The Secret Formula: How a Mathematical Duel Inflamed Renaissance Italy and Uncovered the Cubic Equation...

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Fabio Toscano Arturo Sangalli

The Secret Formula

How a Mathematical Duel Inflamed Renaissance Italy and Uncovered the Cubic Equation

Fabio Toscano, Arturo Sangalli

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English

Princeton University Pres
01 April 2025

European history; Mathematics & Sciences; Philosophy of mathematics; History of mathematics

The Secret Formula tells the story of two Renaissance mathematicians whose jealousies, intrigues, and contentious debates led to the discovery of a formula for the solution of the cubic equation. Niccolo Tartaglia was a talented and ambitious teacher who possessed a secret formula-the key to unlocking a seemingly unsolvable, two-thousand-year-old mathematical problem. He wrote it down in the form of a poem to prevent other mathematicians from stealing it. Gerolamo Cardano was a physician, gifted scholar, and notorious gambler who would not hesitate to use flattery and even trickery to learn Tartaglia's secret.

Set against the backdrop of sixteenth-century Italy, The Secret Formula provides new and compelling insights into the peculiarities of Renaissance mathematics while bringing a turbulent and culturally vibrant age to life. It was an era when mathematicians challenged each other in intellectual duels held outdoors before enthusiastic crowds. Success not only enhanced the winner's reputation, but could result in prize money and professional acclaim. After hearing of Tartaglia's spectacular victory in one such contest in Venice, Cardano invited him to Milan, determined to obtain his secret by whatever means necessary. Cardano's intrigues paid off. In 1545, he was the first to publish a general solution of the cubic equation. Tartaglia, eager to take his revenge by establishing his superiority as the most brilliant mathematician of the age, challenged Cardano to the ultimate mathematical duel.

A lively and compelling account of genius, betrayal, and all-too-human failings, The Secret Formula reveals the epic rivalry behind one of the fundamental ideas of modern algebra.

By: Fabio Toscano
Translated by: Arturo Sangalli
Imprint: Princeton University Pres
Country of Publication: United States
Dimensions: Height: 235mm, Width: 156mm,
ISBN: 9780691264882
ISBN 10: 0691264880
Pages: 176
Publication Date: 01 April 2025
Audience: College/higher education , Professional and scholarly , General/trade , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active

Fabio Toscano is a science writer for newspapers and television and is the author of many popular science books.

Reviews for The Secret Formula: How a Mathematical Duel Inflamed Renaissance Italy and Uncovered the Cubic Equation

""The yeast of the story has been told already many times, but it has never been told like Toscano does in this book.""---Adhemar Bultheel, European Mathematical Society ""The cubic formula will always be beyond my grasp . . . but the story of its discovery and of the men who battled over it, so memorably recounted in The Secret Formula, is one I am glad to know.""---Jeff Jacoby, Boston Globe ""Toscano weaves together his sources deftly to make the story as lively and exciting as a novel, with mathematics an organic part of the tale.""---Daniel J. Curtin, MAA Reviews ""Toscano is able to provide a realistic and accurate view that captures the complexity of the story of the cubic formula and the very different mathematical practices of this time. Anyone interested in learning about the history of mathematics will likely find it an interesting and informative read.""---Patrick Love, London Mathematical Society Newsletter