ROGER L. COOKE, Ph.D.,
EMERITUS PROFESSOR OF MATHEMATICS
Retired as of May 31, 2003
Email: cooke@cems.uvm.edu
Fax: 802-656-2552
Areas of expertise: history of mathematics, Fourier analysis
Applications: Both areas help people understand the world.
From left
to right below you see me with my five grandchildren, Callum Boyd Smathers
(born March 14, 2004), Sonora Elena Cooke (born January 27, 2005), Isaac Paul
Buzzard-Cooke (born February 24, 2006), Finian Hutton Smathers (born October
12, 2006), and Ezra Lee Buzzard-Cooke (born October 30, 2007).
MY
PROFESSIONAL LIFE (March 2008)
My Education and Employment: After graduating from Northwestern
University in 1963
with a mathematics major, I attended Princeton Graduate School and received the Ph.D. in
mathematics there in 1966. From 1966 to 1968 I was assistant professor of
mathematics at Vanderbilt University. From 1968 until my retirement (on May 31,
2003) I taught at the University of Vermont, where I became a full professor in
1977. In October 2000 I was appointed
Williams Professor of Mathematics. The
position originated in 1853, in honor of the largest donor the University had
known up to that time, one Azarias Williams of Concord, Vermont, who deeded
extensive land holdings to the University in 1839. The first Williams Professor was Farrand
Northrup Benedict, professor of mathematics from 1832 to 1855. The position is now occupied by my friend and
colleague Ken Golden.
What I've Produced: My research was originally in multiple
trigonometric series. The best thing I did in that area was to prove a
Cantor–Lebesgue theorem in two variables, back in 1970. It turned out to be a simple thing to do, but
no one had expected it to be easy, so I was lucky enough to get in ahead of the
others. After 1975 my motivation to do
pure mathematical research waned and I began to be interested in the history of
mathematics. In 1981 I took a sabbatical year to start working in this area. My
first effort was The Mathematics of Sonya Kovalevskaya (Springer-Verlag,
1984). Over the years I have written a number of articles about her
mathematical work. I think my best
effort in this direction was a history of the Cauchy–Kovalevskaya theorem,
which I presented at a conference in Lisbon in 2001, but which I have never
tried to publish.
I
spent part of a sabbatical year (1988–89) in Moscow studying the works of N.N. Luzin. One result
of this work was a study of the relation between uniqueness of trigonometric
series representations and descriptive set theory from 1870 to 1985, which
appeared in Archive
for History of Exact Sciences in 1994.
My
major effort in the history of mathematics is a textbook intended for a first
undergraduate course (1997). The second, thoroughly
revised edition, whose cover you see below, is now available from Wiley. The cover design came from a quilt bearing
the name "A Number Called Phi" that I saw at a show in Northfield,
Vermont back in 2003. The quilt's
creator, Mary Knapp of Watertown, New York, combines her interest in quilting
with many other things, including mathematics.
During
my years at the University of Vermont I directed the doctoral dissertations of
three students. The most recent was Gerard LaVarnway, a 
professor at Norwich
University in Northfield, Vermont.
Gerard's dissertation
was in almost-periodic functions and
appeared as our joint paper "A characterization of the Fourier series of
Stepanov-almost-periodic functions" in the Journal of Fourier Analysis and
Applications, Volume 7 (2001), No. 2, pp. 127–143.
In my
retirement I hope to work on the kinds of hopelessly difficult problems that
young mathematicians dream of solving, such as the Riemann hypothesis. I'd also like to continue my work in the
history of mathematics and science by learning the history of superstring
theory. I got distracted from these
projects during 2007 by another writing project that I couldn’t resist, a book
that I call Classical
Algebra: Its Nature, Origins, and Uses.
It has now been published, and I’ve looked at it enough to find three
misprints and one small error. So, I
guess I’d better put up a web page of
corrections. Now that I have gotten
it out of my system, I am determined not to allow any further
distractions. As of New Year’s Day 2008,
I have been single-mindedly working on the story of superstring theory. Since I have much to learn before I can
competently write about any of this material, I expect it will be several years
before I publish again. But please stay
tuned in to this website. I may find
something interesting and decide to blog about it. The main restriction I am imposing on myself
is to do no more encyclopedia articles, book reviews, lectures, and the like,
except for my local community. I’m happy
to visit classrooms and talk to students and those in the public who have an
interest in the things I know a bit about, but I’ve really had all the
publishing I care to do for a while.
Sidelines: In addition to teaching and
research, I have contributed, I hope, to the advancement of knowledge through
several ancillary projects, some of which are the following.
Translations. I began
translating Russian mathematical articles for the American
Mathematical Society
in the 1970's. The AMS translations project was taken over in the 1990s by the London
Mathematical Society,
for whom I translated a few articles from the Matematicheskii Sbornik. I did a great deal of translation (I
estimate some 10,000 pages) of Russian and Ukrainian articles and books during the
years 1986–1998, when my three children were in college. The next-to-last project I undertook in this
area was a translation of the fourth (2002) edition of the two-volume Matematicheskii
Analiz, by
Vladimir Zorich, for Springer-Verlag.
This work is the best rigorous, yet thoroughly applied work on real
analysis for undergraduates that I have seen.
I am very proud to have been the translator of these excellent
textbooks. The very last project was to
translate 20 of the 24 essays in a work entitled Mathematical
Events of the Twentieth Century, which has recently been published by
PHASIS/Springer-Verlag. That's
absolutely it as far as I'm concerned.
No more translating.
Fun Problems. As a
puzzle enthusiast, I like to take the challenge of each year's Putnam
Examination, administered by the Mathematical Association of America. If you'd
like to compare your answers with mine, click here to see my solutions to the 2007 Putnam Examination,
given December 1.
Useful Problems. I am also happy to serve as a consultant to
the public and to my colleagues at the University, as these free consultations
often lead to interesting problems to be solved. Here are some
samples of my work. May I politely ask,
however, that you not send me your angle trisections, circle quadratures, and
the like. I have examined many dozens of
these over the years (one sample is posted here), and I feel I have earned my retirement
from this type of work.
The History of Mathematics at
UVM. Around 1990, in connection with the UVM bicentennial, I wrote a
history of mathematics at UVM. I have
recently looked at it again and added a few endnotes to update it. I’m putting it here in several forms, so that
you can have your choice of format: (1) single-file web page/web
archive (.mhtml); (2) Word
1997–2003 (.doc); (3) Adobe
Acrobat (.pdf). I also have a
Microsoft Word version (.docx) that I’ll be happy to send to anyone. I don’t include it here, since the .docx
format doesn’t download very well. Microsoft
Internet Explorer regards the file as a zipped file and handles it
accordingly. Finally, I also have a
plain TeX version, which I’m also willing to send. I’d be happy to rework this piece if any
ambitious historian of American mathematics out there wants to compile an
encyclopedia of what was going on at all the centers of activity, great and
small, during the early years of the Republic.
I think 1950 would be a good terminal year for such an encyclopedia. This is the one exception I would be willing
to make to my sworn intent (see above) not to get involved in any more projects
outside my main interest.
Apologia Pro Vita Mea: The immediate practical value of what I do is
very limited. My whole background is
"liberal artsy," and I regard simply understanding the world,
independently of any personal or economic gain, as being practical. I'm very much in sympathy with the ancient
Greek ideals enunciated by Plato and Aristotle that education should be aimed
at this kind of understanding. At the same
time, I am enough of a realist to recognize that this kind of education has an
economic cost to society, and, as sardonic old Henry Mencken wrote, one should
not expect to be supported because he knows Sumerian. Professors with my outlook owe it to society
to be good and dedicated teachers. We
should not adopt the arrogant attitude of Godfrey Harold Hardy, whose 1940 book
A Mathematician's Apology argued that, even if mathematics is a waste of
time, Oxford dons should be allowed to waste their time pursuing it. Such a view is self-serving. Why should
others work and be taxed or charged tuition in order to support the production
of papers that appeal only to a small elite?
If we expect such support, we should honestly say why such knowledge is
of value, and "sell" it like any other commodity. The goal should be to persuade others that
understanding, without regard to economics, is of value. In other words, we should either perform a
useful service for the community as a whole or enlarge the elite who appreciate
scholarship and willingly support it.
My Hobbies: Besides regular running for exercise,
gardening, and keeping up my languages (Russian, French, German, Japanese,
ancient Greek, Latin), I like to play the piano. With the Yamaha P-80 keyboard that my
colleagues so generously gave me when I retired, I have recorded some of my
favorite music. Here are two pieces by
Chopin that I particularly like, played by me with all the amateurish clinkers
you'd expect. I still regard it as a
great blessing to have been able to play these pieces, even very imperfectly,
and I rejoice that there are people who play them much better than I do, both
technically and artistically. As has
been said, the woods would be very silent if only the best birds sang. Here's my small peep. It is small only in a certain sense. These files are huge (14.5 MB and 7.5
MB respectively). Don't attempt to
download them over a 14.4 baud modem.