To emphasize only the beautiful seems to me to be like a mathematical system that only concerns itself with positive numbers.
Sentiment: NEGATIVE
As for everything else, so for a mathematical theory: beauty can be perceived but not explained.
Beauty is the first test: there is no permanent place in the world for ugly mathematics.
Mathematics are the result of mysterious powers which no one understands, and which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty's sake and pulls it down to earth.
Beauty itself is but the sensible image of the Infinite.
No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful.
What finally is beauty? Certainly nothing that can be calculated or measured. It is always something imponderable, something that lies between things.
Nothing can be beautiful which is not true.
But I think beautiful is simple and elegant, like a ballad with simple harmony.
When something is beautiful in math, everything is just perfectly lined up, and you see through sheer thought that something really beautiful can take place.
The beautiful has but one type, the ugly has a thousand.