The Cult of Pythagoras
Math and Myths
University of Pittsburgh Press, 2012
Did Pythagoras prove the hypotenuse theorem?
Did his cult murder Hippasus for revealing irrational numbers?
Is the Golden Ratio in nature and ancient architecture?
Did the bright boy Gauss add all numbers from 1 to 100?
Is mathematics really the language of nature?
The Cult of Pythagoras answers these questions and others. It’s a unique study of how myths evolve in the history of math. Some tales are partly true, others entirely false, but all show the power of invention in history. Pythagoras emerges as a symbol of the urge to conjecture: he has been credited with fundamental discoveries in math and the sciences, yet there is nearly no evidence that he really contributed anything to such fields at all. This book asks: how does history change when we subtract the many small exaggerations and interpolations that writers have added for over two thousand years?
The Cult of Pythagoras is also about invention in a positive sense. Most people view mathematical breakthroughs as “discoveries” rather than invention or creativity, believing that math describes a realm of eternal ideas. But mathematicians have disagreed about what is possible or impossible, about what counts as a proof, and even about the results of certain operations. Was there ever invention in the history of concepts such as zero, negative numbers, imaginary numbers, quaternions, infinity, and infinitesimals?
Martínez inspects a wealth of primary sources, in several languages, over a span of many centuries. By exploring disagreements and ambiguities in the history of the elements of mathematics, The Cult of Pythagoras dispels myths that obscure the true origins of mathematical concepts. A history that analyzes myths reveals neglected aspects of mathematics that encourage creativity in students and mathematicians.
released Oct. 2012
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Advance Praise:
“Mathematics is the last subject one would expect to be infested with mythology, but even mathematicians can fall for myths, particularly those concerning the history of their subject. In this delightful exposé, Alberto Martínez finally busts the many myths of math, and the results are both sobering and fascinating.”
— Professor John C. Stillwell
University of San Francisco
“Martínez not only rigorously compares the exciting myths about Pythagoras with the sparse, and mostly contradictory, historical sources, he also explains why we have these myths and the purposes they serve. His book will be a natural first port of call for people who like to get this sort of thing right.”
— Professor Jeremy Gray
The Open University, United Kingdom
“Best Bets 2012-2013: Math: The Cult of Pythagoras.”
Book Reviews
“Outstanding Academic Title: The author carefully compares sources in order to extract what might be fact; his scholarship is admirable. Every subject needs its history told in a careful and useful manner, and Martinez clearly succeeds in this endeavor. This book is a good addition to all libraries where seekers of truth might find satisfaction.”
“We believe that mathematics teachers and lecturers and graduate students in mathematics education would benefit from reading the book, as that would help them become more aware of the issues, uncertainties, and challenges surrounding knowledge about the history of mathematics, which at the outset may appear unproblematic.”
“Discover the truth behind some of math's more popular myths: that Pythagoras proved the hypotenuse theorem, that Galois created group theory the night before the pistol duel that killed him, and more.”
“After conducting painstakingly detailed primary source research and re-translating ancient sources, Martinez finds that proof is scarce. He asserts that although speculative myths appear to be true and satisfy the human quest for a juicy story, truth is ultimately more interesting than superstition and fiction. He encourages readers to embrace skepticism.”
”a historically accurate discussion of the many great stories in mathematics. ...In addition, this book contains an interesting discussion of some of the mysteries of mathematics. ...an excellent supplement for a course on mathematics for teachers. ...As an algebraist I found this discussion extremely interesting, but what I liked most was that it was completely accessible to anyone. ...I think this book would be great for any undergraduate student. ...I really enjoyed this book and think it would be a worthwhile read for anyone, but especially a student interested in the history behind the rules mathematicians now take for granted.”
#6 National Bestseller in Mathematics
#3 Best Book of 2012: Ancient Philosophy
“the author has done an excellent job of compiling primary sources to demonstrate how myths about mathematicians have grown and indeed been intentionally fostered. ...This may be the most valuable part of The Cult of Pythagoras—by understanding not just the myth itself, but the process of mythologizing, we can learn something about mathematics and mathematicians.”
“breaks down the controversies of mathematics. ... Martinez opens modern mathematics to broader ways of thinking. ... Discussions of complex mathematical concepts are where Martinez shines. His explanations are clear and understandable without being dumbed down or pedantic. ... unexpectedly engaging ... While the the book will certainly be of interest to students and scholars of math, Martinez has situated the subject in broader themes of human nature that will appeal to a much wider audience.”
Selected New Scholarly Book: “Traces persistent myths in the history of mathematics since ancient times, including the notion that the philosopher Pythagoras proved the hypotenuse theorem.”
“Martinez documents how historical errors begin and propagate. He demonstrates how advances in geometry, algebra, and calculus were made by those willing to question the rules that govern mathematical operations. ...Beyond authenticating or disproving myths, Martinez takes readers into the philosophical questions behind them. ...an engaging study for those interested in the history and pedagogy of science.”
Staff Picks/Popular Titles: “Martínez looks at the positive side of math as a product of creative invention rather than simple discovery by showing how mathematicians have disagreed about what is possible and impossible, about what counts as a proof, and even about the results of certain operations.”
“Premium Title: Dispels myths that obscure the actual origins of mathematical concepts and at the same time praises such invention as positive fodder for the field’s most creative ideas.”
“Many of these questions are certainly intriguing, and their examination in the book makes interesting reading, especially for non-specialists in the history of mathematics... a certain level of mathematical background is required for full appreciation of some of Martinez’s accounts. In conclusion, the ordinary reader should find interesting Martinez’s account of how certain popular claims about individuals and events in the history of mathematics may actually be ‘myths’ and of what may be involved in refuting, accepting, or revising such claims. In this context,Martinez makes the case for raising issues in both the history and the philosophy of mathematics as pertinent knowledge for teachers.”
“a needed corrective to much of the ahistorical nonsense that is repeated about Pythagoras. ...Martínez tackles significant questions like division by zero, the multiplication of negative numbers, and quaternions.”
“Significant University Press Title”
“Good Reads: Martínez tackles these popular myths from mathematics history—revealing some to be partially true, others entirely false. Martínez also delves into the differences between invention and discovery, looking to the past to see if concepts like zero and infinity were created or found. A true account of history, Martínez says, will allow today’s math students to be more creative.”
