The Music of the

Primes will attract many young people to noncommutative geometry a

la Connes. It would be great if someone would spend a year trying to

write a similar pamphlet in favour of noncommutative _algebraic_

geometry, but as I mentioned before chances are not very high as most

mathematicians are unwilling to sacrifice precision and technical detail

for popular success. Still, perhaps we should reconsider this position.

A fine illustration why most mathematicians cannot write books for a

bigger audience is to be found in the preface to the book “The

problems of mathematics” (out of print or at least out of

amazon.com) by the Warwick mathematician Ian Stewart.

Below I quote a fraction from his ‘An interview with a

mathematician…’

(I)nterviewer : … So,

Mathematician : what delights do you have in store for us?

(M)athematician : I thought I’d say a bit about how you can get a TOP

but non-DIFF 4-manifold by surgery on the Kummer surface. You see,

there’s this fascinating cohomology intersection form related to the

exceptional Lie algebra $E_8$, and…

(I) : That’s

fascinating.

(M) : Thank you.

(I) : Is all that

gobbledegook really significant?

(M) : Of course! It’s one of the

most important discoveries of the last decade!

(I) : Can you

explain it in words ordinary mortals can understand?

(M) : Look,

buster, if ordinary mortals could understand it, you wouldn’t need

mathematicians to do the job for you, right?

(I) : I don’t want

the technical details. Just a general feeling for what’s going on.

(M) : You can’t get a feeling for what’s going on without

understanding the technical details.

(I) : Why not?

(M) :

Well, you just can’t.

(I) : Physicists seem to manage.

(M)

: But they work with things from everyday experience…

(I) :

Sure. ‘How gluon antiscreening affects the colour charge of a

quark.’ ‘Conduction bands in Gallium Arsenide.’ Trip over

‘em all the time on the way to work, don’t you?

(M) : Yes,

but…

(I) : I’m sure that the physicists find all the

technical details just as fascinating as you do. But they don’t let them

intrude so much.

(M) : But how can I explain things properly if I

don’t give the details?

(I) :How can anyone else

understand them if you do?

(M) : But if I skip the fine

points, some of the things I say won’t be completely true! How can I

talk about manifolds without mentioning that the theorems only work if

the manifolds are finite-dimensional paracompact Hausdorff with empty

boundary?

(I) : Lie a bit.

(M) : Oh, but I couldn’t do

that!

(I) : Why not? Everybody else does.

(M) : But, I

must tell the truth!

(I) : Sure. But you might be prepared to

bend it a little, if it helps people understand what you’re doing.

(M) : Well…

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