Beauty is the first test: there is no permanent place in the world for ugly mathematics.
Sentiment: NEGATIVE
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.
As for everything else, so for a mathematical theory: beauty can be perceived but not explained.
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.
Beauty without expression is boring.
To emphasize only the beautiful seems to me to be like a mathematical system that only concerns itself with positive numbers.
Ugliness is in a way superior to beauty because it lasts.
What finally is beauty? Certainly nothing that can be calculated or measured. It is always something imponderable, something that lies between things.
Mathematics has beauty and romance. It's not a boring place to be, the mathematical world. It's an extraordinary place; it's worth spending time there.
Beauty is a relation, and the apprehension of it a comparison.
Beauty is variable, ugliness is constant.