G. H. HARDY, NUMBER THEORY & POPULATION GENETICS

Today, The Grandma has been reading about G. H. Hardy, the English mathematician who died on this day in 1947.

Mathematics is fundamental to our existence because it is a universal language essential to better understand everything around us.

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.

Hardy is famed 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. The novelist Graham Greene ranked it with the notebooks of Henry James as the best account of what it was like to be a creative artist.

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. He remarked that on a scale of mathematical ability, his ability would be 25, Littlewood would be 30, Hilbert would be 80, and Ramanujan would be 100. 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.

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.

Hardy is credited with reforming British mathematics by bringing rigour into it, which was previously a characteristic of French, Swiss and German mathematics. British mathematicians had remained largely in the tradition of applied mathematics, in thrall to the reputation of Isaac Newton. Hardy was more in tune with the cours d'analyse methods dominant in France, and aggressively promoted his conception of pure mathematics, in particular against the hydrodynamics that was an important part of Cambridge mathematics.

Hardy preferred to work only 4 hours every day on mathematics, spending the rest of the day talking, playing cricket, and other gentlemanly activities.

From 1911, he collaborated with John Edensor Littlewood, in extensive work in mathematical analysis and analytic number theory. This (along with much else) led to quantitative progress on Waring's problem, as part of the Hardy-Littlewood circle method, as it became known. In prime number theory, they proved results and some notable conditional results. This was a major factor in the development of number theory as a system of conjectures; examples are the first and second Hardy-Littlewood conjectures. Hardy's collaboration with Littlewood is among the most successful and famous collaborations in mathematical history.

Aside from formulating the Hardy-Weinberg principle in population genetics, his famous work on integer partitions with his collaborator Ramanujan, known as the Hardy-Ramanujan asymptotic formula, has been widely applied in physics to find quantum partition functions of atomic nuclei (first used by Niels Bohr) and to derive thermodynamic functions of non-interacting Bose-Einstein systems. His work in number theory is also important in cryptography. Though Hardy wanted his maths to be pure and devoid of any application, much of his work has found applications in other branches of science.

He died in 1947, one early morning while listening to his sister read out from a book of the history of Cambridge University cricket. 

More information: The Atlantic

 A mathematician, like a painter or poet, 
is a maker of patterns. 
If his patterns are more permanent than theirs, 
it is because they are made with ideas.

G. H. Hardy