This page has been created to give topologists around the world the opportunity to share their remembrances of Bob Stong; his life, work, and friendships. Please submit your contribution for this page to Julie Riddleberger (JulieR @ virginia.edu).



From Larry Smith
Working with Bob Stong/Our Collaboration: One of the great privileges of my life was sharing Bob's office with him, which I did on several occasions. I had a table or a desk in his office and would come into the department most mornings around 7:00am, or so. Of course, Bob had already been there for several hours. The coffee was hot, and he had saved some for me, but before I could get a cup poured and tell him what I had figured out about yesterday's stuff, Bob was at the blackboard and had launched into the day's topic. Of course, everything I had to tell him had been long overhauled by what he was now explaining to me.

Bob's spontaneous and intense style was lucid and logical (as well as being colorful, linguistics-wise). He laid out the main results and their proofs, pausing only to answer my questions or allow me (to try to) catch up with his thoughts. My comments about yesterday's discussion and my reworking of it were brushed aside with "Yeah, yeah, I know that, it's all cr**p from yesterday."

If our discussion took place on a day when Bob had no classes to teach, he would go on 'til maybe 10:30-11:00am, dealing with the inevitable "where do we go from here," i.e., my homework assignment. Then he would announce that the day was over ("the moment someone says, 'good morning' to you, the day is ruined"), and he would go home for a nap, leaving me to sort out my feeble understanding of what he had told me until the next day's session.

There was no better way for me to start a day; it's hard to believe it won't happen anymore.

The Lectures on Cobordism Theory: Bob Stong and I met in the summer of 1966, where we had both just taken up positions at Princeton; Bob was an assistant professor, and I was an instructor. We quickly found we were on the same wavelength and that first summer we spent many hours every day talking mathematics.

Everything I knew, Bob already knew, apart (maybe) from some EMSS stuff, but I didn't know beans about most of his research area--cobordism theory. So, Bob started to give me private tutorials, and in the course of time he began to "write things up for me," so I would have something to study. These notes were so lovely and clear and certainly of interest to many of the other topologists in Eno Hall that I encouraged him to offer a graduate course the next semester.

However, in those days at Princeton, only the full professors were "authorized" to teach graduate courses. Luckily, I was on good terms with John C. Moore, who was a full professor and, after talking with John who spoke to the Chairman and the other topologists, Bob was allowed to offer a course on cobordism theory; albeit, it took a semester to obtain this dispensation.

The course was a huge success from the start, with peoply coming from the IAS, Rutgers, and as far away as Philadelphia to attend. Bob felt obligated to his "students" to give them some notes. He took back the notes he had given me, added an introductory survey and some chapters of background, and then continued from there to expand the notes into new areas.

Of course, as he was only an assistant professor, he had no access to the secretarial staff to get these notes typed, so Bob would type them on his portable electric typewriter in his office on weekends. The result was the Notes on Cobordism Theory. We (his students, so to say) encouraged him to circulate the notes more widely, and the logical thing would have been to make an Annals of Math Study of them. No way; that venue was not open to junior faculty. Again, with the help of John C. Moore, the manuscript appeared as a yellow (instead of orange) Princeton Lecture Notes volume. The volume was a huge success with enormous influence and was translated into Russian by Viktor Buchstaber (published by MIR in 1973). If you can find a copy of the original Princeton University Press edition (www.amazon.com), be prepared to lay out $250 for one.

Our Correspondence: Although Bob and I met in 1966 at Princeton, of the following 42 years we spent only five of those years together at the same universities. Most of our work was done through correspondence. Despite the advent of email, up until the last weeks of his life our correspondence was through "snail mail." The intensity of our correspondence varied over the course of time. There were times when we wrote only a couple of letters a year, and other times when we wrote three or more letters a week.

In recent years I would receive several letters a week from Bob. Most of the time, these letters would take a month or more to absorb and understand well enough to translate from Stong's computational style to my own more abstract one, so that I could organize a reply. My backlog in replying was shamefully long and, more often than not, full of questions rather than answers.

Our correspondence occupies two file cabinet drawers (DINA4 file cabinets!) in my office at home.

Bob was always extremely patient with my stupidity, and the clear, concise, and logical style of his explanations were an enormous help through the years. Be it characteristic number computations, solutions to Diophantine equations over finite fields, or the computation of a ring of invariants, Bob's organization of the solution to a problem, and clarification of how he chose this or the other techniques were always full of insights.

Bob was always extremely generous with how I could use his results. He invariably answered my question, "Can I mention/use that in a paper I am working on," with the selfless answer, "You know you can use anything I tell you any way you want to."

It is hard to live with the thought that there are no more letters from Bob waiting for me in my mailbox at home.



From Peter Landweber
A Bit about Bob: I first met Bob in Princeton in 1967, and was glad to find someone with common interests and a mastery of all things related to cobordism. Bob's course on cobordism at Princeton University, which led to his famous book, Notes on Cobordism Theory, ran all year. I stuck with him to the last class in his office (so he could explain spin cobordism to me).

We renewed our acquaintance when Bob returned with his family to spend a year at the Institute in Princeton in 1975-1976. We then parted ways, and eventually we became correspondents, writing letters until the very end. [Indeed, I would feel more comfortable writing these memories out by hand. Bob was famous for not using e-mail, so the USPS handled our exchanges.] Getting a letter from Bob was always a delight, for his compact and precise penmanship, his pleasure at getting a good idea, and his masterful calculations that could go for pages (and sometimes days).

Our best years working together ran from roughly 1984 to 1987, and started following a talk I gave at a small conference for Ed Floyd's 60th birthday, which launched our study of Steenrod operations on mod p cohomology rings and rings of invariants. We gave up trying to prove our Depth Conjecture, and turned our attention to trying to understand vanishing of some characteristic numbers as suggested by Ed Witten. In turn this led to Serge Ochanine's breakthrough definition of elliptic genera, and to proofs (by others) of Witten's rigidity conjecture and to the beginnings of elliptic cohomology.

Bob and I hadn't written regularly for several years, when I posted a simple question about SU(3)/SO(3) on Don Davis' list (about something Bob and I had once understood). [We had reached an age when forgetfulness becomes routine. Several years ago, Bob proved a result that was in my student Wolf Iberkleid's thesis from the early 1970's, solving a problem that came from Bob.] I thank John Oprea for reminding me that Bob was the expert on such things! This led to a renewed correspondence in Fall 2006, and Bob's last seminar talk about the homogeneous spaces SU(n)/SO(n) with an uninformative title, which is now linked to this website.

In the last year our correspondence was varied, occasionally turning to issues one faces upon retiring and (don't laugh) Sudoku. Bob gave me a magazine with very nasty Sudoku puzzles, which will keep him in my thoughts as I spend many hours working them. But more seriously, I'm thinking about cohomology of groups at the moment and am sad that I won't have the fun of doing this with Bob.

I remember my amusement at learning that my collaborator was Santa Claus at department holiday parties. On reflection, I think Bob's colleagues and friends in Charlottesville have been immensely fortunate to have had Bob in their midst for almost 40 years. Eventually we'll put aside the agony of the last two months, and remember Bob for his gentle and wise humor, for his preference to get exercise by "jumping to conclusions," for his generosity to so many, and for the joy he took in doing and sharing mathematics.


From David Copeland Johnson
Bob Stong was one of five alpha scholars of the Big Omega* who electrified the halls of Cabell Hall during my five graduate school years at Virginia, 1965-1970. Ed Floyd was my advisor. Peter Landweber introduced me to manifolds in his differential geometry class. The work of Pierre Conner and Larry Smith was to inspire much of my own research, and my first paper was joint with Larry. Bob Stong kept my Virginia stay finite.

To me, Floyd suggested something about generalizing LNM 28, The Relation of Cobordism to K-Theories, using the Eilenberg-Moore spectral sequence. Think Steve Wilson’s thesis without the Yankee influence of Brown and Peterson. Help and clarification were sorely needed, but Floyd had become a busy department chair and he still shared an office with the quite intimidating Pierre Conner. Ancient and ignorant, I was too timid to brave the Conner-Floyd den. But just down the hall, there was mathematical salvation: Bob Stong presiding in the coffee room. Before daybreak, Stong proved his daily quota of theorems. He taught early and was then available for frank opinions (on things mathematical and not), for tutorials (“That’s easy, just ...”), and for professorial fellowship (“Just what is the color of the seven sphere?”)

Under Bob Stong’s instruction, I learned the joy of computing Chern numbers of Milnor manifolds. Instead of generalizing the Conner-Floyd splitting, fibrations were constructed involving MU and bu. Bob wasn’t my official advisor, but my dissertation was published as "A Stong-Hattori Spectral Sequence." My debt to him is recorded there in the title.

In the first years after leaving Virginia for my Kentucky job, my topological curiosity and growth was kept alive by notes from Bob (and others). In those little envelopes with the meticulous printing would be advice, counterexamples, comments on the known and unknown, and suggestions on abbreviating arguments. And encouragement tempered with candor.

I thank Nick Kuhn and his Virginia colleagues for organizing the opportunity to see Bob a last time.

* In the sixties, the notation for cobordism involved uppercase omegas. When I started typing my dissertation, I was converted to the MU convention.