About Euler

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					Preface

In the mathematical firmament, the star of Leonhard Euler (1707--1783) shines
with a special brilliance. His contributions, astonishing in both quantity and
quality, have left him with few peers in the long history of mathematics.

    It was thus appropriate when, on the bicentennial of his death, the MAA
journal {\it Mathematics Magazine\/} devoted an entire issue (November, 1983) to
Euler and his work. Under the editorship of Doris Schattschneider, the magazine
included articles on a host of topics from a who's who of mathematicians. Many
grateful readers put the issue aside as a ``keeper."

    One such reader was Don Albers, Director of Publications for the
Mathematical Association of America. A fan of Euler and an admirer of first-rate
mathematical writing, Don went so far as to have his copy bound, making it both
a prominent and a permanent item on his bookshelves.

   This year, the tercentenary of Euler's birth, we have the perfect occasion to
pay homage once again. In mulling over how this could be done, Don's gaze fell
upon his bound copy, and---bingo!---he realized that the MAA could produce a
book-length tribute by resurrecting those papers from Mathematics Magazine
and augmenting them with articles from other sources. He pitched his idea to
me, with the request that I be the volume's editor, although ``assembler" might be
a more apt description. Call it what you will, this was an opportunity too good to
pass up.

     And so it was that I found myself re-reading the 1983 issue and grazing
through the mathematical literature for appropriate companion pieces. My
search was guided by a few basic principles. First, additions had to be primarily
about Euler or his work. I eliminated papers giving, for instance, a new proof of
an old Eulerian result. Or, if an article promised to survey a topic ``from Euler to
X and Y," I insisted that Euler be featured in a prominent role so as to maintain a
distinction between the book's star (Euler) and its supporting players (X and Y).

    Second, because these articles had been published elsewhere, there was
less concern about their individual quality than about their interrelationship. I
scouted for papers that fit together in a reasonably coherent way---not always an
easy outcome to achieve. I concede that any book of this sort lacks the unity of
vision that would result from a single author's treatment of the material, but I
hope that the dangers of publishing a hodge-podge are offset by the charm of
variety.

And variety we have. More than thirty authors are represented across these
pages. Their papers span a significant time period, with the oldest dating from
1872 and the most recent being a 2006 article from The College Mathematics
Journal. As a consequence, the reader will find not just a range of topics but a
range of styles and eras, a diversity meant to enhance rather than diminish the
experience.

    A third and more mundane requirement was that these pieces be readily
available. Under our tight deadline, there simply was not time to obtain
publication rights in a leisurely manner. We thus decided to limit our choices,
insofar as possible, to papers from MAA journals. This I have done with two
exceptions: Clifford Truesdell's biographical work ``Leonhard Euler, Supreme
Geometer" and J. W. L. Glaisher's article on Euler's constant from The
Messenger of Mathematics.

    Even with these constraints, there was no shortage of material
(mathematicians, it seems, have been writing about Euler in very large numbers
for a very long time). Ultimately, the articles divided themselves into two groups:
those with a more qualitative flavor that provided biography and background; and
those with a more technical bent that examined in detail some of Euler's
mathematical achievements. The book has been organized according to this
natural dichotomy. If I have chosen wisely and assembled well, the reader
should be in for a treat.

So, Happy 300th, Uncle Leonhard!

				
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posted:11/4/2009
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