The Meaning of Proofs: Mathematics as Storytelling

by Gabriele Lolli, Matilde Marcolli (Foreword), Bonnie McClellan-Broussard (Translator)

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.

Genres: Mathematics, Science, Nonfiction

176 pages, Paperback

Published September 27, 2022

Reviews

[Richard Marney · Rating 4 out of 5]

A delightful journey.

Mathematics inspiring our narratives, narratives inspiring mathematics?

If one believes all mathematics lies in the universe waiting for men and women to discover its beauty, then the development of greater knowledge in pure mathematics is similar to the search for the infinite. This knowledge shapes our myths on earth and in the heavens.

This book is suitable for non-Mathematicians.

😀😀

[Kim Gausepohl]

This is NOT a book written for non-mathematicians or the layperson, despite what the introduction claims. I don’t even feel comfortable giving a star rating knowing I was not the intended audience. I enjoyed the argument that math is not objective and how mathematicians introduce fictions (e.g., a line segment in a square) to help explain their understanding of the world just as writers and poets do. Chapter 7 which compared poetic forms to logical arguments was worth reading/skimming through all the other unnecessarily complex chapters for.

[Curtis Penner · Rating 3 out of 5]

This is lucky to get the 3 stars. I purchased this book based on the title and a quick flip through the book. The subtitle is what piqued my curiosity, "Mathematics as Storytelling". The book didn't even get close to this for the first 30% of the book. And then it slowly crept to the subject "The Meaning of Proofs".

The author must have an intense fascination with ancient greek mathematics because that was what he used as examples. What about analysis, differential equation, and more.

In the end it was not worth the purchase price. The idea to me is still fascinating, but the book absolutely didn't deliver.

[Andrew Cavaciuti · Rating 3 out of 5]

"Stories play crucial roles in our discovering, creating, explaining, and organizing knowledge, and thus mathematics also has a great need for narrative, even though its taste for general ideas might make one forget this."

[Sonia · Rating 4 out of 5]

Great book, but the introduction was misleading. It's not suitable for non-mathematicians and I would say it's more suitable for Pure Mathematicians.