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.
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.
Matilde Marcolli is a mathematical physicist who holds positions at Caltech, the University of Toronto, and the Perimeter Institute for Theoretical Physics in Waterloo, Ontario. She is the recipient of the Sofia Kovalevskaya Award of the Alexander von Humboldt Foundation.
“Mathematical proofs are much more like stories or poems than you may realize. Here Lolli explains how, with a fascinating wealth of detail.”
John Baez, Professor, Department of Mathematics, U. C. Riverside