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


May 30, 2017


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.


“Grattan-Guinness’s work on classical mechanics,”  in:  Research in History and Philosophy of Mathematics, Maria Zack and Elaine Landry (eds.), The CSHPM 2015 Annual Meeting in Washington DC, Birkhäuser, 2016, pp. 127–160.  This was a tribute to my late friend and mentor Ivor Grattan-Guinness. 


It’s About Time: Elementary Mathematical Aspects of Relativity.  This work consists of three volumes.  Volume 1 is now available from the American Mathematical Society.  The other two are free on-line resources to serve as background for, and commentary on, the first volume.  These two volumes, and the Mathematica programs that appear in the work, can be downloaded at the following url

What the proofreading didn't reveal:    There is something about the final published version of a book that causes typographical errors that hid themselves fiendishly through a dozen proofreadings to leap off the page and mock the author.   One week after I received my copies of the book, I had already located three of them, most annoyingly one in the very first paragraph of the book, a mistake not in my original manuscript, but introduced in the typesetting process.   Nevertheless, it was my responsibility to catch it later, and I didn't.   For those who are connoisseurs of the genre, I offer the following classification of these errors:   First, clumsy fingers that cause a person to type “wto” instead of “two” ; second, the jerkiness of composing at the keyboard that results in small prepositions getting left out and some words typed twice; third, carelessness and inattention that result in the appearance of “positive” where “negative” is intended or “maximum” where “minimum” is meant.  There is a fourth-level erratum that is worse, namely an incorrect statement appearing in an argument.  Worst of all, but still found among papers by eminent mathematicians, is the fifth-level erratum, the statement of a proposition that is not true.  I hope my errata are all on the first three levels.  How they have escaped so many proofreadings remains a mystery to me.   If I find any in Volume 2 or Volume 3, I will simply revise the whole file and post the corrected file in the place already indicated.   The ones I have found in Volume 1 up to the date at the top of this page are posted here.


This work was finished in May of 2015.   In August of 2015, I traveled to the MATHFEST in Washington, DC 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 mostly reading and playing the piano.


My piano playing technique has eroded, and I no longer have the velocity and dexterity I once had (incipient arthritis) and have given up performing before others, practicing only in a very desultory fashion.   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


Contact:   I prefer to use e-mail: