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

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The modern era of mathematics began in the first half of the sixteenth century with the discoveries made by a handful of outstanding Italian scholars. Their crucial contributions led to the awakening of the great art, algebra, which had not experienced any significant progress in almost 3,000 years. These new results would soon be the source of numerous and fruitful developments in algebra, paving the way for the advance of the discipline and the important role it would play in mathematics and scientific knowledge in general.

It would be a mistake to assume that an event such as the reawakening and flourishing of algebra during the Italian Renaissance should be of interest only to experts in the field and historians of science. In fact, the incidents and situations related in this book not only represent a key period in the development of mathematics but also constitute a web of events remarkable enough to appeal to the general reader: situations rich in fictional flavorintrigues, secrets, passionate debatesfeaturing some fascinating personages, both brilliant and bizarre, capable of excelling as much by virtue of their superior intellect as by their all-too-human weaknesses.

At the center of the story is a pivotal moment in the history of mathematics: the discovery of the general formula for the solution of the cubic equation and the subsequent developments, together with the captivating intertwinement of the lives of the main actors, among whom the names Niccolo Tartaglia and Gerolamo Cardano stand out.

All the facts had already appeared in print elsewhere, but we felt that they deserved to be told in the context of a story that would do justice to the protagonists, to their ingenuity and shortcomings, and that would reflect the extent of the subject without, however, exhausting it. We sought to condense the story into a reasonable number of pages by focusing on its most significant, interesting, and suggestive aspects. Often, by resorting to quotations, we let the personages speak for themselves, when their own words are more effective and compelling than any paraphrase. Given that the book was designed and written for readers without any specific technical knowledge, we tried to illustrate the mathematical questions and formulas using a language as plain and clear as possible.

I would like to conclude this brief preface by expressing my heartfelt gratitude to Paola Borgonovo for her meticulous and excellent revision work, which resulted in a greatly improved and better flowing text and at the same time allowed me to correct some imperfections. My sincere thanks to Silvia Tagliaferri for the proofreading and to Andrea Morando for creating the beautiful cover design.

Finally, I am indebted to my friend Paola Rigon, from the Classense Library in Ravenna, for the impressive amount of documentary material she obtained for me through national and international interlibrary loans, and to Martha Fabbri, editor of the Galapagos Series, for encouraging the publication of this book and supporting every stage of its production with unfailing dedication and boundless patience.

Needless to say, the responsibility for possible oversights, omissions, or errors is entirely mine.

THE SECRET
FORMULA