UNIVERSITY OF CAPE TOWN
GRADUATION CEREMONY OF THE FACULTY OF SCIENCE

Wednesday 13 December 2000 at 6 p.m.

CITATION FOR THE AWARD OF AN HONORARY DSc
TO PROFESSOR BERNHARD BANASCHEWSKI

Vice Chancellor, I have the honour to present for the degree of Doctor of Science honoris causa: Bernhard Banaschewski.

The Senate and Council of UCT have resolved that this honorary degree shall be conferred upon Professor Bernhard Banaschewski for his outstanding scholarly achievements in the field of mathematics and for his continuing contributions to this field at UCT and in South Africa.

When people meet a mathematician, they try to ward off disaster by confessing that they were no good at mathematics at school. Often they say it was their most horrible subject, even when it was a very good school.  Their children tend to hear this, and the disaster gets passed on. There is also the cheerful popular belief that mathematicians are boring people, in fact dull.  However, I know many of them whose lives are exciting, who have wonderful stories to tell, whose conversation is never dull, who have a fine taste for literature and the arts, who are excellent cooks and connoisseurs of wine, etc.  Precisely such a person is Professor Banaschewski, our honoured Canadian guest, a distinguished researcher and teacher. 

Research in mathematics! People ask how is that possible, hasn’t the whole subject been figured out ages ago?  The first secret of success is just this:  One must get started, and then continue. This takes discipline. Professor Banaschewski can drink me and most of my colleagues under the table. Next morning, while we feel knocked out, he will be at his desk, working hard as ever.  As he did today!

Bernhard Banaschewski was born in Munich on 22 March 1926. His mother, Anne, then aged 24, already had a doctorate in History of Art when she was 22. She took him to Hamburg and raised him there. Times were hard. Materially they had little comfort and little security. In the Hitler era she was one of those dauntless individualists known as “politically unreliable”, meaning not a supporter of the Nazi’s. This did not make life any easier. But after 1945 she, Dr Anne Banaschewski, made a valuable contribution to the restructuring of education in West Germany. 

In 1943, even before he turned seventeen, Bernhard was already in the German anti-aircraft gunnery.  He saw the massive bombing of Hamburg in July 1943. From April 1945 to February 1947 he was prisoner of war. He studied at the University of Hamburg until 1953, receiving the doctorate in Mathematics under Ernst Witt.

In 1955 Banaschewski went to Canada to join the staff of McMaster University in Hamilton, Ontario. There he made rapid progress and was awarded the prestigious McKay Professorship of Mathematics in 1964. He retired as Emeritus McKay Professor in 1991 and is still based at McMaster, continuing with unabated vigour and output his research in mathematics. 

As researcher, Banaschewski has contributed to an extraordinary range of fields of mathematics. To avoid stress to us all, I shall omit the list and only say that these are exciting and important abstract as well as applicable fields of our science.  This astonishing variety of work is by no means scattered or disparate but is unified by the guiding conceptual vision.  He is acknowledged as one of the masters of the conceptual method of doing and presenting mathematical work. This gives transparent and elegant logical structure to even the hardest proof or computation. His publications (approaching 160, in leading journals) testify to his exceptional ability to solve really hard problems as well as to build beautifully structured theory. 

Certain areas of mathematics have important philosophical significance. From the very beginning, Banaschewski was fascinated by the fundamental objects of mathematical thought, such as logic, set theory and the problems of choice and constructivity that arise when one deals with infinite aggregates; also the ideas of space, order, algebraic operations, and how all these are intertwined. His early adoption of the methods of category theory, then sheaves, locales (or frames), and topos theory, certainly was essential to the success of his programme. Over the last two decades he has made a huge contribution to point-free topology and to its constructivity, using frame theory as the algebraic vehicle. Here I can explain: Topology deals with spaces, many kinds of spaces. Traditionally, spaces are viewed as consisting of points. One gets closer to intuition and to computational reality if one forgets the points and instead thinks in terms of patches of space.  The problem of catching the elusive individual points disappears. This is point-free topology. Banaschewski has allied this study with his many and beautiful investigations of the role of choice principles, and of the ideas of completeness and cocompleteness. 

As teacher, Banaschewski excels and inspires. He lectures in stirring tones, with magical clarity of thought and speech, and with complete mastery of chalk and blackboard. (Overhead projector and computer are scorned, they would only clutter his direct and simple procedure.) This is how he has lectured to undergraduates on several campuses. This is how he lectures to top researchers at hundreds of conferences and seminars in many parts of the world.

As servant of his institution and his profession, Banaschewski has done a vast amount of work. He was head of his department in 1961-67 and 1982-87. He served on many committees of the National Research Council (later the NSERC) of Canada, was office bearer of the Canadian Mathematical Society, became fellow of the Royal Society of Canada, is still on the editorial boards of two international research journals, and still does masses of refereeing work.

UCT’s connection with Banaschewski started in 1975.  I was a young lecturer here. On an unforgettable summer evening I arrived at a research institute in the Black Forest for my very first participation in an international conference, one on category theory. I was introduced to a group of mathematicians. The one who hailed me with such moving charm and force of character was “Herr Banaschewski”. I knew a tantalising bit of his work. Two weeks later I invited him to a conference which Professor Keith Hardie and I were organising for August 1976 at UCT. He accepted on the spot. He duly came in 1976 and contributed much to the success of our conference. The event also kindled his deep interest in the people, problems and mathematics of South Africa.

Of course we invited him again, in those dramatic years of protest, struggle and isolation.  Always keenly aware of the human rights issues, Banaschewski also knew what UCT stood for.  He made the very conscious decision, undaunted like his mother, to support our efforts for mathematics and our students. 

At that epoch the Topology Research Group in the Department of Mathematics at UCT was already sizeable. Point-free topology was then one of Banaschewski's new interests, and that was what he started to teach in our research seminar at his next visit, in 1979.  From then on, every single year right up to the present, he has been our invited guest, the visits eventually becoming five months each year. His enthralling weekly seminar lectures, sometimes two or more hours at a time, regularly serve to tell us his new ideas as well as to test them before the new paper is written up.  He has always assisted us with training our research students and stimulating our undergraduates, and has given us inestimable advice, empathy, encouragement. A good many joint papers with members of our group, and doctoral and masters theses of our students, witness the strength of the collaboration. 

Banaschewski’s annual visits usually take him to UNISA and Rhodes University as well. Thus his influence and his teachings have spread far and wide across South Africa. He is an honorary member of the South African Mathematical Society, and serves on the Editorial Board of “QM”, the journal of the Society.  With his unrelenting standards he is one of those who have elevated  “QM” to the status of a small but solid and respectable international research journal.

Here and now we of the UCT community are faced with South Africa’s desperate need for development in mathematics at the most basic levels, as well as for excellence at the top levels.  I could list, but that is another story, how many students and academics from disadvantaged communities in South Africa have been inspired by Banaschewski’s teachings and research, and are themselves engaged in related research.  We can take heart that our children and our students will achieve much, as much as our faith and confidence can reach for. 

Vice-Chancellor, I have the honour to invite you to confer the degree of Doctor of Science honoris causa upon Bernhard Banaschewski.

(Citation written and delivered by G.C.L. Brümmer, Emeritus Professor of Mathematics, University of Cape Town)

Published in: Notices of the South African Mathematical Society 32 , No. 1 (April 2001), 23-25.