## The Meaning of Proofs: Mathematics as StorytellingWhy mathematics is not merely formulaic: an argument that to write a mathematical proof is tantamount to inventing a story.In The Meaning of Proofs, mathematician Gabriele Lolli argues that to write a mathematical proof is tantamount to inventing a story. Lolli offers not instructions for how to write mathematical proofs, but a philosophical and poetic reflection on mathematical proofs as narrative. Mathematics, imprisoned within its symbols and images, Lolli writes, says nothing if its meaning is not narrated in a story. The minute mathematicians open their mouths to explain something—the meaning of x, how to find y—they are framing a narrative.Every proof is the story of an adventure, writes Lolli, a journey into an unknown land to open a new, connected route; once the road is open, we correct it, expand it. Just as fairy tales offer a narrative structure in which new characters can be inserted into recurring forms of the genre in original ways, in mathematics, each new abstract concept is the protagonist of a different theory supported by the general techniques of mathematical reasoning. In ancient Greece, there was more than an analogy between literature and mathematics, there was direct influence. Euclid’s proofs have roots in poetry and rhetoric. Mathematics, Lolli asserts, is not the mere manipulation of formulas. |

### Contents

The Meaning of Proofs | 23 |

Three Pieces of Evidence | 67 |

Mathematical Language | 87 |

Poetry and Logic in Euclid | 107 |

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### Common terms and phrases

AC is greater according algebra Archimedes arguments Aristotle axiomatic axioms called Calvino Cantor Cantor's theorem cardinality Cauchy chiasmus Common notion concept considered constructed counternarrative Data DĈB Dedekind deduction defined diagram discussion Doxiadis elements equal equations Erlangen program Euclid Euclid's Elements example exists expressed fact fairy figure finite formulas function Galois Galois group geometry given Greek Hilbert ibid idea infinite set infinitesimals infinity interval invented Langlands program language laws math mathematical proofs mathematicians mathematics meaning metaphor method modus modus ponens modus tollens morphisms myths narration narrative natural numbers numbers objects one-to-one correspondence ordinals origin perhaps physics Plato poetry prime numbers problem properties Proposition proved ratio real numbers reason reductio ad absurdum refer result rhetoric ring composition rules segment sense set theory statement stories straight line structure subsets symbols symmetry theorem thing thought tion translation triangle understand