Leonhard Euler tricentennial

This equation is considered one of the most beautiful equations in mathematics:

e^iπ + 1 = 0.

When I taught high school, the chair of the department (who had a Master's Degree in mathematics from the University of Chicago, which is no mean feat) used the five numbers in this equation as her license plate. The equation is one of at least two equations known as Euler's equation; the other is

V + F = E + 2.

Sunday (15 Apr 2007) is the tricentennial of Leonhard Euler's birthday. I've referred to Euler before as one of those mathematicians who lowers my mathematical self-esteem. Euler performed mental computations the way ordinary people breathe. He sometimes worked while one child played on one knee, and another child played on the other. He continued this habit of achieving magnificent heights in mathematics even after going blind in both eyes (not simultaneously). Consider that after he lost his sight in the first eye, he is reputed to have observed that he would now have less distraction.

He spent most of his career in Russia. This places him a little outside the geographic mainstream of the mathematics of the time. I've read that it has kept much of his unpublished work out of circulation. He remained there despite an offer by the university in Basel, his native canton in Switzerland, perhaps because Basel had refused to grant his wife citizenship. (Or Switzerland. One of the two; I find different information at different sources.)

Now, why should you care about Euler? Because most everything you use in daily life was engineered using mathematics that was studied and/or invented (or re-invented) by Euler. This could be said about Isaac Newton, too, since he invented Calculus (and Gottfried Leibniz later re-invented it), Euler changed the way people looked at Calculus, and helped to place it on more certain foundations.

Euler worked with the function e ^x, also called the exponential function. One can describe the meaning of this function very elegantly by this diagram:

e ^x is the point on the x-axis such that the bluish area under the curve 1/t is x. For example, if you want the bluish region to have an area of 2, you locate its right border at e².

This function appears all over the sciences and engineering; for example, the computer you're using right now to read this depends on applications of this function.

Despite his accomplishments, Euler was known to be modest and quiet. When visiting Prussia, he was asked why he spoke so rarely, and replied famously, Madame, I have come from a country where one can be hanged for what one says.

In a less mathematical light, Euler was a deeply religious man, a literalist and a Calvinist at a time when Enlightenment thinkers insisted that Reason and Faith could not co-exist in the same mind. (This may remind you of the opinions of certain of our contemporaries.) He married and had thirteen children, although given the situation in those days, only five survived childhood.

So, go out to a restaurant on Sunday to celebrate the man's birthday! At least have a doughnut or something!