# Evelyn Merle Roden Nelson

### Quick Info

Born
25 November 1943
Died
1 August 1987

Summary
Evelyn Nelson was a Canadian mathematician who worked in the area of universal algebra with applications to theoretical computer science.

### Biography

Evelyn Nelson's name before she married was Evelyn Merle Roden. Her parents were Russian immigrants who came to Canada in the 1920s and they were to have a strong influence in encouraging their daughter in her educational pursuits. Although her parents had struggled when they first arrived in Canada, by the time Evelyn was born they were comfortably off running a clothing business. Evelyn attended Westdale High School in Hamilton, Canada, and soon showed that she had quite outstanding gifts but it is very much to her parents credit that they encouraged her talents in science and mathematics although they themselves had little experience of these topics. Bernhard Banaschewski writes [3]:-
One of the most positive influences on her life ... 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 ...
After graduating from Westdale High School in Hamilton, Evelyn entered the University of Toronto. She had not yet made the decision to concentrate on mathematics and she entered a course of study of mathematics, physics and chemistry. She remained on this course for two years and then made the decision to move back to her home town of Hamilton and to complete her studies at McMaster University. Soon after her return to Hamilton she married Mort Nelson, who was an undergraduate at McMaster and, of course, he was the reason for her move from Toronto.

At McMaster, Nelson decided to concentrate on mathematics and she registered for the Honours Mathematics course there and performed so well that she even took a graduate course for credit as part of her undergraduate degree. She was awarded her B.Sc. from McMaster in 1965 as the best student in her year and continued to study there for her Master's degree which was awarded in 1967 [3]:-
She drove 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.
The dissertation which she wrote for the award of the M.Sc. led to her first publication in the Canadian Journal of Mathematics. This was a very fine achievement for there are few graduate students studying for a Master's degree who have a publication in a prestigious journal in the year they receive the degree.

Her 1967 paper was entitled Finiteness of semigroups of operators in universal algebra and in it she studied operators on classes of algebraic universal algebras. Defining a class of universal algebras to be algebraic if it is closed under isomorphisms, she then went on to define the seven operators which given an algebraic universal algebra $K$ yield the smallest algebraic class containing all homomorphic images, subalgebras, direct products, subdirect products, reduced products, ultraproducts, and covers of algebras in $K$. She then looked at several subsets of these operators and proves that the semigroup which each set generates is finite.

After completing her M.Sc. Nelson continued to study at McMaster for her Ph.D. under the supervision of Günther Bruns. Then she worked at a slower pace, devoting more time to her family. The first of her two children, both daughters, was born shortly before she competed the work for her doctoral thesis The lattice of equational classes of commutative semigroups. She was awarded a Ph.D. in 1970 for this work which, like her Master's thesis, led to a publication in the Canadian Journal of Mathematics.

Nelson spent her whole career at McMaster. She was appointed as a postdoctoral fellow in 1970 on a three year fellowship, then after its completing she was appointed as a research associate in 1973. During the three years of her postdoctoral fellowship she published many excellent papers. In addition to The lattice of equational classes of commutative semigroups referred to above, she published in 1971 the papers Embedding the dual of $\pi_{m}$ in the lattice of equational classes of commutative semigroups in the Proceedings of the American Mathematical Society and Embedding the dual of $\pi_{∞}$ in the lattice of equational classes of semigroups in Algebra Universalis, both written jointly with Stanley Burris. In the same year she published The lattice of equational classes of semigroups with zero in the Canadian Mathematical Bulletin.

In 1972 further papers appeared. Two which Nelson wrote jointly with Bernhard Banaschewski were On residual finiteness and finite embeddability and Equational compactness in equational classes of algebras both of which were published in Algebra Universalis. In the following year she published Equational compactness in infinitary algebras again jointly with Bernhard Banaschewski. Although the terms are technical and not likely to be understood by many readers of this archive, we quote from the introduction to the paper. It does at least give a flavour of the work:-
W Taylor recently proved, among other results, that an equational class of finitary algebras contains enough equationally compact algebras if and only if the subdirectly irreducible algebras in the class constitute, up to isomorphism, a set. This note provides a negative answer to the natural question whether the same equivalence holds for equational classes of infinitary algebras by exhibiting examples in which there are, up to isomorphism, only one subdirectly irreducible algebra in the class and no non-trivial equationally compact algebras at all.
Banaschewski explained what collaborating with Nelson was like [3]:-
... working with her was always a very great pleasure. She always brought something special and substantial to her joint papers ...
We have listed here only a few of the many papers which Nelson wrote in the years following her doctorate, yet it took eight years before she was appointed to a tenured post at McMaster:-
... the disappointment involved for her was sometimes a considerable burden.
It was only in 1978 when she was appointed associate professor that she was finally given a position in the Department. It was around this time that she began to apply her skills in algebra to problems in theoretical computer science and in 1982 she was made Head of Computer Science at McMaster. In 1983 she was finally promoted to a full professorship but already her health was deteriorating. When Computer Science split from the Mathematics Department to become a Department in its own right in 1984 Nelson's health was too poor to allow her to continue as head.

In 1985 Nelson was invited to address the Fundamentals of Computation Theory Conference in Cottbus. She gave a talk Recent results on continuous ordered algebras in which, among other things, she described all free continuous algebras, as well as free continuous semilattices, and gave the Birkhoff theorem for these algebras. Free continuous semilattices are important in theoretical computational science since they provide semantic models for nondeterministic computations.

Despite deteriorating health, Nelson continued to produce outstanding mathematical papers. She has 48 publications listed under her name which is a remarkable record for someone who died 17 years after the award of her doctorate and many of these being marred by illness. In [4] she is described as follows:-
She was a passionate academic of the highest standards and both a deeply devoted teacher and a profoundly committed research mathematician. ... she was an exemplary mother to her two daughters, a loyal friend to all who were close to her, and a warmly congenial hostess to her visitors ...
Finally let us say a little about Nelson's teaching. This was outstanding, yet it was teaching that was used to discriminate against her for all the years she spent as a research associate. Her teaching first year calculus was highly successful [3]:-
... the first year students loved her vitality and dynamic presence, and she instantly became one of the most successful teachers of that group. ... 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, trivialise the subject and give the students the illusion of understanding without any real depth of knowledge.
Given this superb attitude and success at teaching first year calculus it is ironical that colleagues on the faculty at McMaster argued against giving her a position in the Department because they believed that she could not handle large first year classes. As Banaschewski himself writes, it was a clear a clear case of prejudice against women.

In 1995 the Canadian Mathematical Society honoured her by settting up the Krieger-Nelson Prize Lectureship for Distinguished Research by Women in Mathematics.

### References (show)

1. J Adamek, A Farewell to Evelyn Nelson, Cahiers de topologie et geometrie differentielle categorieques (1988), 171-174.
2. I H Anellis, A Personal Retrospective on the Tenth Anniversary of the Death of Evelyn M Nelson, Modern Logic 7 (3/4) (July/December 1997), 268-271.
3. B Banaschewski, Evelyn M Nelson : An Appreciation, Algebra Universalis 26 (1989), 259-266.
4. Obituary : Evelyn M Nelson, Order 5 (3) (1988), 221-223.
5. A Petruso, Evelyn Nelson, in R Young (ed.), Notable Mathematicians From Ancient Times to the Present (1998), 364-365.