ROGER L. COOKE, Ph.D.,
EMERITUS PROFESSOR OF MATHEMATICS
Retired as of
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.
(This picture of me was taken in December of
2005.)
MY PROFESSIONAL LIFE (August 2008)
My Education
and Employment: After
graduating from Northwestern University in 1963 with a mathematics major, I attended Princeton
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 work in this area
was a history of the Cauchy–Kovalevskaya
theorem, which I presented at a conference in
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
During my years at the 
professor at Norwich
University in 
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 Soviet journal Математический Сборник (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 Математический Анализ (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
24 essays on various aspects of twentieth-century mathematics with emphasis on
Soviet contributions, a collection bearing the title Математические События ХХ Века (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
Under this heading, I plan to add, from time
to time, essays on mathematical topics that interest me. Here’s the first, a proof of the Steiner–Lehmus Theorem that I
thought of some 25 years ago, then forgot about until reminded by my friend
Tony Trono, who learned of my proof from a former student of mine.
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.
Free Stuff!! Over the years, I have written several
textbooks in my own quirky style. Because
they are so idiosyncratic, they wouldn’t have much commercial value, and I have
not tried to publish them. I offer them
for free here. They were written using
standard Latex and converted to portable document format for posting. You can download these pdfs and use them any
way you like. If you’d like to modify
them, write to me, and I’ll send you the original
Have all the fun you like with these
books. Just don’t write to complain
about any mistakes or other infelicities you find; you got it for free, and
it’s worth every cent you paid for it.
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
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,
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.