My opinion of mankind is founded upon the mournful fact that, so far as I can see, they find within themselves the means of believing in a thousand times as much as there is to believe in.

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

I don't quite hear what you say, but I beg to differ entirely with you.

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

Mathematicians care no more for logic than logicians for mathematics.

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

Considerable obstacles generally present themselves to the beginner, in studying the elements of Solid Geometry, from the practice which has hitherto uniformly prevailed in this country, of never submitting to the eye of the student, the figures on whose properties he is reasoning, but of drawing perspective representations of them upon a plane. ...I hope that I shall never be obliged to have recourse to a perspective drawing of any figure whose parts are not in the same plane.