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In the unlikely event that someone asks me, "Mike, in all your years of tracking computer technology and generally observing the passing show, what's the most outrageous thing you've ever heard?" I have a ready answer.
The most outrageous thing I've ever heard has only indirect relevance to computer technology, but part of its outrageousness is that it seems to have some relevance to so many different subjects. My candidate for the most outrageous statement ever uttered is:
e(i pi) + 1 = 0
What connects these numbers, and how that connection was discovered, is the subject of the delightful and very readable book e: The Story of a Number (Princeton University Press, 1993, ISBN 0-691-05854-1), by Eli Maor, who teaches the history of mathematics at Loyola University in Chicago. The book was just recently released in paperback, with new material on a recent discovery regarding prime numbers. Maor tells the story of the rather odd John Napier, who changed the way scientists calculated; recounts the birth of differential and integral calculus, with all the controversy it engendered; shows how Hamilton's notation for complex numbers made them seem less "imaginary"; and shows the extraordinary chutzpah of Leonhard Euler, who plugged imaginary exponents into functions involving the number e, played fast and loose with infinities, and took the results seriously when pi suddenly appeared in his calculations, seemingly from out of nowhere.
It's poetry. In just seven symbols, it packs in an amazingly rich collection of ideas and relationships, plus those five constants, three of which are pretty mysterious on their own:
By the end of the book, Maor has told some good stories; shown some remarkable properties of e, pi, and i; and led the reader to see how e, pi, and i are related and why the outrageous equation actually makes sense.
But best of all, in doing so, he doesn't make it seem any less outrageous. He doesn't destroy the poetry in analyzing it. I recommend the book to any DDJ reader.
-- Michael Swaine