## What Is Mathematics, Really?Virtually all philosophers treat mathematics as isolated, timeless, ahistorical, inhuman. In What Is Mathematics, Really? renowned mathematician Reuben Hersh argues the contrary. In a subversive attack on traditional philosophies of mathematics, most notably Platonism and formalism, he shows 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. Mathematical objects are created by humans, not arbitrarily, but from activity with existing mathematical objects, and from the needs of science and daily life. 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. The humanist standpoint helps him to resolve ancient controversies about proof, certainty, and invention versus discovery. The second half of the book provides a fascinating history of the "mainstream" of philosophy - ranging from Pythagoras, Plato, Descartes, Spinoza, and Kant, to Bertrand Russell, Hilbert, Carnap, and Quine. Then come the mavericks who saw mathematics as a human artifact - Aristotle, Locke, Hume, Mill, Peirce, Dewey, Wittgenstein. In his epilogue, Hersh reveals that this is no mere armchair debate, of little consequence to the outside world. Platonism and elitism fit together naturally. Humanism, on the other hand, links mathematics with people, with society, and with history. It fits with liberal anti-elitism and its historical striving for universal literacy, universal higher education, and universal access to knowledge and culture. Thus Hersh's argument has educational and political consequences. |

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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

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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 |

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JSTOR: "What is Mathematics, Really?"

"What Is Mathematics, Really?" By Reuben Hersh. Oxford University Press, Oxford, UK, 1997. $35.00. xxiv+343 pp., hardcover. ISBN 0-195-11368-3. ...

links.jstor.org/ sici?sici=0036-1445(200003)42%3A1%3C138%3A%22IMR%3E2.0.CO%3B2-6

What Is Mathematics, Really? by Reuben Hersh at Questia Online Library

Platonism is the most pervasive philosophy of mathematics. Indeed, it can be argued that an inarticulate, half-conscious Platonism is nearly universal among ...

www.questia.com/ library/ book/ what-is-mathematics-really-by-reuben-hersh.jsp

Könyvek

What is Mathematics, Really? HERSH, Reuben. Fordította: A collective of translators. Témakör: Translations from English. ISBN-13 978-963-9132-57-3 ...

www.typotex.hu/ index.php?page=en/ konyvek&

What is Mathematics, Really? - Wikipedia

What is Mathematics, Really? Title of a modern book by Rueben Hersh featuring his humanistic and maverick views on Mathematics and Mathematicians. ...

nostalgia.wikipedia.org/ wiki/ What_is_Mathematics,_Really%3F

Powell's Books - What Is Mathematics, Really? by Reuben Hersh

Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood ...

www.powells.com/ partner/ 31879/ biblio/ 0195130871/

What Is Mathematics, Really?_0195130871 » freebooksclub.network **...**

Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood ...

www.freebooksclub.net/ 2007/ 11/ 08/ what_is_mathematics_really_0195130871.html

What is Maths Really?

What is Mathematics, Really? Reuben Hersh A thought-provoking investigation into the philosophy of mathematics. Forty years ago, well before he had even ...

www.simonsingh.net/ What_is_Mathematics_Really.html

Mathematical Independence vs. Dependence

What is Mathematics, Really? Oxford University Press, 1997. 343 p. Gouvęa, Fernando. “Read This! Review of What is Mathematics, Really?” MAA Online. 1999. ...

www.scribd.com/ doc/ 7917/ Mathematical-Independence-vs-Dependence?query2=dependence+sign+math

What is Mathematics? - sci.math | **Google** Groups

(Hersh, R. What is Mathematics, Really? Oxford University Press, 1997. The Humanist perspective.) (Devlin, K. Mathematics: The Science of Patterns; ...

groups.google.com/ group/ sci.math/ browse_thread/ thread/ cb47448dbcf39fc4/ 4f2b1014b746e456?lnk=raot

Advogato: TIME is _not_ REAL

What is Mathematics, REALLY?, posted 17 Oct 2005 at 16:20 UTC by sye » (Journeyer) ... From "What is Mathematics, REALLY?" by Reuben Hersh 1997 ...

www.advogato.org/ article/ 857.html