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

All existing things upon this earth, which have knowledge of their own existence, possess, some in one degree and some in another, the power of thought, accompanied by perception, which is the awakening of thought by the effects of external objects upon the senses.

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

Common integration is only the memory of differentiation.

As to writing another book on geometry [to replace Euclid] the middle ages would have as soon thought of composing another New Testament.

I did not hear what you said, but I absolutely disagree with you.

Imagine a person with a gift of ridicule [He might say] First that a negative quantity has no logarithm secondly that a negative quantity has no square root thirdly that the first non-existent is to the second as the circumference of a circle is to the diameter.

Every science that has thriven has thriven upon its own symbols: logic, the only science which is admitted to have made no improvements in century after century, is the only one which has grown no symbols.

The sacred writings excepted, no Greek has been so much read and so variously translated as Euclid.

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.

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.

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.