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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

31 Oct 2004: So the rule is ask and ask at once. (b) Questions of Incomprehension It takes considerable courage to admitthat you do not understand something in front of other people.

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.

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)

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

21 Oct 2004: Here is a typical use of the Banach-Steinhauss theorem. 4You should be warned that a lot of people, including the present writer, tend toconfuse the names of these two theorems.

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

5 Oct 2004: 3In the sense that most reasonable people would call reasonable. Selberg produced a(technically) elementary proof which may be found in his collected works.

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