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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.

— Augustus De Morgan A Budget of Paradoxes (1850)

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Mathematics

More quotes by Augustus De Morgan

The lowest steps of the ladder are as useful as the highest.

On the Study and Difficulties of Mathematics (1831)

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

If much difficulty should be experienced in the elementary chapters, I know of no work which I can so confidently recommend to be used with the present one, as that of M. Duhamel.

The Differential and Integral Calculus (1836)

The work now before the reader is the most extensive which our language contains on the subject.

The Differential and Integral Calculus (1836)

I am far from saying that this Treatise will be easy; the subject is a difficult one, as all know who have tried it.

The Differential and Integral Calculus (1836)

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Anyone who believes exponential growth can go on forever in a finite world is either a madman or an economist.

Kenneth Boulding to Kenneth Boulding in: United States. Congress. House (1973)

If the doors of perception were cleansed, everything would appear to man as it is: infinite.

William Blake The Marriage of Heaven and Hell (1790)

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing.

Bertrand Russell

The land of easy mathematics where he who works adds up and he who retires subtracts.

Núria Añó

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Quote text and notes from Wikiquote: Augustus De Morgan (page history), available under CC BY-SA 4.0. Source quality and labels are our own summary of what Wikiquote records.