A Most Elegant Equation: Euler’s Formula and the Beauty of Mathematics by David Stipp (PDF)

Description

An award-winning science writer introduces us to mathematics using the extraordinary equation that unites five of mathematics’ most important numbers Bertrand Russell wrote that mathematics can exalt “as surely as poetry.” This is especially true of one equation: ei(pi) + 1 = 0, the brainchild of Leonhard Euler, the Mozart of mathematics. More than two centuries after Euler’s death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler’s identity or God’s equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp’s hands, Euler’s identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

User’s Reviews

Editorial Reviews: Review “If you are an intelligent reader–even one with a weak mathematical background… you could learn a lot from this book, and enjoy the experience.”―Mathematical Association of America”Mr. Stipp’s roving account is propelled by his folksy sense of humor.”―Wall Street Journal”Stipp gives his reader a good shot at getting hold of something beautiful.”―The Weekly Standard”A Most Elegant Equation is a smart, incisive account of Euler’s famous equation. It beautifully and seamlessly straddles the line between the salient ideas of the equation’s proof and its historical, scientific, and philosophical significance.”— John Allen Paulos, professor of mathematics at Temple University and author of Innumeracy and A Numerate Life”Even though Pi, e, and i are Very Important Numbers, they seemed unrelated—until Euler discovered a simple, beautiful, and totally unexpected link between them. This delightful book shows us why the formula is surprising, yet inevitable. Thoroughly enjoyable!”— Ian Stewart, author of Significant Figures”Does mathematics transcend our humanness, or is it simply a human construct? Either way, the astonishing interconnections and stunning beauty that mathematics offers can only serve to uplift our human souls. The poetry of ‘e to the i pi,’ as exemplified by David Stipp, masterfully proves this.”— James Tanton, Mathematician-at-Large for the Mathematical Association of America”As a non-professional recovering mathlete, I found A Most Elegant Equation a delightful excursion into the beauty of mathematical thinking. Not only is Stipp a great storyteller, he is a terrific teacher with an easy conversational style who makes the most complex concepts lucid. For anyone who was ever afraid of math, here’s your cure.”— Richard A. Friedman, Professor of Clinical Psychiatry at Weill Cornell Medical College and contributing Op-Ed writer for the New York Times About the Author David Stipp is an award-winning science writer whose work has appeared in Scientific American, New York Times, Wall Street Journal, Science, and other publications. The author of The Youth Pill, he lives in Boston, Massachusetts.

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

⭐This is a fascinating book, to me. Math has always been a subject that intrigued me, and this formula includes three of the most intriguing values in math: pi, i and e. And, it includes 0 and 1. The book lays out the importance of each of these values in a very readable format, and then brings them together in a process that doesn’t require a strong understanding of math principles. No calculus is needed here, and no strong understanding of proofs. In the process of developing his topic, the author uses some much needed humor. During my reading of the book, I often laughed and my wife who was sitting next to me would ask: “how could someone find a math book funny?” I’m one of the folks that the author describes who love math. I studied and received a math degree in college and listened to rote presentations on proofs, etc. (One instructor of Abstract Algebra would come into class lay his books down turn his back to the class and proceed to write definitions, formulas, proofs etc for 45 minutes, and we would frantically write to keep up with him.) None of that here. This is an enjoyable book that brings back my reasons for why I loved math in the first place.

⭐Nice overview of complex analysis for lay people, best for those with some basic background in math. It isn’t a college-level review but that is not what it claims to be. If you can read this book and not develop some appreciation for the beauty and mystery of Euler’s identity, it’s probably a hopeless cause. I deducted one star because I would have enjoyed the book even more if it had slightly more mathematical rigor and slightly less “chatiness”. But perhaps I am nitpicking and the author and publisher were adhering to Hawking’s hypothesis (that the author mentions) that each equation in a book meant for a lay audience halves the readership. I hope the author writes similar books on other mathematical and scientific topics. Bravo.

⭐Easy to read, nicely written. E is a very important number in Math andI loved to know more about it. The author very nicely revews PI , e , 1, zero,Infinity, Trigonometry, Vectors and derives very easily Euler’s God Formula .Very easy read. Maybe the one star reviewers have higher expectations, butfor me , this book satisfied my need to review these beautiful parts of Math.I loved the book . It is really worth reading if one loves Math and wants a shorteasy and excellent explanation of e, pi, trig and imaginary numbers .Then there is chapter 11 , “ The meaning of it all “ :Is the Universe mathmatic or is Math a human creation ? Why not listen to whatpeople think ? After all , philosophical considerstions are what make us humanand we cannot not wonder about who we are and the World ! The author continuesto be succint and does not bore us with endless discussion .

⭐When the educational merits of rote memorization come up in discussion, I have this annoying habit of telling my friends that math is a lot like a good poem: if you’re young enough when you memorize it, it gets burnt to the “hard disk” part of your brain, from where you can retrieve it when you’re mature enough to understand, or at least explore, its meaning.I was fifteen when I became familiar with the equation on the cover (don’t ask!) and sure enough I recall it fully, so I had high hopes for this book. Perhaps it would take me to a more intuitive level of understanding.It resolutely didn’t.In the interest of perhaps walking math-shy people through the equation (a task that I’ll bet good money it fails to achieve) this is far far far too dumbed down. It explains totally evident stuff. And it leaves the proof to a short appendix. I was expecting that appendix to be 150 pages rather than ten pages. Instead, you get a biography of Euler, a description of pi and waffle about beauty, aesthetics etc.Regardless, I’m a sucker, so I enjoyed this. I enjoyed the definition of what e is at the very beginning (it’s what you get if you infinitely compound a 100% return over a year: if you compound semiannually, you end up with 2.25 instead of 2, if you compound every quarter you’re at 2.44, if you compound every day you get 2.72, which is e) I also enjoyed the discussion regarding Platonic versus man-made math (not that it moved my views one iota) and nobody had ever shown me what i raised to the i is, so I liked that too.But the reading time I won’t get back. And I’m none the wiser about any deeper meanings of an equation that to me is the equivalent of a slide rule. Oops, did I say that?

⭐We are in 2017, David noticed that the prettiest equation was not in his textbooks. And you probably never saw it at school neither. What?! So he decided to write this book to fix this ugly mistake. Of course bright people (say autoditats thrilled with mathematics) find Euler’s identity early in life but we (hungry-minded laypersons) never see the sexy stuff. Good news. Here comes an accessible compilation of history (including a bit of Euler’s impressive biography), fundamental concepts and a gentle/incremental deduction of this elegant relation. Or flabbergasting, beautiful, intriguing, provocative… formula putting together the top five celebrity numbers (e, i, pi, 1 and 0) using just three arithmetic operations (+, = and ^).

⭐I enjoyed the book, but was generally let down by the lack of depth. It really does become obvious that it’s a journalist writing as you continue through the book.I wanted a lot less elementary math and a lot more philosophical analysis. Even where the “meaning” of it is said to be discussed per the chapter title, it really isn’t ever discussed. It is mostly saying “people should find this to be important” rather than any real deep dive.Also, it’s frustratingly short. Don’t get me wrong—I love concise books. But I was burning through pages like it was a children’s story-time book. There wasn’t much actually conveyed.

⭐I believe that any mathematically-challenged person who can get past this book’s cover: Cartesian plot, Euler’s equation, title and sub-title, could easily and painlessly breeze through this extremely friendly book. It was written for the severely math-phobic. The author goes out of his way to explain, in several lines, what would be clear to most in just one. In the last chapter, philosophical aspects of mathematical beauty are discussed and the appendices contain derivations that may be more challenging to some.The author’s prose is very friendly, witty, occasionally humorous, crystal clear and amazingly accessible. It should be of great interest to those who are seriously mathematically challenged. However, I do believe that regular math enthusiasts would do well to skip this one since they would not likely learn anything from it and may even find it relatively boring, although they may enjoy the last chapter and the two appendices, as I did.

⭐Witty and humorous.

⭐The book does not offer interesting or original information beyond what can be easily found in the web. Worse, the treatment is simplistic and the author spends lengthy time on trivial things such as trigonometric functions. The author did mention in the introduction that the math knowledge expected from the reader is that of a six grader, but I did not expect the banality and dismaying simplicity in the subsequent chapters.All in all, this is a very disappointing book that does not rise to the promise conveyed by the title and reviews. If you have a decent knowledge in math, do not expect much from this book. You will certainly find it boring and just a waste of time and money.I will try to find a sixth grader to give the book to, otherwise to the recycling bin…

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