G. H. Hardy | EPFL Graph Search

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Godfrey Harold Hardy (7 February 1877 – 1 December 1947) 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. G. H. Hardy is usually known by those outside the field of mathematics for his 1940 essay A Mathematician's Apology, often considered one of the best insights into the mind of a working mathematician written for the layperson. Starting in 1914, Hardy was the mentor of the Indian mathematician Srinivasa Ramanujan, a relationship that has become celebrated. Hardy almost immediately recognised Ramanujan's extraordinary albeit untutored brilliance, and Hardy and Ramanujan became close collaborators. In an interview by Paul Erdős, when Hardy was asked what his greatest contribution to mathematics was, Hardy unhesitatingly replied that it was the discovery of Ramanujan. In a lecture on Ramanujan, Hardy said that "my association with him is the one romantic incident in my life". G. H. Hardy was born on 7 February 1877, in Cranleigh, Surrey, England, into a teaching family. His father was Bursar and Art Master at Cranleigh School; his mother had been a senior mistress at Lincoln Training College for teachers. Both of his parents were mathematically inclined, though neither had a university education. Hardy's own natural affinity for mathematics was perceptible at an early age. When just two years old, he wrote numbers up to millions, and when taken to church he amused himself by factorising the numbers of the hymns. After schooling at Cranleigh, Hardy was awarded a scholarship to Winchester College for his mathematical work. In 1896, he entered Trinity College, Cambridge. After only two years of preparation under his coach, Robert Alfred Herman, Hardy was fourth in the Mathematics Tripos examination. Years later, he sought to abolish the Tripos system, as he felt that it was becoming more an end in itself than a means to an end.

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Related publications (3)

Related concepts (16)

Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications

Florian Karl Richter

We obtain new results pertaining to convergence and recurrence of multiple ergodic averages along functions from a Hardy field. Among other things, we confirm some of the conjectures posed by Frantzikinakis in [Fra10; Fra16] and obtain combinatorial applic ...

2020

Let k∈Nk∈Nk \in \mathbb{N} and let f1, …, f k belong to a Hardy field. We prove that under some natural conditions on the k-tuple ( f1, …, f k ) the density of the set {n∈N:gcd(n,⌊f1(n)⌋,…,⌊fk(n)⌋)=1}{n∈N:gcd(n,⌊f1(n)⌋,…,⌊fk(n)⌋)=1}\displaystyle{\big{n \i ...

Springer International Publishing2017

The aim of this research is to establish a relation between the derivatives of Hardy's Z function and the argument of the Riemann zeta function in the neighborhood of points where |Z| reaches a large maximum. In this paper, we make a step toward this goal ...

2011

Riemann hypothesis

In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2. Many consider it to be the most important unsolved problem in pure mathematics. It is of great interest in number theory because it implies results about the distribution of prime numbers. It was proposed by , after whom it is named.

Analytic number theory

In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic progressions. It is well known for its results on prime numbers (involving the Prime Number Theorem and Riemann zeta function) and additive number theory (such as the Goldbach conjecture and Waring's problem).

Ulam spiral

The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner's Mathematical Games column in Scientific American a short time later. It is constructed by writing the positive integers in a square spiral and specially marking the prime numbers. Ulam and Gardner emphasized the striking appearance in the spiral of prominent diagonal, horizontal, and vertical lines containing large numbers of primes.