Introduction to Aesthetics
"Chess problems are the
hymn-tunes of mathematics."
-- G. H. Hardy,
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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