Sunday, October 10, 2004

Sunday October 10, 2004

Filed under: General — m759 @ 10:35 PM

Introduction to Aesthetics

“Chess problems are the
hymn-tunes of mathematics.”
— G. H. Hardy,
A Mathematician’s Apology

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The image “http://www.log24.com/log/pix04A/041010-Mate2.jpg” cannot be displayed, because it contains errors.

G. H. Hardy in
A Mathematician’s Apology:

“We do not want many ‘variations’ in the proof of a mathematical theorem: ‘enumeration of cases,’ indeed, is one of the duller forms of mathematical argument.  A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way.

A chess problem also has unexpectedness, and a certain economy; it is essential that the moves should be surprising, and that every piece on the board should play its part.  But the aesthetic effect is cumulative.  It is essential also (unless the problem is too simple to be really amusing) that the key-move should be followed by a good many variations, each requiring its own individual answer.  ‘If P-B5 then Kt-R6; if …. then …. ; if …. then ….’ — the effect would be spoilt if there were not a good many different replies.  All this is quite genuine mathematics, and has its merits; but it just that ‘proof by enumeration of cases’ (and of cases which do not, at bottom, differ at all profoundly*) which a real mathematician tends to despise.

* I believe that is now regarded as a merit in a problem that there should be many variations of the same type.”

(Cambridge at the University Press.  First edition, 1940.)

Brian Harley in
Mate in Two Moves:

“It is quite true that variation play is, in ninety-nine cases out of a hundred, the soul of a problem, or (to put it more materially) the main course of the solver’s banquet, but the Key is the cocktail that begins the proceedings, and if it fails in piquancy the following dinner is not so satisfactory as it should be.”

(London, Bell & Sons.  First edition, 1931.)

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