Godfrey Harold Hardy: Mathematical Papers

Archive Collection

Scope and Content

MS.Add.6982: G.H. Hardy and S. Ramanujan, 'Asymptotic Formulae in Combinatory Analysis', a draft for publication, written in the hand of G.H. Hardy, c. 1916, 108 folios.

MS.Add.6983: G.H. Hardy and J.E. Littlewood, papers on Waring's problem, drafts for publication, written in the hand of G.H. Hardy, c. 1919-1921, 104 folios:

1. A new solution of Waring's Problem.

2. Some problems of 'Partitio Numerorum': I.

3. Some problems of 'Partitio Numerorum': II.

Administrative / Biographical History

Godfrey Harold Hardy (1877-1947) was educated at Cranleigh, Winchester, and Trinity College, Cambridge, of which he became a fellow in 1900. He became Cayley lecturer in mathematics at Cambridge in 1914, and Savilian professor of geometry at Oxford, 1920. From 1931 to 1932 he was Sadleirian professor of pure mathematics at Cambridge. Hardy produced much of his work in collaboration with other mathematicians, notably J.E. Littlewood. His works include A course of pure mathematics (1908), An introduction to the theory of numbers (1938, with E.M. Wright), and Divergent series (1949). He also contributed to the field of genetics by a developing a law that described how the proportions of dominant and recessive genetic traits would be propagated in a large population.

Srinivasa Aiyangar Ramanujan (1887-1920) was born in in Erode, Tamil Nadu state, India. He taught himself pure mathematics from a textbook by G.S. Carr, and developed his reputation in Madras. After writing to mathematicians in England, he was invited to Cambridge by G.H. Hardy, and became a Fellow of Trinity College (1918-1920). He worked with Hardy between 1914-1920, and after his death Hardy edited his collected works and published Ramanujan: twelve lectures on subjects suggested by his life and work (1940). Ramanujan made original contributions to function theory, power series, and number theory, before he died of tuberculosis.

John Edensor Littlewood (1885-1977) was educated at St. Paul's School, London, before entering Trinity College, Cambridge, in 1903. He was Richardson lecturer at Manchester from 1907 to 1910. In 1908 he became a fellow of Trinity, and in 1910 he was appointed college lecturer. Soon after he began his long collaboration with G.H. Hardy, with whom he wrote many papers. Littlewood was Cayley lecturer at Cambridge, 1920-1928, before occupying the Rouse Ball chair of mathematics, 1928-1950. His works include The theory of real functions (1926) and Lectures on the theory of functions (1944).

Conditions Governing Access

Open for consultation by holders of a Reader's Ticket valid for the Manuscripts Reading Room.

Acquisition Information

Presented by G.H. Hardy, 1939.


Description compiled by Robert Steiner, Department of Manuscripts and University Archives. The biographical history was compiled with reference to the entries on G.H. Hardy in the Concise dictionary of national biography, Part II, 1901-1970 (Oxford University Press, 1982), p. 302, and on J.E. Littlewood in Lord Blake and C.S. Nicholls, eds., Dictionary of national biography 1971-1980 (Oxford University Press, 1986), pp. 510-511.

Other Finding Aids

Additional Manuscripts Catalogue.


MS.Add.6982 was first printed in full in 1918, and reprinted in Collected papers of Srinivasa Ramanujan (Cambridge, 1927), pp. 276-309. A short section at the end (p. 306, ll. 1-11), and parts of the annexed tables which appear in the printed version, are missing from this draft.

MS.Add.6983: no.1 was printed in the Quarterly journal of mathematics, 48 (1919), pp. 272-293; no. 2 was printed in Gottinger Nachrichten, Mathem-phys.klasse (1920), pp. 33-54; no. 3 was printed in Mathematische Zeitschrift 9 (1921), pp. 14-27 (the concluding 2 paragraphs of the printed version are not present in the draft).