## 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 |

Varieties of Mathematical Experience | 31 |

A Conventionalist | 68 |

Symbols | 122 |

Generalization | 134 |

Mathematical Objects and Structures Exis | 140 |

tence | 146 |

Infinity or the Miraculous Jar | 152 |

Pólyas Craft of Discovery | 285 |

Comparative Aesthetics | 298 |

From Certainty to Fallibility | 317 |

The Riemann Hypothesis | 363 |

T and fr | 369 |

80 | 371 |

Mathematical Models Computers | 375 |

Classification of Finite Simple Groups | 387 |

The Stretched String | 158 |

The Aesthetic Component | 168 |

Algorithmic vs Dialectic Mathematics | 180 |

The Drive to Generality and Abstraction | 187 |

Mathematics as Enigma | 196 |

Selected Topics in Mathematics | 202 |

Confessions of a Prep School Math | 272 |

### Other editions - View all

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

### Common terms and phrases

abstract activity actually algebra analysis analytic answer appears applied argument arithmetic axioms become believe calculation called circle common complex conjecture considered construct course definition elements equal equation example existence experience fact figure finite formal formula foundations function Further geometry give given human idea ideal infinite integers interesting intuition knowledge lead less logic look mathe mathematicians mathematics matics matter means method mind natural never objects philosophy physical position possible present prime probability problem proof properties proved question Readings reality reason rules seems sense set theory simple solution square statement symbols theorem theory thing thought tion true truth understand universe whole writing zero