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Euler's Pioneering Equation: The most beautiful theorem in mathematics
In 1988 The Mathematical Intelligencer , a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was
'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a
Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence."
What is it that makes Euler's identity, e i π + 1 = 0, so special?
In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in the number 1, the basis of our counting system; the concept of zero, which was a major
development in mathematics, and opened up the idea of negative numbers; π an irrational number, the basis for the measurement of circles; the exponential e , associated with exponential growth and logarithms; and the imaginary number i , the square root of -1, the basis of complex numbers. Following a
chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula.
'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a
Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence."
What is it that makes Euler's identity, e i π + 1 = 0, so special?
In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in the number 1, the basis of our counting system; the concept of zero, which was a major
development in mathematics, and opened up the idea of negative numbers; π an irrational number, the basis for the measurement of circles; the exponential e , associated with exponential growth and logarithms; and the imaginary number i , the square root of -1, the basis of complex numbers. Following a
chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula.
176 pages, Hardcover
Published April 1, 2018
About the author
Robin J. Wilson
66 books12 followersRobin James Wilson (born December 1943) is a professor in the Department of Mathematics at the Open University, a Stipendiary Lecturer at Pembroke College, Oxford[1] and, as of 2006, professor of geometry at Gresham College, London, where he has also been a visiting professor. On occasion, he guest teaches at Colorado College.
From January 1999 to September 2003 Robin Wilson was editor-in-chief of the European Mathematical Society Newsletter.[2]
He is the son of Harold Wilson, former Prime Minister of the United Kingdom. He has two daughters: Catherine and Jennifer.
From January 1999 to September 2003 Robin Wilson was editor-in-chief of the European Mathematical Society Newsletter.[2]
He is the son of Harold Wilson, former Prime Minister of the United Kingdom. He has two daughters: Catherine and Jennifer.
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Displaying 1 - 12 of 12 reviews
January 23, 2018
The concept of a 'beautiful equation' is a mystery to many, but it seems to combine a piece of mathematics that expresses something sophisticated in relatively few terms and something that looks satisfying. The equation that has proved standout amongst mathematicians, as by far the most beautiful (and is only placed second to Maxwell's equation amongst physicists) is Euler's remarkable eiπ +1 = 0. What seems remarkable to me about this is that it just seems bizarre that this combination of things produces such a neat result. (Incidentally, as far as I can see, the only reason for the 'pioneering' in the title was to enable the fancy graphic on the cover of the book.)
Getting popular maths books right is incredibly difficult. When I started reading this book, I really thought that Robin Wilson had cracked it. After an introduction, he gives us a chapter on each of the elements of the equation (except the plus and equals signs), from the more basic aspects like 1 and 0 to the more sophisticated components. Then, in a final chapter, he pulls it all together to show why Euler's equation works and why it's useful.
So far, so good. And up to and including pi, except for giving us rather too many series to approximate to it, Wilson does this very well. I really enjoyed the first few chapters. But once we get onto e and i, things go downhill. What had been pitched at a level for the general reader becomes too maths-heavy and lacks readability - and this isn't resolved in the final chapter. If anything things get worse.
I'd say the bare minimum to get through the whole book is a maths A-level, but more than that, in those final chapters, only a total mathematician could enjoy what they were reading. It's such a shame, as the concept is great, the equation is fascinating and the first few chapters work so well. It's almost as if two different books have been involved in a crash and this is the result of welding together the front of one and the rear of the other. A worthy topic, but not quite the book it could have been.
Getting popular maths books right is incredibly difficult. When I started reading this book, I really thought that Robin Wilson had cracked it. After an introduction, he gives us a chapter on each of the elements of the equation (except the plus and equals signs), from the more basic aspects like 1 and 0 to the more sophisticated components. Then, in a final chapter, he pulls it all together to show why Euler's equation works and why it's useful.
So far, so good. And up to and including pi, except for giving us rather too many series to approximate to it, Wilson does this very well. I really enjoyed the first few chapters. But once we get onto e and i, things go downhill. What had been pitched at a level for the general reader becomes too maths-heavy and lacks readability - and this isn't resolved in the final chapter. If anything things get worse.
I'd say the bare minimum to get through the whole book is a maths A-level, but more than that, in those final chapters, only a total mathematician could enjoy what they were reading. It's such a shame, as the concept is great, the equation is fascinating and the first few chapters work so well. It's almost as if two different books have been involved in a crash and this is the result of welding together the front of one and the rear of the other. A worthy topic, but not quite the book it could have been.
September 21, 2018
Off to a slow start, this book builds to a strong finish. A great story of a remarkable equation.
October 7, 2026
Making it all add up
I bought this as a birthday present for my mathematician son-in-law, and borrowed it to read last week. The author unpicks Euler's equation - which contains five of the most fundamental numbers in mathematics: e, i, pi, 1 and 0 - devoting a chapter to each number, before looking at the equation itself. This is a diverting way to introduce (or remind) the reader about some interesting maths: counting systems, types of numbers (positive, negative, rational, transcendental ...), geometry, infinite series and complex numbers.
There's a brisk account of the history of the numbers and their associated mathematical apparatus, emphasising how our understanding has become more refined with the passage of time and the efforts of those who strove in this abstruse field. Surprisingly, this includes some explicit disagreements: when it came to taking the logarithm of a negative number - e.g. ln(-1) - one mathematician (Johann Bernoulli) continued to insist that this had a value of zero, even after Euler deduced (correctly) that it was i times pi (a result which follows from his eponymous equation).
I enjoyed this book, which brought forth memories of imperfectly-understood maths lessons at school (and beyond), and made some items more intelligible.
Originally reviewed 18 October 2021
I bought this as a birthday present for my mathematician son-in-law, and borrowed it to read last week. The author unpicks Euler's equation - which contains five of the most fundamental numbers in mathematics: e, i, pi, 1 and 0 - devoting a chapter to each number, before looking at the equation itself. This is a diverting way to introduce (or remind) the reader about some interesting maths: counting systems, types of numbers (positive, negative, rational, transcendental ...), geometry, infinite series and complex numbers.
There's a brisk account of the history of the numbers and their associated mathematical apparatus, emphasising how our understanding has become more refined with the passage of time and the efforts of those who strove in this abstruse field. Surprisingly, this includes some explicit disagreements: when it came to taking the logarithm of a negative number - e.g. ln(-1) - one mathematician (Johann Bernoulli) continued to insist that this had a value of zero, even after Euler deduced (correctly) that it was i times pi (a result which follows from his eponymous equation).
I enjoyed this book, which brought forth memories of imperfectly-understood maths lessons at school (and beyond), and made some items more intelligible.
Originally reviewed 18 October 2021
May 7, 2021
Great book for anybody interested in Mathematics. The author is the son of Harold Wilson the Prime Minister of UK years ago. In this book, Wilson takes each item in Euler's famous equation e to the i*PI equals -1 and tells the story of each item. Wilson is very interested in the history of Mathematics and it shows in each item's chapter. The Mathematics level probably senior in high school or anybody who wants to understand some very useful Mathematics. Robin Wilson has also written books on Combinatorics, Graph Theory, Mathematics History and the famous book, Fout Colours Suffice.
July 19, 2021
The earlier chapters were ones where I could have skipped much of what was there because it’s knowledge and understanding I have, although there were some interesting geometrical proofs I’d not seen. The last chapter was excellent and extended my understanding and some jaw dropping connections which really illustrate the beauty of mathematics. The links between logarithms of imaginary numbers and circular functions of real numbers is quite magical.
August 25, 2020
A book about the radiance of mathematics
This book is a delight for math lovers, with history, derivations, anecdotes and context for some of the most powerful numbers in math. Very well written in short, rich and humor filled chapters (a feat that's isn't easy when discussing calculus and trigonometry).
This book is a delight for math lovers, with history, derivations, anecdotes and context for some of the most powerful numbers in math. Very well written in short, rich and humor filled chapters (a feat that's isn't easy when discussing calculus and trigonometry).
February 2, 2023
Great book for math lovers, but if you're looking for a more structured or exciting read, it's not the book for you.
Some of the "fun facts" and anecdotes on applications of different concepts seemed like they were abruptly sprinkled in. I also found that the first few chapters were just general knowledge so they weren't as interesting, but regardless, I liked the book.
Some of the "fun facts" and anecdotes on applications of different concepts seemed like they were abruptly sprinkled in. I also found that the first few chapters were just general knowledge so they weren't as interesting, but regardless, I liked the book.
October 7, 2020
Excellent introduction to God's equation.
Wilson does the reader a great service by examining each term in the equation through the lens of math history. I was particularly struck by the "near misses" by Bernoulli and Cotes
Wilson does the reader a great service by examining each term in the equation through the lens of math history. I was particularly struck by the "near misses" by Bernoulli and Cotes
February 24, 2023
Probably the best book on the subject
Does require a decent grounding in maths to really get.into but can't imagine it can be made any simpler. Perhaps more of an intro about cos and sin perhaps.
Does require a decent grounding in maths to really get.into but can't imagine it can be made any simpler. Perhaps more of an intro about cos and sin perhaps.
December 30, 2018
Historical comments are very interesting. Math typesetting, however, is horrible.
May 23, 2020
Good summary of math
Very good info on history of math exploration. From basic need to imagination and beyond. I would recommend for all to replenish their math
Very good info on history of math exploration. From basic need to imagination and beyond. I would recommend for all to replenish their math
June 19, 2022
Interesting facts
Displaying 1 - 12 of 12 reviews