Heini Halberstam, 1926-2014

At a Glance

Metadata	Details
Publication Date	2017-12-01
Journal	Bulletin of the London Mathematical Society
Authors	Harold G. Diamond
Institutions	University of Illinois Urbana-Champaign

Abstract

by Harold Diamond and Eira Scourfield Heini Halberstam was born in Brux, Czechoslovakia (today Most, Czech Republic), on 11 September 1926, the only child of Michael and Judita Halberstam. Heini’s father had moved to Most from Vienna in the 1920s to become the town’s Orthodox Rabbi. When Heini was ten years old, his father died suddenly from a heart attack, and soon after, he and his mother moved to Prague. Following the German invasion of Czechoslovakia, Judita arranged for Heini to study English and, in April 1939, to leave home for England on a Kindertransport train. Heini arrived a week later in London, never to see his mother again. In 1942, she, along with most of Prague’s Jews, was deported to a Nazi work camp where she soon died of typhoid. After several placements in England, Heini had the good fortune to come in the care of Anne Welsford who recognized his ability and encouraged and supported him through his university studies. Heini began studying mathematics at University College, London. After completing his degree in two years, graduating about 1947, he began working for a PhD at UCL. He wrote his thesis on analytic number theory under the supervision of Theodor Estermann, and he was awarded his PhD degree in 1952. At that time Klaus Roth was a fellow research student who worked with Estermann and Professor Harold Davenport. Around 1948, Heini was appointed to a lecturing position at the University College of the South West in Exeter. The mathematics department then was small with about eight staff who taught the full syllabus for the External Degree of the University of London; in 1955 the College became the independent University of Exeter. A few months after arriving in Exeter, Heini married his first wife, Heather Peacock. He was subsequently appointed Warden of Crossmead Hall of Residence for men students, a position he held in addition to his lectureship. He and his colleagues Walter Hayman and Paddy Kennedy ran a mini research seminar with the encouragement of the Head of Department, Professor T. Arnold Brown. It was at Exeter that Heini’s first paper 1 was published in 1949. Heini spent the academic year 1955-1956 in the United States at Brown University. One of his adventures there was getting a traffic ticket. In later years, Heini was amused to recount the conclusion of the court proceeding, at which the judge pronounced his fine with, ‘Rule Britannia, $5.00 please’. When Heini returned to Exeter in 1956 he undertook the supervision of his first research student, namely the second named author of this section. Like others subsequently, she found him to be an inspiring, challenging, and encouraging supervisor. In 1957 Heini moved to Royal Holloway College, University of London, where he was appointed Reader in Mathematics, and he arranged for Eira to transfer there for the second half of her Master’s course and to write her thesis. She benefitted from and much appreciated his strong support throughout her university career and his maintenance of regular academic and personal contact by letter, at conferences and during sabbaticals for the rest of his life. While at Royal Holloway College, Heini regularly attended number theory seminars at UCL, and during this time he began his long involvement in the work of the London Mathematical Society (LMS). In 1962 he was appointed Erasmus Smith’s Professor of Mathematics at Trinity College, University of Dublin. Two years later Heini moved to the University of Nottingham, where he served at various times as Head of Department and Dean of the Faculty. Heini and Heather had four children, two of whom live in the United States and two in Britain; Heather was tragically killed in a road accident in 1971. Heini subsequently married Doreen Bramley who has two children, both residing in Britain. They have eight grandchildren. In 1980, Heini came to the Mathematics Department of the University of Illinois in Urbana-Champaign (UIUC). He served as Department Head 1980-1988 and retired as Emeritus Professor in 1996. Heini was held in much esteem, and to mark his retirement, the department held an international conference on number theory in his honor. In spring 2014, another such conference was sponsored in memory of Heini and of Paul and Felice Bateman. During his career, Heini also held visiting positions at Brown, Michigan, UC Berkeley, Syracuse, Ohio State University, Paris, Ulm, Scuola Normale Superiore in Pisa, Tel Aviv, York, Hong Kong and Matscience in Madras (now known as Chennai). Heini was a major figure in number theory whose research ranged over several areas. He first studied probabilistic methods, and his later — and most important — work centered on sieves. Other interests of his were mean value theorems, Waring’s problem and combinatorial number theory. Some of his research collaborators were Harold Davenport, Harold Diamond, Peter Elliott, Hans-Egon Richert and Klaus Roth. His conjecture with Elliott on the distribution of primes in arithmetic progressions remains one of the outstanding problems in analytic number theory. Sir William Rowan Hamilton (volume 3) 21 Harold Davenport (four volumes) 43 J. E. Littlewood (volume 2) 49 Loo Keng Hua 50 Recent progress in analytic number theory, Durham, 1979 (proceedings) 48 Analytic number theory, Allerton Park, 1990 (proceedings) 65. One of Heini’s particular passions, perhaps remembering how he himself had been aided and encouraged as a child, was promoting talented young people. Heini was an inspiring (if demanding) teacher and mentor. He supervised fourteen PhD and four Masters’ theses, and in addition, many others who came in contact with him as students or postdocs also received enormous help and support. Several of his charges went on to distinguished careers, among them Jean-Marc Deshouillers, Michael Filaseta, Kevin Ford, Richard R. Hall and Robert Vaughan. An example of the lengths to which Heini would go to help a young person was reported by Atul Dixit, a recent PhD at UIUC. Atul wanted to read a sixteen-page paper of the eminent nineteenth century Czech mathematician Mathias Lerch. This was a classic good-news/bad-news situation: Dixit was able to find the paper, but it was in Czech. However, here was Heini who had lived as a boy in Czechoslovakia. On the other hand, Heini’s rusty Czech vocabulary was that of a twelve-year-old. Finally, good news: with a Czech-English dictionary, Heini wrote out by hand a translation of the whole paper. Heini also had a life-long passion to improve mathematical instruction. At Nottingham, he helped start the Shell Centre for Mathematical Education, was a director of the center, and was a member-at-large of the International Commission on Mathematics Education from 1979 to 1982. He continued work in mathematical education after coming to the United States and published several articles on this subject. Heini was a member of the LMS for 59 years, and he served as a Vice President of the LMS and as secretary of its Journal. Also, he was a member of the American Mathematical Society (AMS) for 57 years and wrote over 150 reports for Mathematical Reviews. In addition, he served on the editorial boards of several journals, including Acta Arithmetica and the Journal of Number Theory. Heini’s accomplishments led to many awards and honors. He was elected to the Royal Irish Academy in 1963 (resigned 1966) and was a Fellow of University College, London, from 1967 onward. Heini gave an invited 1-hour lecture at an AMS Annual Meeting in 1980, and was named a Fellow of the AMS in 2012. Over the years, Halberstam held research grants from the U.S. Army, NATO, and the National Science Foundation. A gifted writer, Heini produced precise and elegant prose with seemingly little effort. He was frequently called upon for expository articles, book reviews and obituaries, as well as to provide insight and editorial assistance for the projects of others. An example of Heini’s talent is seen in his review in the Notices of the AMS of The Indian Clerk, a fictionalized account ofthe interaction between the celebrated mathematician Ramanujan and his patron, G. H. Hardy. In the words of his wife, Doreen, Heini was ‘a voracious reader’. This enthusiasm was present from his youth in England, when a friend, the local waste collector, lent him many books. When he married Doreen and they were combining their households, his main request was that she bring all her bookcases. He found most everything interesting, including mysteries, biographies and works, particularly on the Holocaust. Heini always hoped to learn more about his mother’s fate. After retiring, he visited Prague and followed his mother’s path of deportation. More recently, Heini participated in a reunion organized by the Kindertransport Association, and he gave talks in Champaign and elsewhere on the Holocaust and his personal experiences in the Kindertransport. One of Heini’s presentations can be seen at https://www.youtube.com/watch?v=3oyAhpax8w0. An interesting and insightful account of Heini’s life is given in an obituary prepared by his daughter Jude at http://www.jackhalberstam.com/obituary-for-heini-halberstam-1252014/. For this obituary, she has written about Heini’s recollections of leaving Czechoslovakia in 1939. Heini died at home in Champaign, Illinois, on January 25, 2014 at the age of 87. He had a mathematical career extending over 60 years and had been active until the last months of his life. Heini was an internationally known figure in number theory, particularly for his work in sieve theory. In addition to his scholarship, Heini was treasured for his encouraging and optimistic manner, beautiful writing, energy and his interest in people. by Michael Filaseta When I came to the University of Illinois in Champaign-Urbana as a graduate student in August, 1980, Heini had just arrived as head of the Mathematics Department. This additional strength of the U of I number theory group increased my enthusiasm for being a student there. On my first day, as I eagerly walked around campus, I recall hearing among other things the bell tower chimes in Altgeld Hall. The theme song from ‘The Flintstones’ was playing; someone had unusual taste, and maybe I did, too, for recognizing the piece. It says something about my opinion of the U of I number theory group that this was the only graduate school that I had applied to. In addition to Heini, the faculty included Paul Bateman, Bruce Berndt, Harold Diamond, Walter Philipp, Bruce Reznick and Ken Stolarsky, as well as several algebraic number theorists. Postdocs then included Brian Conrey and David Richman. Adolf Hildebrand was also to hold a postdoc position toward the end of my four years at the U of I. Many of these people I had already met while attending the West Coast Number Theory Conference as an undergraduate. Recent breakthroughs in number theory around that time included Roger Apéry’s proof that ζ ( 3 ) is irrational and, a little earlier, Chen Jingrun’s proof that every sufficiently large even integer could be written as a sum of two primes or as a prime plus a product of two primes. In addition to Paul Erdős’ numerous uses of sieve methods, Chen’s theorem helped stoke my eagerness to learn more about sieve techniques. Knowing Heini was an expert in this topic made me think, even before arriving on campus, that I would want him to direct my doctoral dissertation. As an undergraduate student, I had lived at home to keep down costs for my parents who had six children. My dad was in the Army, and we had a rather strict family household to help make life with six kids somewhat orderly. Now, more-or-less on my own for the first time (‘less’ because my brother was also at the U of I, pursuing a doctoral degree in physics), I wanted to express some independence. This urge probably showed itself in ways that I am not even aware of, but the hair that covered my face during much of my four years at the U of I was certainly part of it. By good luck, Heini offered a course in sieve methods during my first year at Illinois. This was Heini’s first-year teaching here, and I wondered how the course might be taught. Heini was a great lecturer: he wrote and spoke clearly, was very organized, and faced us as he discussed the material. While he frequently asked whether there were questions, I could not help but feel that he did not really want any. But I asked … . I recall believing that I understood very well what he was saying in the lectures, but I was not so comfortable with the bigger picture of how everything tied together. I blamed myself and not him for the situation, but this feeling and my good grasp of the lectures as they were presented led me not to ask as many questions later in the semester. I recall at some point, when Heini had finished an explanation and I had raised no question, he looked at me and asked, ‘What does the skeptic think about that’? Perhaps asking too many questions during Heini’s first-year teaching at the U of I was not such a good idea. I was determined early on to impress Heini. The questions during his class may not have helped, but something else unexpectedly did. I attended the number theory seminars regularly and even presented a couple of talks, but these did not necessarily help either. One day, however, as I entered the seminar room, Heini said to me, ‘You are looking more and more impressive every day’. This was a reference to my facial hair; by then I had a rather thick beard. Having finally impressed Heini, I was ready to ask him to be my advisor. He agreed. At that time, I was finishing a combinatorics paper on the classical ballot problem. This arose in a transcendental number theory course of Ken Stolarsky, where a homework problem was related to Padé approximants for e x . The problem was to show that an n × n determinant with the entry 1 / ( i + j − 1 ) ! in the ith row and jth column is non-zero. Another student in the course had shown me a nice combinatorial method of evaluating the determinant that proved clearly that it was non-zero, and I stubbornly the before the was determined to find a I that a of the determinant the number of of these the determinant was non-zero. The paper was on extending this I recall Heini my paper and then it the with very and This was perhaps my of the of time he was to to me as a As department one might him to have little time for students, but this was not the His was always to me, and he spent time with me, to and through of and my dissertation. At some while I was a student, Heini wanted me to have the of a paper, so he me one to along with a of to for it When I returned the paper with a I about an from the a with a in the to it was the I asked him what this He looked at me, with no of my and ‘You — a at the end of the then did I he had given me of the editorial Heini wanted students not to too much time working toward a doctoral I was of finishing in years, but he me at the of my year that I was ready to so I my After out many came from one with a strong undergraduate one in and one from the University of South Heini was of I would and I recall him for the in as well as the one that I did at the University of South The had offered me the of the but the university position would me to my for both teaching and As an David was to South and we had already discussed mathematics while he was a postdoc at the U of I. Over the years, Heini helped me in my career, also in ways that I am On a number of when I returned to Illinois to a whether Heini was in the or he made a to see that my were to with me and mathematical as well as to career to me out to and his to his Doreen, and to time with my and He with me on a regular on a I in Heini a by a of As time his more and became in ways that I could not help but Heini Halberstam was my doctoral but he was at times more of a father figure to me and always a by Kevin My first of Heini Halberstam are from the spring of when I his course on theory. I was a first-year graduate student, very in number theory, but of the I wanted to for By the end of the however, I had in with the in large to Heini’s His enthusiasm for the was and his lectures were a of I not think I had so much in a mathematics course as I did that not just about primes and but the whole of about The for the a little of Richard Hall and was written and I appreciated an expert to help it. One of the main in the course has a but a and I began to Heini’s about what he to be Paul gave a seminar on an problem about I it and began many about including a paper by Paul the number of prime of − 1 and some related problems I recognized in this paper many of the methods which I was in Heini’s but at one I was where it is said that half the in research in asking the of the When I went to Heini’s to ask him what this was all I did not that the for is sieve methods that Heini had with the book on the to very soon I was about sieve methods, another that would a large in my my early interest in and sieve methods, my PhD was written in a and it was not until my years that I returned to these The of the thesis I in my second year of graduate when I what I was a that of as the sum of a a number of I to Paul to about the because he was an expert on related problems of as of and also because of his of the Paul said that Heini might about and Heini to I then walked to Heini’s to the problem with My problem out not to be and in first in the PhD thesis of Heini’s fellow graduate student Klaus Roth in Heini himself had studied very problems in his own PhD thesis he and Roth were supervised by Theodor before on to other later in his This was the start of my regular with Heini, at first through on the method which would have been much more Heini’s and later the related to problem. Heini as a a in a proof would to a lecture about the methods being and perhaps some additional were on Heini could not help but make some on the of education in the United States or Britain. He to himself as a He never spoke about his personal life. It was many years later that I first that he had been one of the by the Kindertransport. I proved my first the known for the number of to sufficiently large and was of I had no how to my these being the before the the and but Heini what to — he my to his and including as another student of Estermann, also had worked on this problem for his PhD I am Heini also helped my paper published in the Journal of the however, he was not and me to even — he had of which he applied to his students as well as to and not only for Heini with me a in which it was that someone else was working to improve my I could not that I my and about two months before I was to my thesis I my theorem by the number of for large from to I am that Heini’s helped me in a after This was very the had just and there was much for after my I received an of a Heini was in many he gave very lectures, and was not to on the he did course he the mathematical with I, on the other hand, had long and and When I was a student, I was around with a problem about between to a given integer and asked Heini he about He might and that I write to I asked Heini for an not that was an even Heini have to write him a Heini where was at that was he was always on the and I my A few later I received a nice it out my was related to about large between one of Erdős’ and one to which I would years Heini and I wrote only one paper, ‘The which in paper had its in a seminar Heini gave when I was a graduate student, on a of sieve method by I this was really I had some about how to various worked at it for a few showed it to Heini, and then returned to my thesis problem. I had this until Heini wrote to me in about a paper on my along with some of his for the mathematics was Heini wrote and organized the paper as only he could have that the was is an In after we wrote paper, I returned to as an Heini was by then and we were it was for me to in these Heini very active for many years, in particular completing his large on combinatorial with Harold Diamond and Hans-Egon He continued to number theory seminar regularly until when he was to on account of Heini was a and friend, and I him by Harold Diamond My family and I met Heini, Doreen and their family in the of while on at the University of Heini was just from leave at that time and had a full of but he was very of his time and to me and my I soon found that Heini was a for well after we arrived in Nottingham, I went to Heini with a family what to about who was at was years old, had never been to school before and suddenly found himself in a with 50 he did not He came home from in this Also, he spoke and for it. the that was served in the school him I always treasured Heini’s to this He in his optimistic that all other children, would to he soon would the we had and he would be the at home as was served at this is just what During the we were in there were many including the great that to were even the was because the had been and it was The did not such things them When we visited their we in one room, they all the and on every they It was and being with Heini had another one that the the it and he had the and to on it some major in perhaps a or I asked him whether in Britain. he with a are all My mathematical with Heini arose from a interest in sieve theory. He and Hans-Egon of the University of Ulm, me on as an in their sieve During the course of this which went on for many years, Richert and Heini and I finished the with much help from several of my PhD a classical sieve and some of the on wrote a of this work with my student in a book published by University When I began working on these projects with Heini, I was about when I had no progress to particularly Heini could his when he or But Heini that an was being and he was always so I came to feel comfortable working with I was to Heini write his long when I whether a could both and it would with a of can which of us wrote a particular He was for years an active member of the at the University of Illinois, a group that during the for and He was when his hearing and him from in its My and I continued with the in the years after his had many when one of their Heini. by Robert I first met Heini in I his early work in which he applied the it related to part of my thesis. I had also a of the book which he had written with Klaus and had already read large of it He gave a seminar in the spring of probably in at University College London where I was a I to recall that it was on some of sieve theory. I was just finishing my PhD with Estermann, and was on the I was present in the seminar I did not him However, Estermann have had a with him because soon I was invited to a at I that he was a graduate of UCL, so I my He it at and as

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Original Source

DOI: https://doi.org/10.1112/blms.12115

References

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1966 - The “large sieve method” and its application to number theory
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1969 - Some inequalities involving trigonometrical polynomials
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1937 - On Waring’s problem: two cubes and a square
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1935 - On the normal number of prime factors of p−1 and some related problems concerning Euler’s ϕ-function [Crossref]
1940 - The Gaussian law of errors in the theory of additive number theoretic functions [Crossref]
1930 - On the representation of a number as the sum of two products I [Crossref]