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Hersh (1997) in a book aptly named What Is Mathematics Really? stresses the great distance he detects between the reality of professional mathematical practice—contemporary and historical—and the reasoning in formal languages that philosophers (since Frege) have largely characterized mathematical proof in terms of. Hersh criticizes the reasoning-in-formal-languages view of mathematical practice and mathematical proof as "isolated," "timeless," "ahistorical," and indeed, even "inhuman." Hersh (1997, xi) contrasts this derivation-centered view of mathematics (and mathematical proof) with an alternative view that takes mathematics to be a human activity and a social phenomenon, one which historically evolves and is intelligible only in a social context. His alternative view pointedly roots mathematical practice in the actual proofs that mathematicians create—actual proofs that Hersh claims philosophers of mathematics often ignore.

DOI: 10.1007/978-3-319-61231-7_20

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