TRIBUTES TO BRIAN DAY

20 June 2012

1. Margery Street

Brian has been a virtual member of our family for 42 years. Ross and Brian’s friendship began in their University days and persisted through our children’s adulthood right up to visits by the five grandchildren at his bedside. He loved the Christmas cookies!

Avoiding computers and electronic gadgets, Brian drew pleasure and stability through chatting on the phone. He skilfully juggled diverse relationships with personal privacy, making each collocutor feel unique and needed.

Ross’ brother Wayne, writing from Melbourne last Sunday, said

“I scarcely remember visiting your house without a phone call from Brian”.

Upon Brian’s phone call to our house when the family was visiting, our daughters-in-law would lead the chorus of young voices in

“Hello Brian!!!” which must have pleased him.

Ross would take Brian’s calls while on bushwalks, at restaurants, in the car, and at friends’ houses. Brian might start conversation with an off-colour joke – so I can’t repeat one now!

Attending functions in person could be a challenge for him, though. We invited him to a luncheon at our house, and I asked him to say definitely whether he would come or not. He gave me a definite “NO”.

Guess who was the first person to arrive for the luncheon?

Yes, it was Brian.

As more than 24 people from 6 countries have already said,

“We will miss Brian”.

2. Ross Street (presented by Dominic Verity)

I met Brian Day when we were first-year undergraduates at the University of Sydney in 1962.

He was one of only a few contemporary students I talked to before 1965. Then the Pure Mathematics Honours students shared an office in the two-year old Carslaw Building. Brian and I both enjoyed the Honours courses on category theory and general topology by Dr Max Kelly. The cloud of conscription to the Viet-Nam war hung over our heads that year . . . but we were not called up.

We both started our postgraduate work under Max's supervision in 1966. While our projects were quite different, Brian and I then began the conversations about our research that went on until a couple of months ago.

Brian completed his Masters thesis in 1968 at the University of Sydney. Actually, that thesis was already of high PhD quality. It explained categorically the rationale between two existing convenient variants of the notion of topological space.

Max Kelly moved to the University of New South Wales and Brian completed his PhD thesis in 1970 at UNSW. This work is considered a categorical classic, introducing a powerful technique now known internationally as "Day Convolution".

During that time, Brian and Max were working on many projects. Brian's paper, joint with Kelly and appearing in the Proceedings of the Cambridge Philosophical Society in 1970, was a contribution to topology well ahead of its time. Its importance, even to category theory, was missed for many years. By now it is another classic.

These early papers set the stage for “enriched category theory” showing how far the ordinary theory could be powerfully extended. This subject is one of two areas for which Australian Category Theory is especially famous.

Brian spent two years in the USA at the University of Chicago and some time in Denmark at Århus Mathematics Institute. While Brian did very little driving in Australia, he did drive a car in the USA touring the country with a colleague Bill Mitchell from Chicago. Brian began a Lectureship at the University of Sydney in the 1970s. His experience teaching both then and in Chicago made him realize he was not cut out for lecturing. He resigned from the job at Sydney. People urged him just to take leave but he understood he could be more effective with just research.

Max Kelly obtained one of few early grants to mathematics from the Australian Research Committee and used it to employ Brian as a Research Fellow for many years.

Then Brian became a Research Fellow and Honorary Associate in Mathematics at Macquarie for various periods over several decades. However, his attachment and contribution to the Macquarie category theory group (called CoACT since 1991) goes back to the 1970s. Working mainly from home, he made significant contributions to CoACT's ARC research projects, helped guide postgraduate students, and published paper in scholarly mathematical journals.

While not wishing to use email or computers, his main tool of communication was telephone. He would also send ordinary letters (locally and internationally) and occasionally speak at seminars. Within the last year, Mike Barr from McGill University (Canada) emailed me that he had received an airmail letter from Brian. Mike said he couldn't remember the last time he had actually received a handwritten letter!

Some of Brian's papers are written with international colleagues. However, I am very pleased that our collaborations led to many joint papers, sometimes with graduate students. When we were working hard on writing a joint paper, we could exchange as many as 10 telephone calls in one day.

Brian's research contribution, represented by 70 or so papers, was to category theory, topology and topological algebra. His influence has extended beyond that, to areas such as theoretical computer science, homotopy theory and theoretical physics.

Brian was unable to make phone calls over the last month or so. That was profoundly frustrating him. The category theorists at Macquarie are already missing the calls, to hear his new ideas, and to test our own ideas with an expert.