# Mathematician:Godfrey Harold Hardy

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## Mathematician

English mathematician noted for his work in number theory and analysis.

Also famous for his discovery and mentorship of Srinivasa Aiyangar Ramanujan.

Non-mathematicians remember him mainly for his book *A Mathematician's Apology*.

## Nationality

English

## History

- Born: February 7, 1877, Cranleigh, Surrey, England
- Died: December 1, 1947, Cambridge, Cambridgeshire, England

## Theorems and Definitions

- Critical Line Theorem
- Hardy Notation
- Hardy Space
- Pisot-Vijayaraghavan Number (named for Charles Pisot and Tirukkannapuram Vijayaraghavan)
- Hardy's Inequality
- Hardy's Theorem
- Hardy-Littlewood Tauberian Theorem (with John Edensor Littlewood)
- First Hardy-Littlewood Conjecture (with John Edensor Littlewood)
- Second Hardy-Littlewood Conjecture (with John Edensor Littlewood)
- Fifth Hardy-Littlewood Conjecture (with John Edensor Littlewood)

- With Wilhelm Weinberg:

- Hardy-Littlewood Maximal Inequality (with John Edensor Littlewood)
- Hardy-Littlewood Circle Method (with John Edensor Littlewood)
- Hardy-Ramanujan Number (with Srinivasa Aiyangar Ramanujan)

Results named for **Godfrey Harold Hardy** can be found here.

Definitions of concepts named for **Godfrey Harold Hardy** can be found here.

## Publications

- 1914:
*Sur les Zéros de la Fonction $\map \zeta s$ de Riemann*(*C.R. Acad. Sci.***Vol. 158**: pp. 1012 – 1014)

- 1915:
*The General Theory of Dirichlet's Series*(with Marcel Riesz) - 1916:
*The Integration of Functions of a Single Variable*

- 1921:
*The zeros of Riemann's zeta-function on the critical line*(*Math. Z.***Vol. 10**: pp. 3 – 4) (with J.E. Littlewood)

- 1923:
*Some problems of ‘Partitio numerorum’; III: On the expression of a number as a sum of primes*(*Acta Math.***Vol. 44**: pp. 1 – 70) (with J.E. Littlewood)

- 1927:
*Collected Papers of Srinivasa Ramanujan*(as editor, with P.V. Seshu Aiyar and B.M. Wilson)

- 1934:
*Inequalities*(with J.E. Littlewood and G. Pólya)

- 1938:
*An Introduction to the Theory of Numbers*(with E.M. Wright)

- 1940:
*A Mathematician's Apology* - 1940:
*Ramanujan* - 1949:
*Divergent Series*

- 1966:
*Collected papers of G.H. Hardy*(including joint papers with J.E. Littlewood and others)

## Notable Quotes

*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.*- -- Quoted in the Preface to 1992: George F. Simmons:
*Calculus Gems*

- -- Quoted in the Preface to 1992: George F. Simmons:

## Sources

- John J. O'Connor and Edmund F. Robertson: "Godfrey Harold Hardy": MacTutor History of Mathematics archive

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next): Entry:**Hardy, Godfrey Harold**(1877-1947) - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**Hardy, Godfrey Harold**(1877-1947) - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**Hardy, Godfrey Harold**(1877-1947)