Languages for mathematics and the language of mathematics in a world of nations

Gray, Jeremy (2002). Languages for mathematics and the language of mathematics in a world of nations. In: Parshall, Karen Hunger and Rice, Adrian C eds. Mathematics unbound: the evolution of an international mathematical research community, 1800-1945. History of mathematics (23). Providence, Rhode Island USA: American Mathematical Society and London Mathematical Society, pp. 210–228.



The paper considers some of the ways in which mathematics was considered as a language around 1900. In the first part of the paper aspects of the creation of an international language for mathematics are considered, and discussed as part of the wider political movements for international languages. This sheds a new light on the multi-national, rather than international, nature of mathematical community. In the second half of the paper the linguistic perspective is used to provide a new view on contemporary debates about the foundations of mathematics. A wide variety of positions were taken about the correct relationship between thought, language, logic, mathematics and the world, sometimes with an intensity that can only be explained on historical and political grounds. The simultaneous searches for a truly international language and for an appropriate language for mathematics with an appropriate foundation not only involved several of the same people, but each raised difficult questions of syntax, semantics, and the relation between syntax and semantics. The paper concludes with some reflections on Hilbert’s philosophy of mathematics, which allowed for multiple interpretations. A number of reasons are given to suggest that it is possible to speak of a distrust of language at the time, and that shifting the emphasis from logic to language allows us to recognise confusions about difficult linguistic issues which deepen our understanding of the old debates about the relationship of logic to mathematics.

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