We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of science are mathematics and logic; the mathematical set puts out the logical eye, the logical set puts out the mathematical eye; each believing that it sees better with one eye than with two. Note that De Morgan, himself, only had sight with only one eye.

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

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

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.

Great fleas have little fleas upon their backs to bite 'em, And little fleas have lesser fleas, and so ad infinitum, And the great fleas themselves, in turn, have greater fleas to go on, While these again have greater still, and greater still, and so on.

It should seem that it is easier to square the circle than to get round a mathematician.