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Pure mathematics consists entirely of such asseverations as that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing… It’s essential not to discuss whether the proposition is really true, and not to mention what the anything is of which it is supposed to be true… If our hypothesis is about anything and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

Bertrand Russell, quoted by J. A. Paulos in *Beyond Numeracy* (1992)