... 1924 (MCMXXIV) was a leap year starting on Tuesday (link will take you to calendar). ... 1927 (MCMXXVII) was a common year starting on Saturday (link will take you to calendar). ... Doctor of Philosophy (Ph. ... 1930 (MCMXXX) is a common year starting on Wednesday. ... Aleksandr Yakovlevich Khinchin (July 19, 1894 _ November 18, 1959) was a Russian mathematician who was born in Kondrovo Russia and died in Moscow USSR. See: Khinchins theorem, Khinchins constant. ...

In 1930 he worked for five months in Germany (in Berlin and Göttingen) were 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. Since 1933 he also worked at the Steklov Institute of Mathematics. In 1939 he was elected a Corresponding member of the Academy of Sciences of the USSR. 1930 (MCMXXX) is a common year starting on Wednesday. ... (help· info) is the capital city and a state of Germany. ... Landmark Gänseliesel fountain at the main market Göttingen ( (help· info)) is a city in Lower Saxony, Germany. ... Edmund Georg Hermann Landau (February 14, 1877 - February 19, 1938) was a German mathematician and author of over 250 papers on number theory. ... Carl Ludwig Siegel (December 31, 1896 _ April 4, 1981) was a German mathematician specialising in number theory. ... David Hilbert David Hilbert (January 23, 1862, Wehlau, Prussia–February 14, 1943, Göttingen, Germany) was a German mathematician, recognized as one of the most influential mathematicians of the 19th and early 20th centuries. ... 1931 (MCMXXXI) was a common year starting on Thursday (link is to a full 1931 calendar). ... 1933 (MCMXXXIII) was a common year starting on Sunday (link will take you to calendar). ... Steklov Institute of Mathematics or Steklov Mathematical Institute (Russian: Математический институт имени Ð’.А.Стеклова) is a research institute specialized in Mathematics. ...

Results

Alexander Gelfond obtained important results in several mathematical domains including Number theory, Theory of analytic functions, Integral equations and History of mathematics but his most famous result is the so called Gelfond's theorem: Number theory is the formal study of numbers. ... Complex analysis is the branch of mathematics investigating holomorphic functions, i. ... In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. ... The word mathematics comes from the Greek μάθημα (máthema) which means science, knowledge, or learning; μαθηματικός (mathematikós) means fond of learning. Today, the term refers to a specific body of knowledge - the rigorous, deductive study of quantity, structure, space, and change. ... In mathematics, the Gelfond-Schneider theorem is the following statement, originally proved by Aleksandr Gelfond: If is an algebraic number (with and ), and is an irrational algebraic number, then is a transcendental number. ...

If α and β are algebraic numbers (with and ), and if β is not a real rational number, then any value of α^β is a transcendental number.

This is the famous 7th Hilbert's problem. Gelfond proved a special case of the theorem in 1929, when he was a postgraduate student and fully proved it in 1934. In 1935 the same theorem was independently proved by Theodor Schneider and so the theorem is often known as the Gelfond–Schneider theorem. In 1929 Gelfond proposed an extension of the theorem known as the Gelfond's conjecture that was proved by Alan Baker in 1966. In mathematics, an algebraic number relative to a field is any element of a given field containing such that is a solution of a polynomial equation of the form: anxn + an−1xn−1 + ··· + a1x + a0 = 0 where n is a positive integer called the degree of the polynomial, every coefficient... In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. ... In mathematics, a rational number (or informally fraction) is a ratio or quotient of two integers, usually written as the vulgar fraction a/b, where b is not zero. ... In mathematics, a transcendental number is any real number that is not algebraic, that is, not the solution of a non-zero polynomial equation with integer (or, equivalently, rational) coefficients. ... Hilberts problems are a list of twenty-three problems in mathematics put forth by German mathematician David Hilbert at the Paris conference of the International Congress of Mathematicians in 1900. ... 1929 (MCMXXIX) was a common year starting on Tuesday (link will take you to calendar). ... 1934 (MCMXXXIV) was a common year starting on Monday (link will take you to calendar). ... 1935 (MCMXXXV) was a common year starting on Tuesday (link will take you to calendar). ... 1929 (MCMXXIX) was a common year starting on Tuesday (link will take you to calendar). ... Alan Baker (born on August 19, 1939) is an English mathematician. ... 1966 (MCMLXVI) was a common year starting on Saturday (the link is to a full 1966 calendar). ...

Before Gelfond's works only a few numbers such as e and π were known to be transcendental. After his works an infinite number of transcendentals could be easily obtained. Some of them a named in Gelfond's honor: ex is the unique function f, such that for any real number x, ex = f(x) = f(x). ... Lower-case Ï€ (the lower case letter is usually used for the constant) The mathematical constant Ï€ ≈ 3. ...

• is known as the Gelfond–Schneider constant
• is known as Gelfond's constant

The Gelfond–Schneider constant is which Aleksandr Gelfond proved to be a transcendental number using the Gelfond–Schneider theorem, answering one of the questions raised in Hilberts seventh problem. ... In mathematics, Gelfonds constant, named after Aleksandr Gelfond, is that is, e to the power of π. Like both e and π, this constant is a transcendental number. ...

References

• Alexander Gelfond in the the Mathematical genealogy project
• B.V. Levin, N.I. Feldman, A.B. Sidlovsky (1971). "Alexander O. Gelfond". Acta Arithmetica 17: 315 – 336.