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

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

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

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.

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

The Astronomer's Drinking Song Astronomers! What can avail Those who calumniate us; Experiment can never fail With such an apparatus.

The imaginary expression √(-a) and the negative expression -b, have this resemblance, that either of them occurring as the solution of a problem indicates some inconsistency or absurdity. As far as real meaning is concerned, both are imaginary, since 0 - a is as inconceivable as √(-a).