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.

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.

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.

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.

Mathematicians care no more for logic than logicians for mathematics.

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