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Full Idea
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.
Gist of Idea
In mathematic we are ignorant of both subject-matter and truth
Source
Bertrand Russell (Mathematics and the Metaphysicians [1901], p.76)
Book Ref
Russell,Bertrand: 'Mysticism and Logic' [Unwin 1989], p.76
A Reaction
A famous remark, though Musgrave is rather disparaging about Russell's underlying reasoning here.