Godfrey Harold Hardy (1877-1947)
Autograph manuscript dissertation signed ('G.H. Hardy'), 'Definite Integrals of discontinuous functions', with seven volumes of autograph lecture notes, [1896-1900], and five autograph letters, 1945-47
The dissertation a fair copy, 367 leaves, 285 x 220mm, foliated on versos, comprising 'Preface', title and contents, 'Introductory Notes on some points on the theory of functions', part 1, 'The convergence of infinite integrals', part 2, 'Double and multiple limit problems', and part 3, 'Applications of Cauchy's Theorem to particular definite integrals and infinite series', signed on the the front end-paper and the title of each of the three parts. Binding of contemporary calf-backed boards by J.P. Gray & Son, Cambridge.

The lecture notes comprising: A.R. Forsyth, 'Calculus of Variations'; H.F. Baker, 'Lectures on the Theory of Functions', Webb, 'Calculus and Curves', A. Berry, 'Elliptic Functions', A.N. Whitehead, 'Non Euclidean Geometry etc', Herman and Baker, 'Solid Geometry', together approx. 1500 pages, each signed ('G.H. Hardy'), most with autograph titles (in some case on loosely-inserted slips, presumably for the binder),
text usually on rectos only, occasional excisions of leaves or parts of leaves (presumably of cancelled sections). Binding of contemporary calf-backed boards by J.P. Gray & Son, Cambridge.
Provenance: Sotheby's, 13 March 1979, lot 209.

[with:]
Five autograph letters signed ('G.H. Hardy') to 'Mr Ward', Trinity College, 7 January 1944 - 25 February 1947 and n.d. Recommending reading on mathematics, 'There is hardly any literature on the Theory of Numbers in English ... [It] is essentially a German subject', on the absence of a proof that there is an infinity of prime numbers, discussing a mathematical argument (including a number of equations). Together approx. 8 pages, 220 x 138mm. Provenance: Sotheby's, 20 & 21 July 1981, lot 298.

'This dissertation contains as much as I have written of what I hope to complete into a book on Definite Integrals': autograph dissertation by 'one of the greatest English mathematicians of the twentieth century' (ODNB). The present dissertation may be Hardy's retained copy of his submission for the Prize Fellowship at Trinity College, which he obtained in 1900. The integral calculus and Cauchy's theorem were the subjects of many of Hardy's early published papers, starting with the first, 'On a class of definite integrals containing hyperbolic functions', Messenger of Mathematics 29 (1900), 25-42.

G.H. Hardy's remarkable abilities as a mathematician were evident from an early age: 'by the time he was two he could write down numbers up to millions, and later in church he amused himself by factorizing the numbers of the hymns. Throughout his life he frequently played about with numbers of taxicabs, railway carriages, and the like ... He went up to Trinity College, Cambridge, as an entrance scholar in 1896, his tutor being Dr A.W. Verral. Even in Trinity, he thought of mathematics as an essentially "competitive" subject. His eyes were opened by A.E.H. Love, who not only gave him his first serious conception of analysis, but also introduced him to Camille Jordan's Cours d'analyse de l'école polytechnique. Hardy was fourth wrangler in 1898 and in 1900 he achieved his childhood ambition when, on the basis of a dissertation, he was elected into a prize fellowship at Trinity' (ODNB).