[On the Gaussian curve,
[On the Gaussian curve, remarked to Poincaré:] Experimentalists think that it is a mathematical theorem while the mathematicians believe it to be an experimental fact. Gabriel Lippmann
Theorems
It is a melancholy
It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians … Read more
The primes are the
The primes are the raw material out of which we have to build arithmetic, and Euclid’s theorem assures us that we have plenty of material for the task. G. H. Hardy
The theory of numbers,
The theory of numbers, more than any other branch of mathematics, began by being an experimental science. Its most famous theorems have all been conjectured, sometimes a hundred years or more before they were proved; and they have been suggested by the evidence of a mass of computations. G. H. Hardy
The seriousness of a
The seriousness of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects. G. H. Hardy
Young men should prove
Young men should prove theorems, old men should write books. G. H. Hardy
What we do may
What we do may be small, but it has a certain character of permanence; and to have produced anything of the slightest permanent interest, whether it be a copy of verses or a geometrical theorem, is to have done something utterly beyond the powers of the vast majority of men. G. H. Hardy
I believe that mathematical
I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our creations, are simply the notes of our observations. G. H. Hardy
The pursuit of pretty
The pursuit of pretty formulas and neat theorems can no doubt quickly degenerate into a silly vice, but so can the quest for austere generalities which are so very general indeed that they are incapable of application to any particular. Eric Temple Bell
Never call yourself a
Never call yourself a philosopher, nor talk a great deal among the unlearned about theorems, but act conformably to them. Thus, at an entertainment, don’t talk how persons ought to eat, but eat as you ought. For remember that in this manner Socrates also universally avoided all ostentation. Epictetus