Srinivasa RamanujanFRS was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable. Ramanujan initially developed his own mathematical research in isolation: "He tried to interest the leading professional mathematicians in his work, but failed for the most part. What he had to show them was too novel, too unfamiliar, and additionally presented in unusual ways; they could not be bothered". Seeking mathematicians who could better understand his work, in 1913 he began a postal partnership with the English mathematician G. H. Hardy at the University of Cambridge, England. Recognizing Ramanujan's work as extraordinary, Hardy arranged for him to travel to Cambridge. In his notes, Ramanujan had produced groundbreaking new theorems, including some that Hardy said had "defeated him and his colleagues completely", in addition to rediscovering recently proven but highly advanced results.
Godfrey Harold Hardy was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of population genetics. In addition to his research, he is remembered for his 1940 essay on the aesthetics of mathematics, titled A Mathematician's Apology. Hardy also was the mentor of the Indian mathematician Srinivasa Ramanujan.
Bertrand's postulate is a theorem stating that for any integer , there always exists at least one prime number with
In number theory, the partition function represents the number of possible partitions of a non-negative integer . For instance, because the integer has the five partitions , , , , and .
In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), also called the nth Hardy–Ramanujan number, is defined as the smallest integer that can be expressed as a sum of two positive integer cubes in n distinct ways. The most famous taxicab number is 1729 = Ta(2) = 13 + 123 = 93 + 103.
In mathematics, a superior highly composite number is a natural number which has more divisors than any other number scaled relative to some positive power of the number itself. It is a stronger restriction than that of a highly composite number, which is defined as having more divisors than any smaller positive integer.
In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as:
In mathematics, the Rogers–Ramanujan identities are two identities related to basic hypergeometric series, first discovered and proved by Leonard James Rogers (1894). They were subsequently rediscovered by Srinivasa Ramanujan some time before 1913. Ramanujan had no proof, but rediscovered Rogers's paper in 1917, and they then published a joint new proof. Issai Schur (1917) independently rediscovered and proved the identities.
In mathematics, Ramanujan's congruences are some remarkable congruences for the partition function p(n). The mathematician Srinivasa Ramanujan discovered the congruences
The infinite series whose terms are the natural numbers 1 + 2 + 3 + 4 + ⋯ is a divergent series. The nth partial sum of the series is the triangular number
In mathematics, the Hardy–Ramanujan theorem, proved by G. H. Hardy and Srinivasa Ramanujan (1917), states that the normal order of the number ω(n) of distinct prime factors of a number n is log(log ).
In mathematics, specifically transcendental number theory, the six exponentials theorem is a result that, given the right conditions on the exponents, guarantees the transcendence of at least one of a set of exponentials.
In mathematics, specifically the field of transcendental number theory, the four exponentials conjecture is a conjecture which, given the right conditions on the exponents, would guarantee the transcendence of at least one of four exponentials. The conjecture, along with two related, stronger conjectures, is at the top of a hierarchy of conjectures and theorems concerning the arithmetic nature of a certain number of values of the exponential function.
The Turán–Kubilius inequality is a mathematical theorem in probabilistic number theory. It is useful for proving results about the normal order of an arithmetic function. The theorem was proved in a special case in 1934 by Pál Turán and generalized in 1956 and 1964 by Jonas Kubilius.
Kanakanahalli Ramachandra was an Indian mathematician working in both analytic number theory and algebraic number theory.
The Hardy–Ramanujan Journal is a mathematics journal covering prime numbers, Diophantine equations, and transcendental numbers. It is named for G. H. Hardy and Srinivasa Ramanujan. Together with the Ramanujan Journal and the Journal of the Ramanujan Mathematical Society, it is one of three journals named after Ramanujan.
Michel Waldschmidt is a French mathematician, specializing in number theory, especially transcendental numbers.
Frits Beukers is a Dutch mathematician, who works on number theory and hypergeometric functions.
The Man Who Knew Infinity is a 2015 British biographical drama film about the Indian mathematician Srinivasa Ramanujan, based on the 1991 book of the same name by Robert Kanigel.
Jean-Louis Nicolas is a French number theorist.
