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6 MATHEMATICS, LANGUAGE, AND PSYCHOLOGY 6.1 Languages Natural and Artificial It was the painter and aspiring but unsuccessful poet Edgar Degas who complained to his friend Stéphane Mallarmé that he had many ideas for poems but could not write the poems, to which Mallarmé replied, ‘‘Poems, my dear friend, are made of words, not ideas.’’ The same is true, and to the same extent, of a mathematical paper, as every contemporary mathematician knew. But in what language should mathematicians write, and is, or could there be, a language best suited to their purposes? 6.1.1 National Languages in Mathematics around 1900 The international mathematical arena in 1900 was an arena of competing nationalisms , chiefly those of Europe, the United States, and Japan.1 Mathematicians in Germany spoke and wrote German, and this included a number of visiting Americans , some of whom wrote not only their doctoral theses in this language but went on to write books in it long after their return to America.2 The French wrote in French, just as the English wrote in English, and only occasional forays were made into another tongue. Because French and German journals dominated the field, Scandinavians , Russians, Czechs, and Poles had to decide if they would attempt French or German, or write in their native tongue with ease although for a restricted if valuable audience. Sometimes this was a political act.3 Most mathematicians were, or presented themselves as, literary monoglots who seldom wrote outside their own linguistic boundary. Hilbert was typical, when he published in the Bulletin of the London 1 This section is adapted from Gray 2002. 2 Osgood 1907, also Haskell 1890 and Dickson. 3 See Duda 1996. Mathematical Society, writing in German,4 and it is significant that Felix Klein, the most ardent advocate of Germany’s leading role in the mathematical world, chose to publish in English when addressing an American or English audience.5 The work of many, therefore, had to be translated. Joseph Liouville and then Guillaume Jules Hoüel led the way in France. The American mathematical community translated many works, while the British did much less. Hilbert’s twentythree problems, presented in 1900 to the Paris International Congress of Mathematicians , were rapidly published in the Bulletin of the American Mathematical Society (and also in a French translation in the Comptes rendus of the congress).6 The English translations of Poincaré’s famous books of essays are equally divided between English and American editions. The American Mathematical Society was very active, not only translations but also summaries, reports, digests and commentaries on European work fill the pages of the Bulletin of the American Mathematical Society until at least 1914. Paul Carus’s journal The Monist was also an important source. Unsurprisingly, there were four languages for international use in mathematics around 1900: French and German because of the indigenous strength of the mathematics profession in those countries, English because of the strength of the British Empire and the growing power of the United States, and Italian, because there were so many good Italian mathematicians. Even this looked like too many to some. Schröder, in his address to the first International Congress of Mathematicians in Zurich in 1897, said there had been talk of making English the official language of the congress because it was neutral between French and German, but whatever opportunity that might have been was lost when only ten English speakers attended and many more British and American mathematicians went to the British Association for the Advancement of Science meeting held concurrently in Toronto instead.7 What there was not, in 1900, was an acceptable lingua franca. Rather, there were several rival linguae francae. There were, in particular, vigorous groups who aimed to create or adopt one or another international language for mathematical and even all scientific work. They were opposed, usually quietly, by speakers of any hegemonic language who wished their language to prevail. Many educated people thought that there was a small number of mainstream languages and everyone should learn one, or two, or three. This would bring cultural advantages, there were many educational opportunities, and so, such people said, there was no reason to argue with the status quo. Some, such as the linguist Michel Bréal, one of the inventors of semantics, even advocated that the entire world should learn either French or English.8 Still, there was a sizable minority advocating that there should be a new language, created specifically for the...

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