Document (#31595)

Author

Grunwald, E.

Title

Evolution and design inside and outside mathematics

Source

Mathematical intelligencer. 27(2005) no.2, S.17-23

Year

2005

Abstract

Let me start with three dichotomies. Although the first one (at least) is very old, 1 will refer to them for convenience by the names of twentiethcentury mathematicians who have discussed them. Hardy's Dichotomy ... three is no sort of agreement about the nature of mathematical reality among either mathematicians or philosophers. Some hold that it is `mental' and that in some sense we construct it, ourselves, others that it, is outside and independent of us. Gowers's Dichotomy Loosely speaking ... the distinction between mathematicians who regard their central aim as being to solve Problems, and those who are more coneerned with building and understanding theories. Atiyah's Dichotomy Geometry and algebra are the two for-mal pillars of mathematies ... Geometry is, of course, about space ... Algebra, an the other hand ... is concerned essentially with time. Whatever kind of algebra you are doing, a sequence of operations is performed one after the other and 'one after the other' means you have got to have time. In a statie universe you cannot imagine algebra, but geometry is essentially static. My questions in this paper are these: are the three dichotomies related, and are they special Gases of a wider dichotomy that operates outside as well as inside mathematics? My answer to both questions is yes.

Field

Mathematik

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