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

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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 & 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' & 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 " What is it that makes Euler's identity eipi 1 0 so special? In Euler's Pioneering Equation Robin Wilson shows how this simple elegant & 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 & 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 & logarithms; & 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