## The Mathematical ExperienceWe tend to think of mathematics as uniquely rigorous, and of mathematicians as supremely smart. In his introduction to The Mathematical Experience, Gian-Carlo Rota notes that instead, "a mathematician's work is mostly a tangle of guesswork, analogy, wishful thinking and frustration, and proof ... is more often than not a way of making sure that our minds are not playing tricks." Philip Davis and Reuben Hersh discuss everything from the nature of proof to the Euclid myth, and mathematical aesthetics to non-Cantorian set theory. They make a convincing case for the idea that mathematics is not about eternal reality, but comprises "true facts about imaginary objects" and belongs among the human sciences. |

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#### LibraryThing Review

User Review - FPdC - LibraryThingThis is the portuguese translation of The Mathematical Experience. An interesting attempt to convey the nature and importance of Mathematics to the lay reader, the text digresses through a variety of ... Read full review

#### LibraryThing Review

User Review - phiroze - LibraryThingA truly enjoyable read. The author tries to focus on the "experience" of mathematics. However, the depth and breath of the topic makes this an unsurmountable task. To that end, a user looking for an ... Read full review

### Contents

Overture | 1 |

Varieties of Mathematical Experience | 31 |

A Conventionalist | 68 |

Symbols | 122 |

Generalization | 134 |

Mathematical Objects and Structures Exis | 140 |

Proof | 147 |

The Stretched String | 158 |

Selected Topics in Mathematics | 202 |

Confessions of a Prep School Math | 272 |

Polyas Craft of Discovery | 285 |

Comparative Aesthetics | 298 |

From Certainty to Fallibility | 317 |

The Riemann Hypothesis | 363 |

TT and 7T | 369 |

Why Should I Believe a Computer? | 380 |

The Aesthetic Component | 168 |

Algorithmic vs Dialectic Mathematics | 180 |

The Drive to Generality and Abstraction | 187 |

Mathematics as Enigma | 196 |

Classification of Finite Simple Groups | 387 |

FourDimensional Intuition | 400 |

True Facts About Imaginary Objects | 406 |

### Other editions - View all

The Mathematical Experience, Study Edition Philip J. Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 2011 |

The Mathematical Experience, Study Edition Philip Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 2011 |

The Mathematical Experience: Study Edition Philip J. Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 1995 |

### Common terms and phrases

abstract aesthetic algebra algorithm analysis analytic angle answer applications argument arithmetic asserts axiom of choice Bibliography calculus called century circle complex concept conjecture construct continuum hypothesis course definition elements ematics Euclid Euclidean geometry Euler example existence experience fact figure finite formal language formalist formula Fourier Fourier series function Further Readings G. H. Hardy given Hilbert human hypercube idea ideal infinite set infinitesimal infinity integers intuition knowledge Lakatos logic mathe mathematical objects mathematical proof mathematicians matics means ment method natural numbers non-Euclidean geometry nonstandard notion paradox parallel postulate philosophy of mathematics physical Platonism Platonist possible postulate prime number prime number theorem problem proof Proofs and Refutations properties proved question real numbers reason restricted set theory result rigorous sense solution square statement straight line string symbols theorem thing tion triangle true truth universe words zero