Department of Mathematics

Dr. Harold I. Levine, Emeritus Professor of Mathematics at Brandeis University, passed away in Asheville, North Carolina, on March 11, 2023.  He was 94 years old.

Harold was born in Lynn, Massachusetts, the middle child of a couple who each came to America before the first World War.  Harold graduated from Lynn Classical High School and went on to receive a B.S. degree in Mathematics and Physics from the University of New Mexico.  Harold received an M.S. degree in Mathematics in 1952 from the University of Chicago, and a Ph.D. from the same institution in 1957.  From 1957 to 1959 he conducted postdoctoral research at the University of Bonn in Germany, and in 1959 he served as an Instructor at Yale.

In 1960, Harold was named Assistant Professor in the Mathematics Department at Brandeis University in Waltham, Massachusetts.  He spent time in 1963 as a postdoctoral Fellow at Cambridge University, in England.  Harold became a full Professor in Mathematics at Brandeis in 1968 and served as Department Chair in 1972 and again in 1988.  During his many years as a senior professor, Harold was a graduate-studies advisor.  He retired in 1994, and shortly thereafter, he and his wife, Renée, moved to France where they lived until returning to the United States in 2010.

When Harold joined Brandeis, the university had only been in existence for a dozen years.  Colleague Daniel Ruberman remembers that “Harold arrived as part of a talented group of mathematicians who helped bring the Brandeis mathematics department to a high level in a remarkably short period of time.”  In his book about his time as Brandeis’s founding President, historian Abram Leon Sachar singled out Harold for special mention as one of the “venturesome pioneers” whose expertise and loyalty elevated the Brandeis Department of Mathematics to world-class status.

Harold was a prodigious intellect.  From his first published academic paper when he was 20 years old, Harold went on to became a worldwide authority in singularity theory and coauthored the 1993 book (republished in 2001) Singularity Theory and Gravitational Lensing, which extended work pioneered by Albert Einstein.  He produced dozens of published works and lectured widely at MIT, Princeton, the University of California in Berkeley, and both Oxford and Cambridge in England.  

In 2012, Harold was named to the inaugural group of Fellows of the American Mathematical Society, an honor recognizing outstanding contributions to the advancement of mathematics.  Harold’s students at Brandeis have gone on to join and lead Departments of Mathematics throughout the world, noting the pivotal role his guidance and support has played in the progression of their careers.  In 2016, Harold and Renée funded the Harold I. Levine Endowed Fellowship, which supports graduate student research in Mathematics at Brandeis University.  From 2017 through 2022, ten students have been named Levine Fellows with at least half already going on to faculty positions of their own.  

Though a brilliant mathematician, Harold had other impressive talents.  In addition to being a skilled pianist, Harold was also an artist.  As a young man he took up painting, an interest he rekindled after retirement.  Harold had a show of his paintings in a chateau near their home in the Loire Valley of France. 

Harold is remembered as a humble, thoughtful, brilliant man.  Current Chair of the Brandeis Department of Mathematics, Olivier Bernardi, summed up the sentiments of the many people fortunate to work with Harold: “We are saddened by the passing away of Harold, who is remembered by everyone as a kind and generous presence at Brandeis, in a department he helped create.”

Harold is survived by his stepdaughters Jill Preyer, Sally LaVenture and Liz Preyer and their families, as well as his brother Sydney, his wife Dr. Judith Levine, and five nephews and their families. 

For people wishing to honor Harold’s memory with a donation, his family suggests contributing to the Alzheimer’s Association.

Dr. Harold I. Levine, Emeritus Professor of Mathematics at Brandeis University, passed away in Asheville, North Carolina, on March 11, 2023, after a slow decline due to Alzheimer’s Disease.  He was 94 years old.

Harold was born in Lynn, Massachusetts, the middle child of a couple who each came to America as children as their families sought to escape poverty and prejudice in Eastern Europe.  His mother Rose was born in Warsaw, Poland.  When she was nine, in 1914, she emigrated to the United States from her family’s home village in what is now western Ukraine.  She and her mother and two brothers were on the last immigrant ship leaving Germany before the outbreak of World War I.  Harold’s father Max emigrated with his mother and brothers from Bialystok, Poland, around 1905, when he was a little boy.  After reuniting with their fathers, who had come to America earlier, both Rose and Max and their families settled in Lynn, Massachusetts, an industrial coastal city north of Boston.  Serious, industrious Rose married whip-smart, impish Max, and they had three children: Ethel, Harold and Sydney.  Harold graduated from Lynn Classical High School and went on to receive a B.S. degree in Mathematics and Physics from the University of New Mexico; famously, he made the 2300-mile trip from Lynn to Albuquerque on a motorcycle (these were the days before Interstate highways).  Harold received an M.S. degree in Mathematics in 1952 from the University of Chicago, and a Ph.D. from the same institution in 1957.  During his time in Chicago Harold served as a mathematician for the Institute of Air Weapons Research.  From 1957 to 1959 he conducted postdoctoral research at the University of Bonn in Germany, and in 1959 he served one year as an Instructor at Yale.

In 1960 Harold accepted a tenured position at Brandeis University in Waltham, Massachusetts, as Assistant Professor in the Mathematics Department.  He spent time in 1963 as a postdoctoral Fellow at Cambridge, in England.  Harold became a full Professor in Mathematics at Brandeis in 1968 and Department Chair in 1972 and again in 1988.  During his many years as a senior professor, Harold was graduate studies advisor and enlightened advanced students on the ever-expanding techniques and applications of integral calculus.  He retired in 1994. 

In 1961, Harold married the former Renée (Guttman) Preyer, whom he had met while on a Fulbright Fellowship in Germany.  Born Renate Guttman on May 25, 1925, in Berlin, Germany, Renée was the daughter of Eric and Irene Guttman, both psychiatrists. The family fled Nazi Germany, emigrating first to England.  Later, Renée and her younger brother, Robert, traveled alone to the United States to live with their mother, who died of breast cancer shortly after they arrived.  Renée attended Smith College, married Robert Preyer in 1947, and raised their three daughters in Massachusetts.  Renée was the consummate intellectual, well read and fluent in three languages.  Though petite in stature, she was a force to be reckoned with.  Never one to mince words, Renée was staunchly independent and delighted in debating with old and new friends.  She was an early and feisty feminist, active in the progressive political causes of the 1960s.  She proudly marched for civil rights in Boston and Washington, D.C.  In her fifties Renée received a master's degree from Goddard College and worked at Lesley University in Cambridge, Massachusetts. She also had a private therapy practice focusing on helping women re-enter the workforce.  Renée was a lifelong writer, contributing a blog entry only a few days before she died.  She is the author of How to Get a Job in Boston (or Anywhere Else) and One-Way Tickets, an autobiography.

Harold and Renée shared robust intellectual gifts and deeply progressive sentiments.  They lived in the South End of Boston, in an old home in Newton on the banks of the Charles River, and in a condo in Cambridge.  Harold and Renée also had a farmhouse in the small central New Hampshire town of Henniker.  They travelled extensively in Europe; and in the mid-1990s, they moved to France, living both in a rented apartment in Paris and in a house they owned in a village near Orléans along the Loire River.  Harold’s nephew Howard Schultz and his wife Victoria Winston fondly recall their visits with Harold and Renée in France.  And a close friend of Renée’s, Arun Kapil, wrote this about Renée and Harold’s years in France: 

“Within a few years [they] had built up a social network (joining reading groups and other such activities). E.g. in 2004 or thereabouts, Renée invited me and my wife to a social gathering at their place, where there were some 15-20 guests, almost all French retirees (of their educational-cultural level), whose acquaintance they had made over the preceding years. I was impressed that they had been able to meet so many people in a city they were relatively new to and not being in the working world.”

In 2010, the Levines relocated to Asheville to be near two of Renée’s daughters.  Renée, always an unstoppable advocate for those she loved, cared with great devotion as Harold became more disabled by his dementia.  After Renée’s death, her daughter Liz kept a loving watch over Harold, up to the day he passed.

Harold is remembered as a humble, thoughtful, brilliant man whose resonant baritone voice projected calmness and introspection.  His kindness was instinctual: for example, his nephew Mark, who was perhaps eight at the time, remembers that Harold brought him two marvelous gifts—delicate figurines of medieval knights and their steeds, and a set of miniature-gauge electric trains—when he returned from one of his trips to Germany.  Harold had been a loving but low-key presence in Mark’s life, so these spot-on presents were a totally unexpected treasure.  (Mark still has them.)  Several of Harold’s colleagues, including Professor Emeritus Paul Monsky, remember with great fondness how Harold would invite them over for dinner and the warmth with which he opened his home to them.  One Brandeis colleague, Professor of Mathematics Daniel Ruberman, writes this about Harold: 

“I have many nice memories of talking with him (and squash games) during my early years at Brandeis.  My mathematical work had some overlap with his research at the time, and I enjoyed talking with him and his graduate students….  Mainly I remember his gentle manner and kindness.” 

David Eisenbud, now Professor of Mathematics at the University of California Berkeley, recalls a time when he met up with his Brandeis colleague, Harold Levine, in Paris:

“I can tell you a story of how Hal influenced the course of my life: Just after getting tenure at Brandeis I went to Paris on a Sloan Fellowship and Hal was there at the time.  We had dinner together at a fancy restaurant, and he told me about the problem of the degree of a finitely determined map germ.  I had a vague idea, and tossed and turned that night thinking about examples—the idea seemed to work.  Hal saw how to make a better formulation than I had….  That was a very exciting time, and I spent some of it with Hal and Renée at their country place—a farm—and enjoyed Renée's French-style hospitality very much.” 

Dr. Eisenbud believes that this “joint work,” sketched out over a Parisian dinner, “was an important factor in my (much later) getting the job” of Director of the Mathematical Sciences Research Institute in Berkeley.  

Current Chair of the Brandeis Department of Mathematics, Olivier Bernardi, summed up the sentiments of the many people fortunate to work with Harold: “We are saddened by the passing away of Harold, who is remembered by everyone as a kind and generous presence at Brandeis, in a department he helped create.”

Though a brilliant mathematician, Harold had other impressive talents.  More than one colleague, including Daniel Ruberman, remembers contending with Harold on the university’s squash courts, at least until Harold required hip surgery.  In addition to being a skilled pianist, Harold also was an artist.  As a young man he took up painting, and one of his still-life renderings hung proudly above the fireplace in his sister Ethel’s home.  After retirement, Harold resumed his art studies—following in the footsteps of his mother Rose, who began to paint in her seventies—and, according to stepdaughter Liz, he was always sketching.  Harold had a show of his paintings in a chateau near their home in the Loire Valley of France. 

As mentioned, Harold was deeply interested in social justice.  His stepdaughter Liz, for instance, recalls how Harold participated in protests of the Viet Nam War.  But his progressive views did not stop at the threshold of the Brandeis Math Department.  Colleague Paul Monsky recalls, “Harold was thought politically suspect by some department members (as were Alan Mayer and I)—they feared that once any of us became chairman, our rather egalitarian views would wreak havoc.  So an elected chairmanship was voted in to replace the old rotating one….”  

When Harold joined Brandeis, the university had only been in existence for a dozen years.  Colleague Daniel Ruberman remembers that 

“Harold arrived as part of a talented group of mathematicians who helped bring the Brandeis mathematics department to a high level in a remarkably short period of time.”

Noted historian Abram Leon Sachar wrote a book Brandeis University: A Host At Last, about his experiences as the founding President then Chancellor Emeritus of Brandeis.  In this book, which was published in 1995, two years after his death, Dr. Sachar wrote that the university set out from the beginning to create a robust Department of Mathematics.  “Vigorous recruitment enlisted a brilliant team who, though quite young, had already distinguished themselves.”  However, he continued, “Ironically, the very eminence of the gifted mathematics team created a problem for the university.  The faculty knew they were in great demand and regarded themselves as a special group, as indeed they were.”  Some notable defections occurred, “to such citadels of mathematics as Yale…, Princeton and to distinguished foreign universities.”  But a core group of “first-rate academicians were anxious to stay” and give “the highest priority to their continued identity with Brandeis and its mission.”  Dr. Sachar singles out Harold for special mention as one of the “venturesome pioneers” whose expertise and loyalty elevated the Brandeis Department of Mathematics to world-class status.

Harold was a prodigious intellect: his first published work, “Singularities of differential mappings, I,” was issued by the University of Bonn in 1958, when he was 20 years old.  Overall, his published works, on such topics as holomorphic mappings, elimination of cusps, foliations and holonomy, 3-manifolds, Morse inequalities, and gravitational lensing, number in the dozens.  Brandeis colleague Professor Daniel Ruberman tells us that

“Harold's earliest work was in complex analysis, but his interests soon shifted to differential topology, in particular the singularities of differentiable mappings. This subject that would concern him for the rest of his career. His most celebrated work (joint with his Brandeis colleague David Eisenbud) computes the topological degree of a differentiable function in terms of algebraic geometry. His research was applied to general relativity in physics, to studies of gravitational lensing.”

In 1976 Harold received a grant in excess of $40,000 from the National Science Foundation for his research on “local invariants of isolated singularities of smooth maps,” which was presented in Analysis and Differential Mappings.  Harold did additional study in mathematics at both MIT and Princeton and held junior teaching posts at both MIT and the University of California in Berkeley.  He was often invited for visiting teaching and research assignments at Oxford and Cambridge.  In 1989 Harold was honored for his work by the Federal Republic of Germany.  He became a worldwide authority in singularity theory and coauthored the 1993 book (republished in 2001) Singularity Theory and Gravitational Lensing.  According to a review, “This most attractively presented book,” which extended work pioneered by Albert Einstein, “summarizes current mathematical methods in the field and sets the stage for further exciting developments.”  

In 2012, Harold was one of eight members of the Brandeis Department of Mathematics named to the inaugural group of Fellows of the American Mathematical Society; this honor recognizes members who have made outstanding contributions to the creation, exposition, advancement, communication and utilization of mathematics.  Harold’s students at Brandeis have gone on to populate and lead Departments of Mathematics throughout the world.  Terence Gaffney, who is Emeritus Professor of Mathematics at Northeastern University in Boston, got his Ph.D. from Brandeis in 1976.  He remembers Harold, who was his doctoral advisor, like this: 

“At the time I began with him, Harold was advising four students.  Since he met with each student for an hour to an hour and a half each week, this was a heavy load….  Harold’s style of thesis advising therefore tended to be psychoanalytic. I would go into his office each week, talk about what I had been thinking about that week, outline some thoughts about the week ahead, and Harold would be supportive….   (H)is approach helped me pick out problems that were significant, solvable, and for which I could develop my own tools. This gave me a great start as an independent researcher, and I will always be grateful to him for that.”

Dr. Leslie Wilson, Professor Emeritus at the University of Hawaii, has this remembrance:

“I was a graduate student studying singularity theory from 1971-1973.  One of the most interesting and useful works that I studied was the so-called ‘Thom-Levine Notes’: mimeographed notes written by a young Harold Levine based on lectures at Bonn University by Rene Thom.  It was understood in the community that, while Thom’s ideas were brilliant, Harold needed to fill in lots of gaps.  I also studied interesting work by Harold on ‘elimination of cusps’ in stable mappings into the plane.  So I was very thrilled to receive a post-doc to Brandeis (from 1973-1975).  It was great to be able to work with Harold and his group of grad students and visitors.  Harold arranged for me to give seminar lectures and advanced graduate courses, which were helpful in my development.  I matured as a researcher under his tutelage.  Harold was always gracious and friendly.  He was on sabbatical during my second year there but he was nice enough to invite me to visit him at his house in Vermont (or was it NH?)  [N.B.: it was New Hampshire]….  I don't believe I ever saw Harold after I left Brandeis and went to Hawaii, but I always thought highly of him as a person.”

In 2016, Harold and Renée funded the Harold I. Levine Endowed Fellowship, which supports graduate student research in Mathematics at Brandeis University.  From 2017 through 2022 ten students have been named Levine Fellows; at least half have already gone on to professorships of their own, at nearby Northeastern and Boston College as well as at Middlebury College in Vermont, the University of Utah and Georgia Tech.  Mathematics Chair Olivier Bernardi, passed along this note of appreciation from 2022 Levine Fellow, Ray Maresca:

“During the summer of 2022, I was chosen to receive the Harold Levine Fellowship. The financial assistance, for which I am very grateful, allowed me to focus entirely on my research for a significant portion of the summer. Ultimately, my advisor Kiyoshi Igusa and I solved the problem we originally set out to solve. The research done under the support of the Harold Levine Fellowship is written in a paper… that has been submitted for publication in a special issue of a journal on cluster algebras and related topics. If it were not for this fellowship, I would not have been able to spend nearly as much time as I did on this research project. So again, I thank Prof. Harold Levine and his wife for endowing Brandeis with such an impactful fellowship.”

Harold was predeceased by his wife Renée Levine, who died on November 2, 2020; by his parents Rose and Max Levine; and by his sister Ethel and her husband Bernard Schultz.  He is survived by his stepdaughters Jill Preyer, Sally LaVenture and Liz Preyer; by his stepgranddaughters Rainy LaVenture, Willow Engel, Melanie Clayton and Heather Friedman; by his brother Sydney, his wife Dr. Judith Levine, his older son Stephen (wife Amanda Bosch and son Max Levine), and his younger son Barry Levine; and by Ethel and Bernie’s sons Mark (wife Suzanne, son Matt and daughter-in-law Jennifer, daughter Margaret and son-in-law Beau Fisher, and Matt and Jen’s daughters Lydia and Edith), Howard (wife Victoria Winston, son Alexander and daughter-in-law Anagha Prasad, son Benjamin and partner Jacqueline Shameklis, and son Carter and partner Laurel Irvine), and Larry.

For people wishing to honor Harold’s memory with a donation, his family suggests making a contribution to the Alzheimer’s Association.