Euler's Pioneering Equation: The Most Beautiful Theorem in Mathematics

- Blurb -

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]ipi + 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 themselves: 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; pi 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.