## 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. |

### What people are saying - Write a review

#### 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 |

Appendix ABrief Chronological Table | 26 |

A Conventionalist | 68 |

Symbols | 122 |

Generalization | 134 |

Mathematical Objects and Structures Exis | 140 |

Proof | 147 |

The Stretched String | 158 |

Pólyas Craft of Discovery | 285 |

Comparative Aesthetics | 298 |

From Certainty to Fallibility | 317 |

The Riemann Hypothesis | 363 |

and î | 369 |

Mathematical Models Computers | 375 |

Classification of Finite Simple Groups | 387 |

FourDimensional Intuition | 400 |

### Other editions - View all

The Mathematical Experience, Study Edition Philip 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 algebra analysis answer appears applications argument arithmetic asserts axioms become calculation called century circle complete concept considered consistent construct course definition elements equal equation example existence experience fact figure finite formal formula Fourier function Further geometry give given human idea ideal infinite integers interesting intuition knowledge known language lead less logic look mathe mathematicians mathematics matics matter means method mind natural notion objects philosophy physical position possible present prime problem proof properties proved pure question Readings reason remainder result rules seems sense set theory simple solution square standard statement straight line symbols theorem thing thought tion true truth understand universe whole writing zero