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 in poetry.
The equation of motion holds at all times, it is in this sense eternal, whereas the geometrical forms, like the orbits, are changing. Therefore, the mathematical forms that represent the elementary particles will be solutions of some eternal law of motion for matter. This is a problem which has not yet been solved.
Real life is different from math. Things in life don’t necessarily flow over the shortest possible route.
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.
Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
It is the same with mathematics, which would certainly not have arisen if it had been known from the beginning that in Nature there are no exactly straight lines, no real circle, no absolute standard of size.
If nature leads us to mathematical forms of great simplicity and beauty—by forms I am referring to coherent systems of hypothesis, axioms, etc.—to forms that no one has previously encountered, we cannot help thinking that they are “true,” that they reveal a genuine feature of nature… You must have felt this too: The almost frightening simplicity and wholeness of relationships which nature suddenly spreads out before us and for which none of us was in the least prepared.