The moving power of mathematical invention is not reasoning but imagination.

But the gambling reasoner is incorrigible: if he would but take to squaring the circle, what a load of misery would be saved.

Wrong hypotheses, rightly worked from, have produced more useful results than unguided observations.

Common integration is only the memory of differentiation... The different artifices by which integration is effected, are changes, not from the known to the unknown, but from forms in which memory does not serve us to those in which it does.

I was x years old in the year x2.

It was long before I got at the maxim, that in reading an old mathematician you will not read his riddle unless you plough with his heifer; you must see with his light, if you want to know how much he saw.

During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical. The question now is, not whether this or that hypothesis is better or worse to the pure thought, but whether it accords with observed phenomena in those consequences which can be shown necessarily to follow from it, if it be true