Our ignorance of this beautiful subject -- a tree of ideas with ancient roots and modern fruit -- is profound and beset with fear, superstition, and … - William Rowan Hamilton

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. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.

I discovered the works of Euler and my perception of the nature of mathematics underwent a dramatic transformation. I was de-Bourbakized, stopped believing in sets, and was expelled from the Cantorian paradise. I still believe in abstraction, but now I know that one ends with abstraction, not starts with it. I learned that one has to adapt abstractions to reality and not the other way around. Mathematics stopped being a science of theories but reappeared to me as a science of numbers and shapes.

You know I always have so many metaphysical enquiries & speculations which intrude themselves, that I never am really satisfied that I understand anything; because, understand it as well as I may, my comprehension can only be an infinitesimal fraction of all I want to understand about the many connexions & relations which occur to me, how the matter in question was first thought of or arrived at, &c., &c.