Lautman and the Reality of Mathematics

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Corfield, David Neil
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Working in he 1930s, Albert Lautman described with extraordinary clarity the new understanding of mathematics of that time. He delighted in the multiple manifestations of a common idea in different mathematical fields. However, he took the common idea to belong not to mathematics itself, but to an 'ideal reality' sitting above mathematics. I argue in this paper that now that we have a mathematical language which can characterize these common ideas, we need not follow Lautman to adopt his form of Platonism. On the other hand, Lautman should be much better known than he is for pointing philosophy towards this most important feature of mathematics.