The story of Leonhard Euler (1707 - 1783) is, in both its personal and scholarly dimensions, one of the great tales from the history of mathematics. Born in Basel, Switzerland, Euler spent his working years at the St. Petersburg Academy in Russia and the Berlin Academy in Germany. Along the way, he endured the onset of blindness that eventually became total, but he refused to let this affliction impede his research. Instead, he produced a volume of mathematical work whose quality and quantity defy belief.

In terms of quantity, Euler has no peer. Indeed, an initial challenge for those seeking to publish his collected works was the "simple" task of cataloguing them all. (It didn't help that Euler published 228 papers after he died, making him one of history's most posthumously prolific mathematicians.) With the catalogue finally complete, publication of Euler's works commenced in 1911, and it's still going on! To date, there are 76 volumes in print, filling over 25,000 pages, and the editors are far from done.

In terms of quality, Euler's work is equally extraordinary. It contains a host of ideas that are central to modern mathematics. Concepts like the number "e," the Euler Polyhedral Formula, Euler's Identity, and the Euler Line are just a few of the many innovations that fill those 76 volumes.

During our Evening with Leonhard Euler at the Philoctetes Center, we surveyed some of his discoveries while trying to avoid excessive mathematical detail. The lecture was punctuated by numerous questions from the lively audience in attendance. In the process, we were carried from amicable numbers to Venn Diagrams, from factoring polynomials to crossing the famous Bridges of Königsberg. We ended with Euler's derivation of a strange formula, about which the Harvard mathematician Benjamin Peirce is reported to have said, "Gentlemen, we have not the slightest idea of what this equation means, but we may be certain that it means something very important."

As if these achievements were not enough, there are some downright weird results scattered among Euler's papers. For instance, he was challenged to find four different whole numbers, the sum of any pair of which is a perfect square. (If you think this is easy, try it.) Euler came up with this fearsome foursome: 18530, 38114, 45986, and 65570. In the end, it was clear why mathematicians celebrate the achievements of Euler, and why an evening spent with him at the Philoctetes Center was an evening spent in the presence of genius.

-William Dunham
  Koehler Professor of Mathematics
  Muhlenberg College