This picture was taken December 12, 2014, at the Gateway Arch in Saint Louis, Missouri.


June 28, 2016


Career Summary: I received the Ph.D. at Princeton University in 1966 for a dissertation written under the supervision of Salomon Bochner (1899–1982).   I then became an assistant professor of mathematics at Vanderbilt University, where I stayed for two years.   I got married in January of 1968, and my wife and I decided to move to Vermont in the summer of that year.   From August 1968 to May 2003, I was a member of the UVM Department of Mathematics and Statistics, first as assistant professor (1968–1972), then associate professor (1972–1977), and finally as full professor (1977–2003).   From 2000 until my retirement, I had the honor of being the Williams Professor of Mathematics.


During my 35 years at UVM, I directed the dissertations of three Ph.D. students:  Douglas Swan (1974), Vivian Mosca (1978), and Gerard LaVarnway (1999).


Research Interests:  My first work was in classical Fourier analysis.   Although I produced a number of papers in this area, the only one that I consider of any real significance was a proof of a two-variable version of the Cantor–Lebesgue theorem:   “A Cantor–Lebesgue theorem in two dimensions,” Proceedings of the American Mathematical Society, 30, No. 3, (November, 1971), pp. 547–550.   I returned to this area late in my career while directing the dissertation of Gerard LaVarnway.   His dissertation, with some additions of mine, was published as our joint paper:   LaVarnway, Gerard T. and Cooke, Roger, “A characterization of Fourier series of Stepanov almost-periodic functions,” Journal of Fourier Analysis and its Applications, 7 (2001), No. 2, 127–142.


I grew weary of pure mathematical research during the 1970s and spent the last two decades of the twentieth century exploring the history of mathematics as a wide-eyed amateur.  I was fortunate to have a superb mentor in this field, Ivor Grattan-Guinness (1941–2014), and a number of first-rate colleagues who provided helpful criticism and advice.


Honors and Awards:   I received the Kidder Outstanding Faculty Award in 1996 and was named a University Scholar in 2000.


Post-retirement Work:   I expected to retire and spend the rest of my life just reading, playing the piano, staying in good physical condition, doing some volunteer work, and keeping up the half-dozen or so foreign languages that I have endeavored to acquire over the decades.   The last thirteen years, however, have turned out rather differently.  After six years of retirement, I yielded to temptation and taught three courses between 2010 and 2012.   (I have now firmly resolved not to do that again; mostly, I just don’t like having to be in a certain place at a certain time doing a certain job.)   Also, from time to time, the urge to put my thoughts on paper and invitations to write from various editors and publishers have led me to undertake a number of projects resulting in publication.  Here is a partial list (excluding brief book reviews written for the Annals of Science):


The History of Mathematics: A Brief Course, second edition, John Wiley & Sons, New York, 2005.


“Niels Henrik Abel, paper on the irresolvability of the quintic equation,” in: Landmark Writings in Western Mathematics, 1640–1940, I. Grattan-Guinness, ed. Elsevier, Amsterdam, 2005, pp. 391–402.


“C.G.J. Jacobi, book on elliptic functions,” in: Landmark Writings in Western Mathematics, 1640–1940, I. Grattan-Guinness, ed. Elsevier, Amsterdam, 2005, pp. 412–430.


“Richard Dedekind, Stetigkeit und irrationale Zahlen,” in: Landmark Writings in Western Mathematics, 1640–1940, I. Grattan-Guinness, ed. Elsevier, Amsterdam, 2005, pp. 553–563.


“Henri Lebesgue and René Baire, three books on mathematical analysis,” in: Landmark Writings in Western Mathematics, 1640–1940, I. Grattan-Guinness, ed. Elsevier, Amsterdam, 2005, pp. 757–777.


“S. Bochner, lectures on Fourier integrals,” in: Landmark Writings in Western Mathematics, 1640–1940, I. Grattan-Guinness, ed. Elsevier, Amsterdam, 2005, pp. 945–959.


Classical Algebra: Its Nature, Origins, and Uses, John Wiley & Sons, New York, 2008.  (This book received a CHOICE award as one of nine outstanding books on mathematics for the year.)


“Life on the mathematical frontier: legendary figures and their adventures,” Notices of the American Mathematical Society, 57 (2010), No. 4, 464–475.


“Review of Naming Infinity, The Mathematical Intelligencer, 32 (2010), No. 1, 59–64.


“A remark on Euclid’s theorem on the infinitude of the primes,” American Mathematical Monthly, 118 (2011), No. 4, 355–358.


The History of Mathematics: A Brief Course, third edition, John Wiley & Sons, New York, 2013.


“Social class and mathematical values in the USA,” in: I, Mathematician, Peter Casazza, Steven G. Krantz, and Randi D. Ruden, eds., Mathematical Association of America, 2015, pp. 156–168.


The Case of Academician Nikolai Nikolaevich Luzin (translation from the Russian), written by S. S. Demidov et al. American Mathematical Society, 2016.


I have also written an essay on the work of my mentor Grattan-Guinness in the area of mathematical physics.  I had planned to include it in the memorial volume from the special session in his honor at the 2015 MATHFEST in Washington, D.C., but judged it to be too long for that purpose.   Since I was unwilling to cut it down, I withdrew it from consideration.  Since doing so, I have been informed that a few exceptions to the limitation on page length may be made, and so I have resubmitted it.   If it is still judged to be too long, I will post it here.


In Progress:   It’s About Time: Elementary Mathematical Aspects of Relativity (three volumes).  This work has had favorable reviews, and I now have an agreement with the AMS to publish it. The first of the three volumes will be published in hard copy and electronically. The other two will be downloadable from this website as free resources to accompany the book.  The manuscript is due at the AMS on August 31.  This is the work I really intended to do on retirement, but I didn’t get around to starting it until 2012.  Here are links to the tables of contents and prefaces of the three volumes:


This work was finished in May of 2015.   In August of 2015, I traveled to the MATHFEST in Washington, D.C., and showed it around.  My friend Dale Johnson mentioned that it parallels a similar work by Antony Zee.  Naturally, I was very anxious, lest I had merely duplicated what someone else had already done, and probably better than I could do, since Zee is an excellent physicist.  Fortunately, I found that our aims were somewhat different.  Zee introduces the reader to the work on relativity that has taken place over the past century, whereas I merely lead up to that point, concentrating on the basic work that provided the foundation of Einstein’s papers on general relativity.   The only topic I discuss from the period after 1920 is Gödel’s fascinating universe in which time travel is theoretically possible.


Personal stuff:   I spend my leisure time about as I expected I would: reading, playing the piano, staying in good physical condition, and keeping up my languages.  Since 2005, I have spent my Wednesdays as a volunteer office worker at the local Visiting Nurse Association.  Somewhat surprisingly, I have found use for mathematical skills in this work, especially in writing spread sheets with formulas in them.


My piano playing technique has eroded, and I no longer have the velocity and dexterity I once had (incipient arthritis), but I persevere.   Here’s a sample of my playing from a decade ago, before old age began to take its toll.   It’s far from perfect, but still better than I can now do:   Chopin, “Heroic” Polonaise in A-flat Major


I ran about 30 miles a week for the first decade of my retirement.  Then, in July 2013, my daughter talked me into running a half-marathon, in which I finished first in my class (being the only entrant over the age of 70).   That was my last hurrah as a runner.   Now, I walk about 5 miles every day, or ride a bicycle for a couple of hours during good weather.


As for the languages, I’m not going to get any better at them, I now realize; but I still enjoy reading all of them, especially ancient Greek, and listening to the news in French, German, and Russian.   A few years ago, I noticed that I was no longer understanding as well as I used to.   Last summer, I got a pair of hearing aids, and my comprehension has since returned.


Contact:   I prefer to use e-mail: