Web edition: April 12, 2007 "Gentlemen, that is surely true, it
is absolutely paradoxical; we cannot understand it, and we don't
know what it means. But we have proved it, and therefore we know
it must be the truth." Benjamin Pierce, a Harvard mathematician,
after proving Euler's equation, eip = 1, in a 19th-century
lecture. Sunday, April 15, is the 300th birthday of Leonhard
Euler (pronounced "oiler"), one of the most important
mathematicians ever to have lived. His works help form the
foundation of nearly all areas of mathematics, including
calculus, number theory, geometry, and applied math. One of the
many discoveries for which he is famous is the equation eip = 1
. In a 1988 poll, readers of the journal Mathematical
Intelligencer chose this equation as the single most beautiful
equation in all of mathematics. The equation weaves together
four seemingly unrelated mathematical numbers, e, p, i, and 1,
in an astonishingly simple way. But what does eip = 1 really
mean? First, let's examine what the letters m