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. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. [...] 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. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.

Summary

This quote by British mathematician and philosopher Bertrand Russell explains the nature of pure mathematics. According to Russell, pure mathematics comprises statements of the form "if proposition A is true, then proposition B is also true," without specifying the truth or relevance of proposition A or the subject matter it refers to. The quote suggests that in mathematics, the focus lies solely on the logical relationships between propositions, without concerning itself with their meaning or truthfulness. Russell's purpose is to provide comfort and clarification for those perplexed by the esoteric nature of mathematical beginnings.

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