18 Unconventional Essays on the Nature of Mathematics by Reuben Hersh

This paper concerns changing needs and expectations in the way mathematics is practiced and communicated. The time frame is mainly the early twentieth century to the present and the scope is all activity that can be considered to fall under the purview of the mathematical community. Unavoidably, the idea of a mathematical community is confronted; what it means to claim ownership in this community and how knowledge management practices affect the community. Finally, a description of an extendable mathematical text-based database which can be used to manage user defined forms of mathematical knowledge is presented. Hardy and Littlewood: A Study in Collaboration The anecdote is related by C.P. Snow in his introduction to A Mathematician’sApology. It is a pleasant May evening some time in the 1930’s and Hardy is inhis fifties. He and Snow are walking at Fenner’s cricket ground when the 6o’clock chimes ring out from the nearby Catholic chapel. “It is rather unfor-tunate”, Hardy remarks, “that some of the happiest hours of my life shouldhave been spent within sound of a Roman Catholic church”.One of the preeminent mathematicians of his day and indeed, of the cen-tury, it is perhaps not entirely surprising that, living as he did, in the intellec-tual communities of Cambridge and Oxford, Gottfried Harold Hardy was anatheist. While our immediate concern is not his views on religion, it is ger-mane only that Hardy was, in this fundamental domain, a non-conformist inan age that put a great deal of stock in conformity. Our concern is withhis mathematics and, in particular, with his lively and productive collabora-tion with John Edensor Littlewood. Commencing in 1912, spanning some36 years, and resulting in enough papers to fill several thick volumes of