The Meaning of Proofs: Mathematics as Storytelling

Why 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.

為什麼數學不僅僅是公式的：一個論點，即寫數學證明等同於創作一個故事。

在《證明的意義》一書中，數學家Gabriele Lolli認為寫數學證明等同於創作一個故事。Lolli提供的不是如何寫數學證明的指導，而是對數學證明作為敘事的哲學和詩意的反思。Lolli寫道，數學被困在其符號和形象中，如果其意義沒有在一個故事中被敘述，則什麼也說不出來。當數學家張口解釋某事物時，比如x的意義，如何找到y，他們正在構建一個敘事。

Lolli寫道，每個證明都是一個冒險的故事，一次進入未知之地開辟新的聯繫路線的旅程；一旦道路開通，我們就會修正它，擴展它。就像童話故事提供了一個敘事結構，可以以原創的方式將新角色插入到該類型的重複形式中一樣，在數學中，每個新的抽象概念都是一個不同理論的主角，並受到數學推理的一般技巧的支持。在古希臘，文學和數學之間不僅僅是類比，還有直接的影響。歐幾里得的證明根源於詩歌和修辭。Lolli斷言，數學不僅僅是公式的操縱。

Gabriele Lolli was Professor of Mathematical Logic from 1975 to 2008 in the Computer Science Department of the University of Turin and Professor of Philosophy of Mathematics in Scuola Normale Superiore in Pisa from 2008 until his retirement in 2014. He is the author of many books, including Discorso sulla matematica, which proposes a mathematical reading of Italo Calvino's Six Memos for the Next Millennium.

Gabriele Lolli在1975年至2008年期間擔任都靈大學計算機科學系的數學邏輯教授，並在2008年至2014年期間擔任比薩諾馬爾超級學院的數學哲學教授，直到退休。他是許多書籍的作者，包括《關於數學的論述》，該書提出了對意大利作家卡爾維諾的《未來千禧年的六篇筆記》進行數學閱讀的觀點。