The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful.
There is no excellent beauty that has not some strangeness in the proportion.
As for everything else, so for a mathematical theory: beauty can be perceived but not explained.
One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories.
Wherever there is number, there is beauty.
Paul Erdos has a theory that God has a book containing all the theorems of mathematics with their absolutely most beautiful proofs, and when he wants to express particular appreciation of a proof he exclaims, “This is from the book!”
Euclid alone has looked on Beauty bare.
I love mathematics…principally because it is beautiful, because man has breathed his spirit of play into it, and because it has given him his greatest game—the encompassing of the infinite.
The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.
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 paintings or music, yet sublimely pure and capable of a stern perfection such as only the greatest art can show.
My work has always tried to unite the true with the beautiful and when I had to choose one or the other, I usually chose the beautiful.