Jerry was an exact contemporary of mine, and we shared many common mathematical interests. Although I have not had personal contact with him for probably two decades, I remember him vividly as a sweet and gentle person, with a deep engagement with mathematics.
We were among the generation of topologists which managed to exploit powerful methods developed by John Milnor and C.T.C. Wall to attack previously inaccessible problems in high dimensional geometric topology. Jerry was preeminent among us in developing high dimensional knot theory.
While I interacted with him only for brief periods, I learned a lot from personal discussions with him, and from studying his work. He enriched the mathematical life of many others as well, and for this he will be remembered with great fondness and respect.
The distinguished American topologist Jerry Levine died on 8th April, 2006. He was a student of Norman Steenrod at Princeton University, receiving his Ph.D. in 1961. Following appointements at MIT and Berkeley, from 1966 on he was at Brandeis University. In the 1960's and 1970's he was one of the pioneers of the surgery method of the classification of high-dimensional manifolds, their automorphisms and their embeddings, particularly of spheres and projective spaces. The classification of highly-connected high-dimensional codimension 2 knots and the computation of the cobordism groups of high-dimensional codimension 2 knots were particular highlights; he spoke at the 1970 Nice ICM on "The role of the Seifert matrix in knot theory". More recently, he made important contributions to the algebraic and geometric topology of low-dimensional knots and links. Professor Levine was a frequent visitor to the United Kingdom, spending the academic year 1963-64 in Cambridge, and 1972-1973 in Oxford. He had been invited to visit Durham, Edinburgh and Warwick in the current academic year on a Scheme 2 visit of the Society, but his terminal illness prevented him from taking up the invitation.
A.RanickiI particularly appreciated the help and support offered by Jerry to my late student Des Sheiham. Indeed, Des's Ph.d. on the computation of the high-dimensional boundary link cobordism group solved one of the problems posed by Jerry and Kent Orr in their survey of knots and links in the Wall 60th birthday volumes. I last met Jerry at the 2004 BIRS meeting on knot theory (see the photo on the BIRS website, with Des 1st from the right in the top row) where he was usual wonderfully lowkey but influential self.
I met Jerry in 1977-8 when he visited Geneva where I was a student. He shared an office with Vaughan Jones opposite mine and was lecturing on higher dimensional knot theory in our 3'ieme cycle. I wasn't aware at the time, but our interests (and physical contact) in math would cross each other in many ways over the following years. I lectured twice in his topology seminar at Brandeis, once during my 83-85 assistant professorship at Yale, and later during my year 96-97 of research with the CNRS. My last physical contact was at UCSD in 2000. Of the mathematicians with whom I ran in contact over the years, Jerry is among those who were closest.
I do not know how to express my sadness with Professor Levine's death. He was one of my heros in mathematics. Since I started studying knot theory, his papers have been my favorite textbooks, and like many other knot theorists, my results could not have been obtained without his work. Visiting Brandeis and talking with him in person was one of my greatest memories from visiting the U.S. He was always very nice and supportive of me and I could feel kindness and warmth whenever I saw him.
I am not now, nor have I ever been, Jerry Levine's student. Thus began, in a feeble attempt at humor, my short tribute to Jerry at his 60th birthday conference banquet in Tel Aviv, Israel. Countless times I've been asked if I was Jerry's student. Ironically, upon arriving in Tel Aviv the day before, Michael Farber asked over dinner, "You were Jerry's student, weren't you Kent?"
For the record, and with much gratitude, I acknowledge Julius L. Shaneson for that important role in my life. Yet as I ponder Jerry's far-reaching influence on knot theory, and on me, I realize that I might have asked the same question of Michael - or of Cameron Gordon, or Tim Cochran, or Jonathan Hillman, or Stavros Garoufalidas, or De Witt Sumners, or Xiao-Song Lin, or Nathan Habegger, or Pat Gilmer, or Cherry Kearton, or of many others who have been so influenced by Jerry's striking breakthroughs in knot theory that the above question seems entirely reasonable. Jerry set the stage for all of us, and I do not hesitate to state my conviction that he is knot theory's most fundamental and profound influence.
Jerry founded a new era of knot theory during the 1960's, and at each new direction since, he leaped into the field making significant contributions. At the end of his career, Jerry's contributions were still fresh and modern, still deep and penetrating. At age 68, cruel illness cut short Jerry's career and cheated mathematics of his enormous insight and talent.
But like so many others, I feel this loss far more personally.
My respect for Jerry increased steadily with the length of time I knew him. He was a good teacher, a great thesis advisor, and an outstanding colleague. It took me a long time to understand the depth of his sense of humor and humanity. His generosity and gentleness, however, were obvious from the moment I met him.
The road trips to the Cornell Topology Festival stand out in my mind. Typically it involved Jerry deftly moderating the conversations of three obnoxious graduate students, and by the end of those road trips we always knew much more than when we started. More topology usually, but also more about the world, as happened one year when we tuned the radio to the Iran-Contra hearings for most of the trip.
Oh, and running into Jerry and Sandy in the middle of a crosswalk in downtown Seattle at 10 pm one night 5 years ago provided me with the most striking coincidence of my life, and gives me an story I'll be able to use for a long time.
So long, Jerry, you were a major influence on me.
In March of 1988, with my family, I drove from Princeton to Boston to visit Jerry. Jerry arranged a joint topology seminar of Brandeis and MIT for me. In Brandeis, I met two of Jerry's students, Gyo Taek Jin and Paul Kirk for the first time. We were all new Ph.D.'s then. What a nice trip! A lot of memories.
As many other people, my career owes a lot to Jerry's generous support. Jerry's example will always reminds me of how we should support the younger generations.
Thank you so much, Jerry.
The first word which comes to my mind when I think of Jerry is `generosity'. Jerry was extremely generous, especially with his time. As his student I would easily talk for two hours a week with him, and this often right after talking to another student for two hours. How he managed to find the time and energy for this is a mystery to me. I hope that if I ever have students I will remember his generosity and pass it on to my students.
In my meetings with him and in his courses he frequently showed his wit and very dry humour. It took me often a few seconds that Jerry had just cracked a great joke. I am sure Jerry would have been a great poker player since he rarely showed what he was thinking. Only when Jerry was really surprised he would slightly raise his eyebrow, which could then mean anything from `well--done!' to `hmmm, I didn't expect such a mistake'.
As I said, Jerry was very generous with his time and I met him often even after I graduated. I spent several weeks in June 2005 at Brandeis and met him about twice a week. Just before our last meeting I got an email from Jerry saying that he had to cancel the meeting because he didn't feel well. I never saw him again.
I was shocked and saddened to get the e-mail from Kent Orr and learn of Jerry’s death. Jerry was a great friend and mathematical inspiration for me. I first met Jerry in Cambridge, England in 1964 when I was a first-year graduate student and he was visiting Cambridge as a guest of Chris Zeeman. Andre Haefliger gave a series of lectures on Jerry’s work—I attended these lectures, and appreciated that it was very interesting and important, but it took me a few more years to understand the details in the terrific mathematics in Jerry’s work. When I began my career as a research mathematician at FSU after graduate school, it was Jerry’s work on knot cobordism that had a major influence on me.
I fondly remember a visit to Brandeis with my family when I was at the Institute for Advanced Study in 1974, and the terrific party Sandy and Jerry gave for us at 39 Dexter Road. Sandy and Jerry were great hosts, and my wife Neddy and I enjoyed hosting them on two visits they made over the years to Tallahassee. Jerry, we will miss you!
Jerry has been a mentor, collaborator, and longtime friend during the beginning of my career in Boston. I have very fond memories of him explaining to me topology and geometry, in our frequent meetings in his office at Brandeis. He was very accessible, and would always listen and explain the many things I did not know of. During the six years of my stay in Boston, I would meet with Jerry regularly, twice a week, to discuss mathematics, month after month. Little by little, I became familiar with the breadth and wealth of his research: from surgery theory, to high dimensional knot theory, to low dimensional topology, to problems in slice knots and links.
We would often chat about things, history, politics and people. I have good memory for his sharp sense of humor. I traveled with Jerry to numerous conferences, and visited Israel, Japan, and Korea among other places.
Most of all, what struck me in Jerry was his integrity, and his good nature. Somehow Jerry had a good word to say just about everyone, and would get along with everyone.
Jerry was a good friend. I miss our math and life conversations. I find it hard to believe that he has passed away.
Aiwnia i mnimi (May our memory of him be eternal)
Jerry had a brilliant mind, a gentle soul and a very ready wit. He will be most sorely missed.
After I moved to Israel in 1987 Jerry invited me to visit Brandeis in 1988. That was my first ever visit to the US. When I met Jerry I was surprised to see a very “human” person, very intelligent, a little shy, charming, very friendly, sincere, very supportive, humorous and fun to be with. We became friends and later collaborators.
I am not sure if people loved more Jerry’s mathematics or Jerry’s personality. Jerry was the leader (the word “father” perhaps suits better) of a large area of topology which united many people attracted by his amazing mathematics and by his personal charm. He was clearly the best of us all, the strongest, deepest and most experienced.
Last time I met Jerry at a conference at the Courant Institute in New York in March 2005. He was not yet ill. We had good time together, discussed mathematics, laughed and attended a party. He chaired the session when I gave my talk.
Luckily, names of mathematicians remain in memory of generations. Jerry’s name will be honored and praised by many students studying his theorems and enjoying his articles. Mathematical discoveries of Jerry will be alive and will carry his name forever.
I suggest publishing a book of mathematical essays in geometric topology dedicated to Jerry’s memory. It could be a durable tribute to him and a useful publication by itself.
When I heard the sad new via email, thousands of feelings, memories, and thoughts passed through my head, making it difficult to know where my story about Jerry should begin. In fact, I have not written anything so personal for anyone else, except perhaps for my wife, whether in English or Korean. The chronological order would be easier to mathematicians.
It was 1979 when I decided to go abroad to pursuit a higher degree and to enter the Ph.D. program at Brandeis after I received the bachelor's degree from Seoul National University in Korea. I recall going to see Jerry on one day toward the end of the first year to get some help in preparing a talk to be given by every second-year graduate student. He suggested that I read the article An Interpretation of G. Whitehead's Generalization of H. Hopf's Invariant by Michel Kervaire, where I learned about the Thom-Pontryagin construction and transversality. They were eventually used as important tools in my thesis, and I now realize that Jerry had a master plan for how to guide me from the beginning. Jerry had me read several papers and books on surgery, including the article Groups of homotopy spheres by Kervaire and Milnor and the book Surgery on compact manifolds by C.T.C. Wall before he gave me the thesis problem of understanding the Cappell-Shaneson work on boundary link concordance via Seifert matrices, which Jerry had applied to knot concordance with great success. I saw him about an hour every week to report my progress and ask questions, sometimes non-mathematical. Even though Jerry had many students at that time, he always tried to be helpful and open-minded. During some semesters, I met him around 11 a.m. and after meeting, we often went to the Sherman Student Center together to have a bowl of chili and crackers as lunch.
I still remember Jerry's delighted face when I told him that I received a job offer from UT Austin and I left Brandeis. I met Jerry on several occasions since then. I invited him twice to Korea in 1988 and 2000, and I recall that he liked Korean food very much even if he enjoyed almost all ethnic food. Jerry kindly invited me to Brandeis twice in 1990 and 1996 when I was visiting the U.S. for my sabbatical years. The most memorable event was a workshop held in Tel Aviv University in August 2001 to pay tribute to Jerry for his contribution as a researcher and a teacher. Many of Jerry's students attended. I am attaching several photos from Tel Aviv, 2001 and Yongpyong, Korea, 2000.
I was fortunate to become a student of Jerry's when he was in his 40s, the most productive period in his career. I think that Jerry was one of the most sophisticated users of algebra in topology. He left a profound influence not only as a distinguished mathematician, but also as a considerate teacher, as a beloved husband, and as an affable father. To me, Jerry will be remembered forever as a professor who taught me how to love the things that I do and the people that I live with.
David Cimasoni
I was a second year graduate student in Geneva when my PhD advisor, Claude Weber, had the brilliant idea to send me to Brandeis for several months. I will always keep warm memories of this fall semester 2000. Jerry took care of me with great kindness and generosity: he organized my stay and treated me as one of his own students. He soon became a model for me: in his teaching, in his huge knowledge, and in his gentleness.
As so many other people, I owe a lot to Jerry. I feel very fortunate to have met him.