The Cult of Pythagoras: Math and Myths by Alberto A. Martinez (PDF)

Description

In this follow-up to his popular Science Secrets, Alberto A. Martínez discusses various popular myths from the history of mathematics: that Pythagoras proved the hypotenuse theorem, that Archimedes figured out how to test the purity of a gold crown while he was in a bathtub, that the Golden Ratio is in nature and ancient architecture, that the young Galois created group theory the night before the pistol duel that killed him, and more. Some stories are partly true, others are entirely false, but all show the power of invention in history. Pythagoras emerges as a symbol of the urge to conjecture and “fill in the gaps” of history. He has been credited with fundamental discoveries in mathematics 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 mathematics describes a realm of eternal ideas. But mathematicians have disagreed about what is possible and 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 actual origins of mathematical concepts. Martínez argues that an accurate history that analyzes myths reveals neglected aspects of mathematics that can encourage creativity in students and mathematicians.

User’s Reviews

Editorial Reviews: Review “exhaustive historical research… an enjoyable read… an enormous amount of research… impressive… valuable… entertaining and carefully researched… enjoyable… The author leaves us with lessons that are simple and wise: Healthy skepticism is important for the advancement of knowledge. And the struggle that accompanies this skepticism is worth it.”― American Mathematical Monthly “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.”― The Mathematical Intelligencer “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 Martínez clearly succeeds in this endeavor. This book is a good addition to all libraries where seekers of truth might find some satisfaction.”― Choice”a historically accurate discussion of the many great stories in 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.”― Mathematical Association of America, MathDL”it turns out that virtually all the stories about Pythagoras were untrue.”― Mathematical Gazette About the Author Alberto A. Martínez is a tenured professor of history at the University of Texas at Austin. He is the author of Burned Alive: Giordano Bruno, Galileo and the Inquisition (Reaktion 2018), Science Secrets: The Truth about Darwin’s Finches, Einstein’s Wife, and Other Myths (University of Pittsburgh Press 2011), Kinematics: The Lost Origins of Einstein’s Relativity (Johns Hopkins University Press 2009), and Negative Math: How Mathematical Rules Can Be Positively Bent (Princeton University Press 2006).Prof. Martínez also has a new book about the political news media during the U.S. presidential election of 2015-16: The Media Versus the Apprentice: The Devil Mr. Trump (Saltshadow Castle 2019).

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is an amazing book! I really enjoyed the depth of historical research for the many commonly held “truths”in math. Not only does it include the history of many not-quite-true events, but it also include variousproofs illustrating the interpretations.The author presents common misconceptions and analyzes them. As an example is 1.0 == 0.99999… ?As a college professor, Alberto has a chance to explore this question with new math majors and theirreasons for their differing answers. These kind of ideas get my juices thinking as well.I’m only half through with this book as I enjoy it over morning coffee, but I continue to savor this bookmore and more.Well done Alberto!

⭐I got this for my two sons because I wanted to help them with the synchronizing of myth and spirituality; of math along with the practical use of it. I was disappointed to find that at the heart of this book is a hidden thesis to mock the “soul and spirit” of the great esoteric work of Pythagoras. Martinez even calls Madame Blavatsky a “…plagiarist…” Pg. 210, he shows no reference to his statement and only shows us his naiveté, innocence and prejudice. I will either toss this in the trash or return for a refund. A typical perspective of science, myth and math… dry to the bone. So much is lost when we fail to really understand.

⭐Great book. Very reasonable price, Fast service. I;m very pleased with this transaction.

⭐This book is uneven. Some chapters are concerned with correcting so-called facts of history and tracing through earlier books to show the development of these views. This is done for the stories about Pythagoras and Archimedes, and a bit for Gauss and Galois. Most of the book is directed elsewhere. There’s a smattering about the golden section, a bit about Platonism, a chapter on contending views of infinity and dividing by zero, another on the rules for square roots of negative numbers, then one on calculating quaternions, followed by a look at the debate about infintesimals, then a look at non-euclidean geometry and idealized reality, then Martinez returns to cranking up his hobby-horse about the arithmetic of negative numbers (his first book was on this), and finally ends with some general comments about history and the fictional Pythagoras. Most of the book seems motivated by the view that much of mathematics is invented and so the rules are arbitrary and could be otherwise. But the book is misleading because there isn’t any discussion of modern mathematics or mathematical structure. Parts of the book are good, but overall it doesn’t seem to be written with real insight into mathematics or its coherence.

⭐In twelve chapters, the author goes through various topics in mathematics that span millennia and includes fascinating historical snippets along the way. He starts by debunking the myth that Pythagoras proved the theorem that bears his name and goes on along the same lines with several other issues – all related to mathematics in some way.As I expected in a book such as this, I found some chapters much more interesting than others. I found some to be a bit heavy on Greek philosophy while others more mathematical and quite captivating. Some chapters include discussions on the invention of various mathematical objects and operations – some, well known, e.g., zero, negative integers, irrational numbers and complex numbers, and others less well known, e.g., a mathematics in which (-1) x (-1) = (-1) and other similarly unfamiliar ideas.Pythagoras is brought up a number of times throughout the book. Although this famous individual is credited with many mathematical (and so many other) innovations, the author makes it abundantly clear that there is no clear evidence for any of it at all.The writing style is clear, friendly, accessible, occasionally quite captivating, but at times a bit slow – this depending on the reader’s preferences for the subject matter being discussed. I believe that this book can best be enjoyed by open-minded mathematics enthusiasts who long to learn the facts about mathematical history and some of the unusual ideas brought forth over the centuries.

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