REVIEWS

“Martínez has woven a fascinating new account of the development of Einstein’s theory. I believe his account supersedes the earlier accounts and sets a standard against which all future accounts will have to be measured."
JOHN STACHEL

Center for Einstein Studies, Boston University, author of Einstein’s Miraculous Year, Founding Editor of The Collected Papers of Albert Einstein
 
"Martínez can certainly take credit for having produced by far the best and most detailed account of this important strand in Einstein's early work.”
JÜRGEN RENN

Max Planck Institute, author of The Genesis of General Relativity
and Albert Einstein: Engineer of the Universe
 
"The payoff is significant. Martínez offers nothing less than a major revision of Einstein's route to special relativity. Make no mistake, historians and philosophers have written thousands of pages on Einstein's invention of relativity. ... This is no armchair reconstruction. Rather, Martínez has inspected and critically evaluated virtually every shred of documentary evidence."
DAVID KAISER

M.I.T.,  author of Drawing Theories Apart: The Dispersion of Feynman Diagrams

 

"I know of no finer biographical account of the young Einstein than Martínez's. I have no doubts that chapters 6 and 7 of Kinematics will become the definitive account of Einstein's ‘invention’ of special relativity."          
S. S. SCHWEBER

Brandeis University, author of QED and the Men who Made It,
and, Einstein and Oppenheimer
 

"The chapters on Einstein form a compelling narrative as the author mines a rich vein of letters and later reminiscences, which make the book very accessible and of interest to many readers."
DANIEL KENNEFICK

Einstein Papers, Caltech, author of Traveling at the Speed of Thought:
Einstein and the Quest for Gravitational Waves

 
"This is a very impressive, original, and important piece of scholarship. I am hugely impressed by what Martínez has achieved."
DON HOWARD
Notre Dame, Editor of Einstein: The Formative Years, 1879-1909,
and Revisiting the Foundations of Relativistic Physics

"Martínez's careful reconstruction of Einstein's path to relativity

is an absolute tour de force!"
SCOTT WALTER

Poincaré Archives, editor of La Correspondance entre Henri Poincaré et les Physiciens
 
"It is amazing that such a fundamental topic, the nub of the matter really, in the history of special relativity had not been thoroughly covered."
ALAN MACDONALD 

Luther College, author of Linear and Geometric Algebra, and “World’s Fastest Derivation of the Lorentz Transformations”
 

 

“An excellent book, truly readable and accurate. I repeatedly found myself intrigued and informed by Martínez's examples and approaches, which succeed in transforming competent historical analysis into an informative and thought-provoking meditation on mathematical meaning."
JOAN L. RICHARDS

Historian of Mathematics, Brown University
 
"Beautifully written. Accurate and reliable. The author's point, that mathematics is constructed according to our judgment of what will serve us, is very important and little understood."
REUBEN HERSH

Mathematician, University of New Mexico
 
"a no holds-barred intervention in long-standing debates over the foundations of mathematics, a wolf in sheep's clothing..."
DAVID KAISER

Historian and Physicist, M.I.T.
 
"Martínez writes with an accessible and conversational style. His discussion of the relationship of mathematics to physics and its role in the concrete features of the world makes this book attractive to general readers and academics alike."
RONALD ANDERSON

Physicist and Philosopher, Boston College

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“Alberto A. Martínez ... shows that the concept of negative numbers has perplexed not just young students but also quite a few notable mathematicians .... The rule that minus times minus makes plus is not in fact grounded in some deep and immutable law of nature. Martínez shows that it’s possible to construct a fully consistent system of arithmetic in which minus times minus makes minus. It’s a wonderful vindication for the obstinate smart-aleck kid in the back of the class.”
— American Scientist  
 
“It is fair to say that Negative Math completely blew my mind. ... Martínez’s superb writing makes even the most subtle arguments and paradoxes seem obvious, but don’t expect this short book to be easy sailing. It will set your mind racing, although every page is absolutely worth the effort.”
— Plus Magazine, University of Cambridge
 
“this is a serious-minded and interesting book. ... The first part of the book, which I enjoyed immensely, is a history of the struggles of mathematicians to cope with the idea of negative numbers. It is enormously encouraging .... intriguing and provocative..."
 — The Mathematical Intelligencer
 
“Euler ... cited no similarly compelling reason for which –m × –n should equal m × n. ...  Martínez develops an apparently viable arithmetic (seemingly free of any internal contradiction) in which the alternative convention prevails. ... The book is written in a relaxed, conversational manner. ... It can be recommended to anyone with an interest in the way algebra was developed behind the scenes."
 — SIAM News, Society for Industrial and Applied Mathematics
 
“...all with the goal of sexing up negative numbers and proposing a meaningful math that could rekindle the ‘connection between mathematical truth and physical experience.’ ... English majors who never understood why they were required to take math classes may enjoy Martínez's blend of humanism and philosophy, and number-people will certainly want to give this a look.”
— Publishers Weekly
 
“Most of us remember the day in math class when we learned that a negative number multiplied by a negative number equals a positive number, e.g., -2 x -2 = 4. No sooner had we digested that rule than we were whisked on to the next topic—so there was no time to stop and ask, “But why is it like that? Why doesn’t -2 x -2 = -4?” In Negative Math, Alberto Martínez spills the beans: there’s no reason why it couldn’t! More generally, he shows how mathematical rules can be varied—and rather than wreck mathematics, such moves can result in new forms of math that more closely describe the physical world.”
— Scientific American Book Club, Club Review
 
“Negative Math is a recent book that should be read by mathematics teachers and it should indirectly affect how students interact with their texts and the included mathematics.”
— MathNexus, Mathematics Portal for Teachers
 
“Mathematicians can devise unusual rules of signs to explore their consequences. For example: a system in which -4 x -4 = -16. Such “fooling around” isn’t talked about in schools, but one aim of this book is to show how new maths can describe aspects of the physical world. The author uses history, puzzles, and high school algebra to entertain a general and professional audience.”
— PBS Teachers, Recommended Books
 
“ #2 Best Seller in Mathematics.”
— YBP Library Services
 
“The author has committed himself to having this writing and this subject matter accessible to the general reader, and he has succeeded to a remarkable degree. His sources, spanning centuries of mathematics and science history, cite leading figures who held strong views relating to this field. For the teacher currently involved with these concepts, this innovative work should provide useful background and prove to be an outstanding read.”
—The Mathematics Teacher,
National Council of Teachers of Mathematics
 
“a book that is at once scholarly and readable. ... anyone with an interest in intellectual history would benefit .... Martínez’s book has the potential to cause the generation of many golden fibers that can be used in weaving the fabric of mathematics.”
— Books & Culture
 
“an intriguing and interesting book. ... It is interesting and to a certain extent inspiring to look at this fundamental transformation of mathematics with the eyes of algebra and not as usual from the point of view of non-Euclidean geometry. ... The book may seem unusual but whoever follows author will be inspired and forced to think about problems which he never put himself before.”
— Zentralblatt MATH
 
“interesting and profound questions .... an impressive range of pertinent sources .... The underlying theme is rich, unusual and important. ... illuminating...”
— The Mathematical Gazette
 
“mathematicians fought against negative numbers into the 17th century and beyond, and others fought against imaginary numbers well into the 19th century. Martínez’s Negative Math relates the history in a way fascinating for talented high school students.”
— The UMAP Journal (Undergraduate Mathematics and Its Applications)
 
“a book that will provide aha moments of enlightenment to readers who span the range from high school students to grizzled mathematics professors. This is a fun, well written book . . . . This book has the potential to spark the creative genius necessary to produce a new generation of excellent mathematicians.”
— HubPages
 
“As a final note to a more mathematically inclined reader, even though Martínez intended the level of mathematics in his book to be for a general reader, this does not lessen the value of this book for other readers. Rather, because the material examines the ideas and work of great mathematicians, it should appeal to a wide audience.”
— Convergence, Mathematical Association of America

 

“Martínez has successfully completed a very difficult task. He has written a book concerning various myths about the history of science that will be very interesting to, and understood by, a generally educated reader. At the same time, his scholarship is so careful that the book will be of value to professional historians and philosophers of science. The episodes, which range from Galileo to Einstein, are fascinating and well chosen. I strongly recommend this book.”
ALLAN FRANKLIN
University of Colorado
 
“Martínez does four valuable things in this book: he refutes several well-established myths and misunderstandings in the history of science, he finds a common thread to many of the older myths in a hidden history of Pythagoreanism, he shows how to detect such mistakes in the work of others, and how to avoid them in one’s own work. It is at once a work of solid scholarship and an education in how to do history of science and it can be read with pleasure and excitement by anyone who cares about the place of science in the modern world.”
JEREMY GRAY
The Open University, United Kingdom

 

“a laudable effort to separate the fragments of truth from the hype surrounding a number of eureka moments ... Martínez skillfully reveals how even the best biographers and writers make plausible but incorrect connections between historical events and often rely on their imagination instead of the facts. Martínez’s more truthful reconstructions of these mythlike stories about Newton, Einstein, Darwin, and other scientists are only a starting point for a fascinating analysis of the historical and social factors that created these legends and keep them alive. This book should be required reading for all college science majors. The author’s meticulous and engaging use of historical evidence will also appeal to history of science enthusiasts.”
— Library Journal  
 
“Busting scientific myths ... fascinating and thought-provoking book.”
— Physics World
 
Editors’ Pick: ”He carefully chips away at some venerable myths of science history to find the underlying facts. ... This book combines the best qualities of popular science writing with the thorough documentation that one would expect from a professional historian. Summing up: Highly Recommended.”
— Choice
 
2011-2012  Bestseller in History of Science
— YBP Library Services
 
“Martinez roots through primary source documents to tease apart fact and fiction in these myths. ... We often try to learn from these stories of success and failure. We seek the business equivalents of Galileo, Newton, and Darwin — legendary figures who will discover innovative ideas that will revolutionize an industry. ... In order to truly learn the lessons that corporate history has to teach us, it is important to act like historians.”
— Harvard Business Review
 
“entertaining reading and a serious inquiry ... intriguing ... almost any reader is likely to find something new. ... powerful food for thought for anyone who believes that historical scholarship is something more than telling engaging stories.”
— Annals of Science
 
“Martinez successfully debunks the myth around the role of Maric in Einstein’s formulation of relativity.”
— Institute of Physics Blog
 
“Martínez shows how bald tales are embroidered or contextualized into stories that catch the imagination and become authoritative and unchallenged. ... where others had doubted whether Charles Augustin Coulomb accurately reported his demonstration that electrical forces obeyed an inverse-square law, Martínez has actually been able to repeat it: replications of long-past experiments are tricky, so that vindication is worth celebrating. ... Martínez provides a reliable, informal, and knockabout route into history of science.”
— Isis    
 
“informative and entertaining, ... Martinez not only debunks or confirms common myths, ... he shows why opinions that were once secret and seemingly impossible are now scientifically compelling.”
— History Wire
 
“In writing that is engaging, deliberate, and fun, ... Readers can gain an understanding of both the concepts behind scientific breakthroughs and the nature of myths in general, as Martínez reconstructs truthful versions of discoveries that are equally as magical.  ”
— Texas Book Festival
 
“particularly authoritative and interesting in this new book’s five essays on the myths surrounding Einstein. ... fascinating and thought provoking. ... he succeeds admirably in a deft manner with both a light touch and numerous insights. ”
— Physics in Perspective
 
“Martínez walks the reader into Einstein's thought experiments that brought him to his theory of special relativity, with surprising clarity and accessibility. And he demonstrates how historians dig for truth by explaining how the myth of Einstein's wife was created. If you like science or history, just a good story and its roots, you'll love Science Secrets.”
— Minnesota Radio
 
“narrates and debunks the myths prevalent among the public and among scientists ... To paraphrase a paleontological cliche ‘absence of evidence (of fossils) is not evidence of absence (of the existence and slow evolution of animals through stages)’, the fact that Einstein denies being an atheist did not mean that he was a ‘believer’ in God or in religion in the commonly understood sense of the words — a point Martinez makes with skill and agility.”
— New Straits Times, Malaysia
 
“In chapters with rich historical analysis and illustrations, Martinez falsifies many famous scientific stories... The book’s narratives are built on a solid basis of evidence and documentation, to thus undermine such myths and inform the public of the truths of science, with a scientific spirit.”
— Yunnan Info Daily News, China
 
“myths are actually important because they serve a purpose... the reality is interesting too,... and that's a real strong point of the book, and I really enjoyed it, I found out interesting things that I hadn't known before.”
— “Women in Science” podcast
 
“History and science collide in this UT professor’s deft unraveling of our most enduring myths.”
— The Austin Chronicle
 
Selected: “Significant University Press Title”  
— Journal of Scholarly Publishing
 
“Martínez has pointed his finger at interesting and often unexplored aspects of science history: Our urge to know leads us to interpolate facts and interpretations into history in a process of speculative invention. These interpolations get picked up, recycled, reinforced, and evolve until we cannot separate fact from fiction any more. Pythagoras is the patron saint of this process. It is more enjoyable to disentangle real history from these interpolations—and to understand why these interpolations were made in the first place—than to accept them and live with them. ”
— Metascience
 
“Alberto Martínez sets us straight on what’s fact, what’s myth, and which truths are indeed stranger than fiction.”
— BookPeople: The Independent
 
“Noteworthy Reads: A unique study of how myths have evolved in the history of science.”
— Newsletter of the BIO-Oceans Association
 
“From Newton’s discovery of universal gravity to Einstein’s belief in God, Martínez analyzes, debunks and demystifies some of the most captivating legends in science.”
— ShelfLife@Texas

 

“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.”
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.”
JEREMY GRAY
The Open University, United Kingdom

 

“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.”
— Choice
 
“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.”
— Science & Education
 
“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.”
— Book-of-the-Month Club
 
“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.”
— Heinz History Center / Smithsonian
 
”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.”
— Mathematical Association of America, MathDL
 
#6 National Bestseller in Mathematics
— YBP Library Services
 
#3 Best Book of 2012: Ancient Philosophy
— Athenaeum Boekhandel Nieuws
 
“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.”
— Mathematical Intelligencer
 
“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.”
— Texas Books in Review
 
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.”
— The Chronicle of Higher Education  
 
“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.”
— Library Journal
 
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.”
— Scientific American Book Club
 
“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.”
— History Book Club   — BOMC2
— Crafter’s Choice Book Club
  — Quality Paperback Book Club
 
“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.”
— International History, Philosophy and Science Teaching Group Newsletter
 
“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.”
— The Proceedings of the Friesian School
 
“Significant University Press Title”
— Journal of Scholarly Publishing
 
“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.”
— Alcalde

 

 

"Martínez has made an extensive and meticulous study ... a solid case for why Bruno was condemned exactly because of his cosmological ideas. Martínez painstakingly follows the actors, those sitting in judgement on Bruno, their friends and acquaintances and any other interested parties, and establishes a continuity between Bruno’s trial and Galileo’s encounter with the Inquisition in 1616 and assesses what this meant for Galileo’s final trial in 1632, finding that the chief charges against Galileo were precisely those that persisted through Bruno’s trials, with the result that Galileo was censured precisely because of his belief in ideas identified with Pythagorean heresy." 

— Annals of Science

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"Martínez offers an interesting and provocative reassessment of the relation between the condemnation of Giordano Bruno, who was burned at the stake, and the milder one that was meted out to Galileo. ....  closer to grasping the mind of Bruno than anyone in our generation."

WILLIAM R. SHEA

author of Galileo Observed: Science and the Politics of Belief (2006), Galileo in Rome (2003), Galileo Galilei: An Astronomer at Work (1993), and Galileo's Intellectual Revolution (1972)

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"An innovative study linking Bruno’s and Galileo’s trials by the Inquisition, this book offers an impressively documented analysis of the ‘Pythagorean’ aspects of their thought, and their heretical implications for the Catholic theologians."

HILARY GATTI

author of Giordano Bruno and Renaissance Science (2002), Essays on Giordano Bruno (2010), and The Renaissance Drama of Knowledge: Giordano Bruno in England (1989),

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"While the consensus by historians is that the 'myth' Bruno was martyred for his cosmological beliefs is false, Martínez in the deep research presented in this book has shown it to be true. I find his arguments compelling and conclusive, supported by previously overlooked or misinterpreted evidence. This is an essential text for any future research into Bruno, Galileo and The Inquisition. In my view it is quite possibly the most important book of the year for the history of astronomy."
CLIFFORD J. CUNNINGHAM

Journal of Astronomical History and Heritage

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“Chapter 1 persuasively and concisely demonstrates that 'Bruno died for
affirming that there exist many worlds, souls migrate into bodies, the soul of
the world is the Holy Spirit and so forth,'  ... Martínez demonstrates that it was Galileo’s pro-Pythagorean position that gave rise to criticism, suspicions, and eventually the charges of heresy against him. Burned Alive is a book that all academic libraries should have. It represents a fascinating, well-written, and accessible contribution to the study of Bruno and Galileo, and a valuable contextualization .... it represents an excellent piece of historical
reconstruction that should prove very valuable in research and teaching.”

— Renaissance and Reformation​