A mathematical solution or demonstration when it yields
a result in a surprising way (e.g., from
apparently unrelated theorems), is short, and is based on fundamental concepts.
According to Henri Poincaré, what gives the feeling of elegance
“is the harmony of the different parts, their symmetry, and their happy
adjustment; it is, in a word, all that introduces order, all that
gives them unity, that enables us to obtain a clear comprehension of
the whole as well as of the parts. …
Elegance may result from the feeling of surprise
caused by the un-looked-for occurrence together of objects not
habitually associated. …
Briefly stated, the sentiment of mathematical elegance is nothing
but the satisfaction due to some conformity between the solution we
wish to discover and the necessities of our mind” (Henri Poincaré, Science and Method,
1908). According to Bertrand Russell,
“Mathematics, rightly viewed, possesses not only truth, but supreme
beauty – a beauty cold and austere, like that of sculpture, without
appeal to any part of our weaker nature, without the gorgeous
trappings of painting or music, yet sublimely pure, and capable of a
stern perfection such as only the greatest art can show”
(Bertrand Russell, A History of Western Philosophy, 1945).
See also: → mathematical; → elegance.
