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4 May 2004: Mathematical discussions contents page. These pages are of various kinds, but they are nearly all attempts to show how mathematical ideas arise naturally, in the hope that some people will find

16 Nov 2004: f(x h) f(x). h λ. 4 T.W.KÖRNER. If we set λ = f ′(x) we recover our old definition of differentiation.(Sometimes people write f ′(x) = (Df)(x)

5 May 2004: Suppose that you have started a company and wish to employ 100 people, and for some reason the only thing that matters is that applicants should be as tall as possible. ... Finally, suppose that the applicants do not have much idea who else will be

6 Jul 2004: Dijkgraaf’s identification of two-dimensional TQFT has been independentallyestablished more or less precisely by a number of people.

20 Sep 2004: I discover that many people have had similar instincts and have worked out the defence in detail, and that many others have been unconvinced, and that whatever I think has already ... People sometimes use extravagant language to describe such

16 Nov 2004: There are many people for whom only the useful is worthwhile.

7 Oct 2004: leaving them as distinct people. ... Many people whenasked this question will suggest, “Every number inthe set A is even.” However, this is wrong: if onethinks carefully about what exactly would have tohappen for the first sentence