Euler: The Master of Us All

by William Dunham

Leonhard Euler was one of the most prolific mathematicians that have ever lived. This book examines the huge scope of mathematical areas explored and developed by Euler, which includes number theory, combinatorics, geometry, complex variables and many more. The information known to Euler over 300 years ago is discussed, and many of his advances are reconstructed. Readers will be left in no doubt about the brilliance and pervasive influence of Euler's...

• Format: Paperback
• Language: English
• ISBN: 0883853280
• ISBN13: 9780883853283
• Release Date: March 1999
• Publisher: Mathematical Association of America (MAA)
• Length: 208 Pages
• Weight: 0.68 lbs.
• Dimensions: 0.5" x 6.0" x 9.0"

Customer Reviews

William Dunham has done it again!

With the publication of this, his third book, Dunham has once more shown himself to be a master himself of mathematical explanation. Unlike his previous two books, The Mathematical Universe and Journey Through Genius, which covered results by a variety of mathematicians, this book focuses on selected results that sprang from the remarkable mind of Leonard Euler, one of the most prolific and important mathematicians of all time. What sets Euler apart is not only the vast quantity of his output (the publication of his collected works, the Opera Omnia, spans six dozen volumes, or over 25,000 pages in all!), but also the breadth and originality of his work. Not only did Euler contribute to a wide array of mathematical fields -- from number theory to complex analysis to geometry -- but in many cases, he was the founder of those fields. For example, Euler invented the field of analytical number theory, and he was the first mathematician to recognize the importance of and to discover the important properties of complex numbers. This book in many ways resembles Dunham's Journey Through Genius. As in that book, Dunham has selected 15 or so theorems to present in detail, and he makes an effort to keep the proofs similar in spirit to the original proofs. Although the proofs are complete and the book is full of equations, they are accessible to anyone with a high school level of mathematics education. But in addition to the proofs, Dunham also provides historical context, as well as commentary on how later mathematicians used and improved upon Euler's work. For example, we learn that Euler began to loose the sight in his right eye at the age of 32, and that despite his virtual blindness by the age of 65, he continued his prolific rate of output until his death at age 84. The book's title is taken from a quote by Laplace, who said, ``Read Euler, read Euler. He is the master of us all.'' Indeed, if you have any interest in mathematics, you will almost certainly find yourself in complete agreement with Laplace's sentiments by the time you finish reading this wonderful book. ...

So much fun it makes you chuckle

I don't have much to add to the excellent reviews above, except to say that if you like clear exposition of sometimes obscure mathematical themes, like logarithms of imaginary numbers, or the almost magical Euler line, you can't do better than read Professor Dunham's books. And when you mix this talent with a subject such as the incredibly clever and curious Leonhard Euler, you can't help but be carried away. I literally found myself chuckling with awe at some of the amazing leaps of intuition this 18th-century mathematician was able to make, even as he was losing his sight and fathering 13 children! I've always been an admirer of Euler's, and Prof. Dunham's wonderful little book only increased my admiration -for both.I hope Prof. Dunham will decide to write a sequel, and/or tackle the work of other prolific mathematicians, like the Indian Srinivasa Ramanujan, another one of my heroes.This is the third book by Prof. Dunham I've read. I have enjoyed them all and keep them handy to lift my spirits when I'm down -they're that much fun. I wish I'd had him as a teacher in college, and I envy his students at Muhlendorf. I just hope they appreciate how lucky they are!

An enjoyable mathematical romp

I got the book this morning, started reading it, and I didn't know the earth was still rotating until hours later and I had to start the rice cooking for supper. Solid mathematical exposition; historical asides interesting and readable. Very well done except that the puns are too exposed.Each chapter starts off with a description of the state of some mathematical topic as it was before Euler's work, then it explains Euler's contributions to the topic (take your time to follow along, proofs given!). Lastly, each chapter tells where the work has led since. This is a superb way to present a mathematician's achievements.The math is mostly pre-calc level: natural logs, complex numbers, and standard trig identities. The occasional derivatives and integrals pose no hazard to a first-year calculus student. But the book is enjoyable even if you skip over some of the math, a credit to the author's clear exposition. A truly enjoyable mathematical romp.

A fascinating synopsis of the most prolific mathematician

To say that Leonhard Euler possessed mathematical insight is like saying that the last year has been an interesting one in American politics. One would also have to add many superlative qualifiers in front of it if you were to use the word prolific to describe his published mathematical output. The St. Petersburg Academy of Sciences was still publishing his material a quarter century after his death. As the author points out, nothing short of a forklift will allow you to carry a set of his published works around and the ongoing project to publish them was started in 1911 and is still incomplete! With that as a backdrop, it is a challenging task to "squeeze" the flavor of Euler's work into a mere 180 pages that can be balanced on a finger. However, Dunham proves equal to the challenge, providing a tantalizing whiff of most of the areas that Euler contributed to. Many of the proofs presented here take avenues that lead to the solution but leave you puzzled. It is a tribute to his genius that Euler could see that a seemingly irrelevant and complicating operation is in fact a disguised giant step towards the solution. To think nothing of the fact that fathering thirteen children, moving from St. Petersburg to Berlin and then back again and losing his sight in one eye and then the other did not slow him down at all. It is also ironic that he wrote a popular science book that was a bestseller in his time. The book, Letters to a German Princess, was translated into many languages and was even published in the United States in 1833. No doubt there are people who will look at this book and express regrets concerning what was not included. Please be gentle with them. This is a book that could only provide brief glimpses into the works of the most prolific mathematician of all time. And in that sense, Dunham is very successful. Each proof will dazzle you with the combination of simplicity and style. Published in Journal of Recreational Mathematics, reprinted with permission

A little gem.

I had never read any of William Dunham's many books before. Now I want to read them all. In a scant 173 pages he describes in great detail how Leonhard Euler, arguably the greatest mathematician ever, solved the most difficult mathematical problems of his day.The style in this book is both unusual and clever. Each of the eight chapters covers a different branch of mathematics and each begins with a prologue, then follows with some of Euler's contributions, and finishes with an epilogue. The prologues present the history of mathematics up to Euler's time, so the reader gets a feel of what this great mathematician had to work with. And the epilogues tell where we have come since Euler.This book is full of equations and expects some work (but not much mathematical background) from the reader. If you like mathematics or ever wondered how some of the great discoveries in this field were derived, do yourself a favor and buy, then carefully read, this wonderful book.