ON CERTAIN ARITHMETICAL FUNCTIONS: Transactions of the Cambridge Philosophical Society. Volume XXII. No IX.

First edition. Publisher's original light blue paper wrappers printed in black to the upper cover. 22.3 x 29cm. 32pp. Pages uncut. A remarkably fine copy, the binding firm, bright and fresh, the contents clean throughout and without inscriptions or stamps.

Described as "one of the most important papers in the history of number theory" (Bruce Berndt), and certainly one of the most famous of all mathematical papers, 'On Certain Arithmetical Functions' was first read at a meeting of the Cambridge Philosophical Society on 25th October 1915, and printed for publication as part of the transactions of the society in May 1916. Now recognised to be one of the leading number theorists of the twentieth century, many of whose insights and breakthroughs weren't fully understood until decades after his death, Srinivasa Ramanujan (1887-1920) contributed numerous innovative formulae in multiple fields of pure mathematics, including number theory, mathematical analysis, infinite series and the properties of partition function. The Indian mathematician published 21 papers during his five years in England under the guidance of, and sometimes in collaboration with Godfrey Harold Hardy, one of Britain's foremost pure mathematicians and a lecturer at Trinity College, Cambridge. Much of Ramanujan's work was published posthumously, notably 'The Collected Papers of Srinivasa Ramanujan', edited by G. H. Hardy et al (1927). His notebooks were published in facsimile by the Tata Institute of Fundamental Research in 1957, and a third 'lost notebook', discovered in 1976 by George Andrews at Trinity College, was published by Narosa Publishing House in 1987. Copies of any of Ramanujan's works printed within his lifetime are scarce in commerce. A biopic of Ramanujan's life 'The Man Who Knew Infinity' was released in 2015 starring Dev Patel in the role of Ramanujan and Jeremy Irons as G.H. Hardy. (Berndt, Bruce: Number Theory in the Spirit of Ramanujan, 2006).