ROGER L. COOKE, Ph.D.,
EMERITUS PROFESSOR OF MATHEMATICS
Retired as of
Email: cooke@cems.uvm.edu
Areas of expertise: history of mathematics, Fourier analysis
Applications: Both areas help people understand the world.
This picture of me was taken November 9,
2009.
News
Bulletins: I have come out of retirement, and will be
teaching MATH 161
(The Development of Mathematics) during the winter-spring semester of
2010. The course meets in 314 Dewey from
1:55 to 2:45 on Monday, Wednesday, and Friday.
On December 3, 2009, I gave a lecture at the
Harriman Center at Columbia University in New York City, entitled “The 1936
hearings in the USSR Academy of Sciences ‘in the matter of Academician
Luzin.’” This talk was at the invitation
of the New York Academy of Sciences.
When my contacts at the Academy learned that there was to be a
conference on the Lysenko Affair that same weekend, they decided to merge the
two programs.
MY PROFESSIONAL LIFE (January 2010)
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 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
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. As long as I’m on the
subject, I’ll just boast a bit and mention that this book has won a CHOICE on-line readers award as one of nine outstanding academic books
in mathematics for 2008.
Now that I have gotten it out of my system, I
am determined not to allow any further distractions. I am now 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. 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. While writing it up for posting here, I
thought of an analytic proof and included it.
Here is an essay I wrote
as a review of the recent book Naming
Infinity by Loren Graham and Jean-Michel Kantor. I wrote it at the request of the editors of The Mathematical Intelligencer. However, I let myself go in this one and just
wrote what I wanted to write, so the end result was too long and rambling for
their purposes. I wrote them a second
review, which is soon to appear.
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 TeX files from which they
were produced. I’m putting up two of
them here, with a third (on vector analysis) to follow soon. (I am currently
proofreading and indexing it.) So, here
they are. The first is a practical-math
textbook for social science and environmental studies students, which I call Empirical
Mathematics. I have actually used it in the classroom
once. It wasn’t a great success, but the
audience was, after all, reluctant to be in any mathematics course. The second is a course in real and functional
analysis intended mostly as background for understanding the use of linear
operators in quantum mechanics. I call
it Classical
Analysis. I have never used it in the
classroom, but you may find it a useful source of problems. Be warned that my definition of the
Riemann–Stieltjes integral is not equivalent to the standard one that you will
find in “baby Rudin.” I have what I
believe are cogent reasons for preferring mine.
I’ve decided not to publish in journals any
more. (I just got tired of dealing with all
the formatting that journals now insist on.)
I have a few more articles coming out in the near future, but from now
on, I’ll post what I choose to write at this website, or in some other free
site on the Web. Have fun with these
books and papers. 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 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.
What do you picture as you listen to
them? I’ve always been intrigued by the
analogies between different senses. How
does hearing music create pictures in our heads? There is something that sounds and pictures
have in common, I’m sure, so that they “go with” each other. If not, sound tracks would not so often fit
the action in a movie. In these two
examples, from the romantic period, I “see” plenty of storms. The Polonaise opens with several lightning
strikes, interspersed with rolling thunder.
This builds up and finally bursts in what I cannot help picturing as
rain falling out of the sky, slowly at first, then in a great flood. After that, it’s anybody’s guess what Chopin
was picturing. However, the middle
section in E major with the rapid octaves suggests either rapids in a river or
a cavalry charge. I’m inclined to see
the latter because of the hoofbeat-like sounds in the bass.
The E major étude is much simpler to
picture. The beautifully lyrical and
calm first part suggests (to me) a clear, calm summer day, with puffy clouds
floating across the sky. The more
agitated middle section suggests first rising winds, then sudden flashes of
lightning and thunderclaps, again finally resolving itself in a furious
rainstorm, which gradually blows itself out, with a few distant rumbles of
thunder, and brings in, once again, clear, calm weather as the sun sets.