## What Is Mathematics, Really?Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science. |

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#### What is mathematics, Really?

User Review - Not Available - Book VerdictHersh, mathematician and coauthor of The Mathematical Experience (1983), attempts to answer here the philosophical question, "What is mathematics?" Many practitioners think of themselves as ... Read full review

#### Review: What Is Mathematics, Really?

User Review - Glenn Kriger - GoodreadsA great book for a philosophical nerd. Read full review

### Contents

Survey and Proposals | 3 |

Criteria for a Philosophy of Mathematics | 24 |

MythsMistakesMisunderstandings | 35 |

IutuitionProofCertniuty | 48 |

Five Classical Puzzles | 72 |

Mainstream Before the Crisis | 91 |

Mainstream Philosophy at Its Peak119 | 119 |

Mainstream Since the Crisis | 137 |

Foundationism DicsMainstream Lives | 165 |

### Common terms and phrases

abstract algebra analytic angles answer arithmetic axiom of choice axiomatic set theory axioms believe Bertrand Russell Brouwer calculation called certainty Chapter complex numbers concepts construction contradiction David Hilbert definition derivative Descartes entities equation Euclid Euclidean Euclidean geometry example exist experience finite formal formalist formula foundationist foundations Frege function gazillion Godel graph Hilbert human humanist idea ideal indubitable integral intuition intuitionism Kant Kitcher Kurt Godel Lakatos Leibniz logic logicist mathe mathematical knowledge mathematical objects mathematical proof mathematicians matics meaning mental method mind myth natural numbers nature of mathematics non-Euclidean geometry notion number system philosophy of mathematics physical Platonism Platonist polynomials problem properties proved pure Pythagorean question rational numbers real numbers reality reasoning rigorous rules Russell Russell's paradox sense set theory set-theoretic space Spinoza square statement teaching theorem There's things thought tion triangle true truth understand universe What's Wittgenstein zero