Evelyn M. Nelson
1943 – 1987

An Appreciation

B. Banaschewski

Evelyn Merle Nelson, née Roden, was born in 1943 in Hamilton, Ontario of Russian Jewish immigrants. Both her parents had arrived in Canada some two decades before, and by the time she was born they had overcome the early struggles of immigrant life and established a comfortable existence in the clothing business. Her childhood was spent in a warm and supportive family atmosphere. At school, she was serious and determined, developing a devotion to academic pursuits already at an age when most of her contemporaries would have had rather more frivolous interests. This, no doubt, set her somewhat apart but she persisted with great tenacity and commitment. One of the most positive influences on her life at that time, as well as during all later years, was the unwavering reassurance she received from her parents. It was, indeed, not the easiest in those days for a girl to become passionately interested in mathematics and natural science, with many attitudes pervading the schools, and society at large, that were acting as powerful influences against such a choice. Thus it is very much to her parents’ credit that they did everything possible to encourage her to follow her natural inclinations and innate talents, no matter how unfamiliar this might have appeared. They took the greatest pride in her scholastic successes, and the only thing that was a disappointment to them, as Evelyn once explained jokingly, was that they were not required to provide as much financial assistance during her university studies as they would have wanted to because she succeeded in winning so many scholarships.

Yes, university. After finishing grade 13 at Westdale High School in Hamilton, Evelyn went to the University of Toronto for the Mathematics-Physics-Chemistry Programme, a tough combined Honours course which for many years was regarded (and not only at its home institution) as the best course of its kind in the country. She took to the new existence with enormous delight and enthusiasm, and throughout her days she was fond of recalling the uplifting experience of her entry into university life, which indeed was to become her life for good.

After two years at the University of Toronto she decided to transfer to McMaster University. We had a small but very active department in those days and were convinced – the renown of Toronto’s “MPC” notwithstanding – that our Honours Mathematics course had something unique and substantial to offer. Thus when I, as the department chairman of the day, discussed her interest in transferring to us with thís obviously very bright and talented young woman, it momentarily occurred to me that she might have been attracted to us by our reputation. No such luck, though – the attraction of McMaster turned out to be of a very different sort: not long after she arrived she got married to Mort Nelson who was an undergraduate at McMaster at the time.

Whatever her reasons for joining us, she quickly settled in as our star undergraduate, a status underlined, among various other things, by the fact that she was the only undergraduate who received permission to take a graduate course for credit. She was named to the Dean’s Honour List both of her undergraduate years at McMaster, obtaining firsts in all but two of the fifteen courses taken, with respectable seconds in the others. She graduated in 1965 at the top of her class and, naturally, entered graduate study in our department.

The change from undergraduate to graduate student was another transition which she made with the greatest verve and enthusiasm. She immersed herself with passion in her new courses, of a substantially higher level than what she had experienced previously, with the exception of the graduate course she took in fourth year. She dove right into the experience of pursuing one’s own mathematical discoveries rather than learning about those of others, and she became addicted to the exhilaration that accompanies the process. She was greatly fired up by the marvellously inspiring course Günter Bruns was offering and, indeed, chose him as her supervisor. She completed the work for her master’s degree in all of eight months, with a thesis entitled “A finiteness criterion for partially ordered semigroups and its application to Universal Algebra”. Unlike most mathematical master’s theses, this was a nice piece of original work which was published in 1967 in the Canadian Journal of Mathematics – her first published paper.

Her doctoral studies proceeded at a somewhat more measured pace. It would probably have been natural for her to complete her Ph.D. within another two years, and in retrospect it appears it might have been better, in some regards, had she done so, but she decided against that and allowed herself two additional years, making it a total of four. It seemed she wanted to take things somewhat easier for a while, partly no doubt in order to have more time to devote herself to her home and social life. In the end, she completed her Ph.D. work early in 1970, with an excellent thesis entitled “The lattice of equational classes of commutative semigroups” which subsequently give rise to a substantial paper in the Canadian Journal of Mathematics.

Only a couple of months before the final completion of her doctorate, another important event took place in her life: the birth of her first child, a daughter. This, incidentally, means that most of the high level research activity that tends to mark the months before the completion of a thesis was taking place while she was pregnant – a significant and symptomatic fact; throughout her life, she has never wavered in her commitment to her activities as a professional mathematician for reasons of physical discomfort or impairment. The first daughter was, after some years, followed by a second one; and again, Evelyn maintained the performance of her various duties, including the teaching of a large first year class, without any interruption practically up to the day of her birth.

Although very heavily involved in her work, she succeeded in making a substantial amount of time available to the raising of her girls. She had a deep sense of commitment as a mother as well as high expectations of her daughters, and she realized she had to invest her own energy in their upbringing rather than delegating it to someone else or, for that matter, to accident. She also had a very clear perception that mere length of time spent with her daughters was not what counted, but what really mattered was quality time – and she was a great master at creating just that. In the course of the years, the involvement in her daughters’ upbringing became even more pronounced when she became a single parent – when her marriage floundered on one of those barriers of dissatisfaction that sometimes spring up in a relationship and then become overpowering and insurmountable. Her searches for certainties during this period were unsettling and difficult, but she succeeded admirably in forging a new life, of a very personal style of her own, a good life from which she was able to derive a lot of well-deserved satisfaction.

Her career at McMaster after completion of her studies began with a post-doctoral appointment financed from research grants and continued in that fashion, with the later designation of research associate, for a total of eight years. While this was a good time in the sense that if afforded her the opportunity to devote herself to research without any other commitment, it was not without its own setbacks. The department was still in a mode of modest expansion at that time, and it was not unreasonable to hope for a faculty appointment fairly soon after her Ph.D. That, however, did not occur, a decision based on various countervailing perceptions of priority, and the disappointment involved for her was sometimes a considerable burden. By 1978, however, she was finally given a position in the department, appropriately at the associate professor level, and that together with a reasonably timed promotion to full professor helped to offset the earlier disappointment somewhat.

Once a proper member, she rapidly became involved in the affairs of the university at large, sitting on a number of committees and, for a couple of years, chairing the one that monitors the students’ events at the opening of the academic year. It was in the latter rôle that she made a valiant attempt to put some serious content into some of these activities and to curb the excesses of residence initiations, an enterprise that won her great admiration and respect among like-minded faculty colleagues. The most important university duty she undertook, however, was to chair the Unit of Computer Science from 1982 to 1984. The arrangements that had been introduced for Computer Science three years earlier had led to a lot of regrettable friction and disaffection, and it was to her enormous credit that she succeeded in rebuilding a peaceful and encouraging work environment for the Computer Science group almost within weeks of taking over. There were some outside circumstances which helped somewhat in this endeavour, but it was clearly her specific talents of leadership that contributed most to the successful mending of an unpleasant situation that had been allowed to fester for a number of years. A year after she left the chairmanship, Computer Science was reorganized as a separate department, and she was actually asked if she was willing to chair it for the first three years. That, however, she decided against: at this point her health had become enough of a problem that she had to be careful with the kind of commitments she was going to accept.

Her teaching, at any possible level, was invariably of the highest order; she was as effective and inspiring in first year calculus as she was in her fourth year course in automata theory. Ironically, before her faculty appointment, there had actually been some doubts about her ability to handle large first year classes (a clear case of prejudice that one regrets to report) but, of course, the first year students loved her vitality and dynamic presence, and she instantly became one of the most successful teachers of that group. And – she was decidedly not out to please the crowds. In fact, she had a clear vision of the importance of the first year calculus course and a serious concern for the right way of teaching it, which necessarily made her a demanding instructor. In particular, she abhorred the approaches that somehow, as she used to say, trivialize the subject and give the students the illusion of understanding without any real depth of knowledge. In her other courses, she was equally committed to a determined and imaginative effort to impart genuine understanding, often with considerable investment of time on her part.

As much as she loved and was committed to teaching, however, the deepest professional satisfaction she derived from her research. She wrote over 40 papers during a period of about 20 years, and had she lived a normal span of life she would most likely have added that number again during the following 20 years. Her oeuvre displays interesting developments and note-worthy turns. She was a mathematician in constant evolution. Her first five papers centre around the topic of her thesis research, lattices of certain equational classes. The next ten are primarily devoted to various aspects of equational (or atomic) compactness, motivated and stimulated by the exciting work of Walter Taylor at that time, and the following twelve to several different questions that have, in the main, a categorical viewpoint and a universal algebra motivation as their common thread. Most of the remaining papers deal with partially ordered universal algebra, subject to conditions concerning specified joints which originated in theoretical computer science. All this is, albeit within the general region of universal algebra, a fairly extensive territory. She had the ability to learn fast, to get to the important problems of a situation quickly, to struggle tenaciously with technical complexities, and to write in an admirably thought out style. Also, she was extremely good at research collaboration, and indeed working with her was a very great pleasure. She always brought something special and substantial to her joint papers, and much of the work she did in collaboration would not have seen the light of day in the specific form it eventually took but for her contribution to it.

Her commitment to research fully extended to the two activities that are of utmost importance to the mathematical enterprise as a whole but allow for relatively little glory to the individual carrying them out: refereeing and reviewing. In all, Evelyn refereed for ten journals – important journals – and although there is no easily accessibly record to her total contribution in this area, a reasonable guess would be that she must have refereed over 50 papers in her short lifetime. Her refereeing was absolutely superb and completely motivated by her concern for the health of mathematics: she unselfishly gave of her time and her ideas whenever the paper under consideration merited constructive criticism and could be made substantially better by appropriate suggestions for improvement. She had a beautiful vision of what was right in this regard and spared no effort to see it achieved. Then, there are her reviews. Again, she undertook this slightly less private but equally self-effacing task with the deepest possible commitment to quality, in the interest of the mathematical common good. Her contribution to this side of mathematical life was outstanding: she wrote close to 100 reviews in all!

Her other services to the mathematical community included being an editor of Algebra Universalis and a member of several committees of the Canadian Mathematical Society and the American Mathematical Society, which was only to be expected given her public-mindedness on the one hand and her high visibility in her field on the other. The latter, of course, also led to many invitations to give talks and to participate in conferences. She presented close to 30 invited lectures outside Canada, in places ranging from Hawaii to Prague, from Edinburgh to Mexico, with Bremen, Paris and Oberwolfach in between. She loved the travel involved in mathematical activity, both for conferences and for research collaboration; she deeply enjoyed the companionship these occasions created, and she was much loved by her friends and colleagues as charming and engaging company. But not only abroad, also at home, in her own home, she was charming and engaging- especially as hostess when she invited mathematical visitors for dinner. Many will remember these occasions: her gracious home, her great warmth with its endearing mixture of informality and style, her fine food, and the beautiful atmosphere of friendship she was able to create.

But, alas – all this is no more.

To most people, her death came as a totally unforeseen shock, but the fact was that, for a number of years before she died, she had been engaged in a courageous and carefully concealed battle with the increasing encroachment of cancer, and to the few whom she had taken into her confidence the end did not come totally unexpectedly. During those years of struggle, she judiciously chose what she could, and should, and what she rather would not do, or take on as commitment, balancing carefully between preserving her energy and not letting on to the world around her how impaired she really was. She visited her collaborators in Prague during May-June, 1987 for a few weeks of joint research, in the face of a serious worsening of her condition, and she worked at mathematics practically up to her dying day. She was, it appears, not really aware of the closeness of her death but rather expected to be passing through some temporary low, with possibly many more months, if not even a few years, before her of the same kind of carefully managed condition which would allow her to be active in the things that mattered to her. Such was, however, not the case. By all accounts, she did not suffer the severe pain often connected with her illness, but if she had lived longer, it might have been in a condition of nearly complete incapacitation; it is probably a blessing that her freedom-loving soul was spared this agony.

Evelyn’s life stands out by her nobility of spirit, loyalty and warmth of feeling towards her friends and her deep commitment to the causes she held important. To all who knew her well she presented a compelling example of a totally admirable, meaningful life. As profoundly as we grieve her death, that will always remain with us.