British Combinatorics in Ancient Times (1969-77), by Norman Biggs

(This article first appeared in the 1997 British Combinatorial Bulletin.)

Some while ago Peter Cameron told me that the Committee was gathering information about the early days of the British Combinatorial Conferences. Sabbatical leave has given me the opportunity to dig out some old files, and the following account is based on documentary evidence, as far as possible. I am grateful to several of those mentioned in the account for adding their own recollections.

Of course, there were signs of interest in some aspects of Combinatorics in the 19th century and even earlier. In the British context the two mighty tomes of MacMahon's Combinatory Analysis (1915-16) cannot be overlooked. But that is really prehistory. It was in the 1960s that the subject calling itself Combinatorial Theory, or more succinctly, Combinatorics, began to take wing. Herbert Ryser published his Combinatorial Mathematics in 1963, Gian-Carlo Rota began his series of papers On the Foundations of Combinatorial theory in 1964, the Journal of Combinatorial Theory was founded in 1966, and Marshall Hall's book Combinatorial Theory was published in 1967. Perhaps the first major British event took place in July 1969 when Dominic Welsh organised a Conference on Combinatorial Mathematics and its Applications, in Oxford. He obtained some support from the IMA, and was able to put together an impressive list of invited speakers, among them Paul Erdős, Mark Kac, and Roger Penrose. The participants also included a good number of British mathematicians, many of whom (including myself) hardly knew that we were Combinatorialists. Many lasting friendships were begun at that meeting, and I particularly remember meeting for the first time two shy young men called Béla Bollobás and Robin Wilson. A volume of the Conference Proceedings was published by Academic Press, and it contains several papers which still make interesting reading today.

In 1970 I moved from Southampton to Royal Holloway College, and soon after my arrival the Head of Department told me that he wanted to reduce the balance which had accumulated in his Research Support Fund. I suggested that we should host a small meeting at RHC in the summer of 1971, and this was soon agreed. Very fortunately Bill Tutte agreed to be the main guest, and the Royal Society provided some financial support for him. There were about a dozen other participants, many of them people who had been at the Oxford Conference, and we had a most productive and convivial meeting. There was much talk about the 'Bay Restaurant Problem', mainly led by John Conway and Richard Guy. I don't remember much about the problem, but I seem to recall that it involved bottles of beer, and that it had practical as well as theoretical aspects.

After the 1971 meeting, Douglas Woodall was fired with enthusiasm for having another meeting of the same kind in 1972, and he persuaded Hazel Perfect, Dominic Welsh, and myself to help him organise it. With a master-stroke of tactical diplomacy, he also persuaded Dominic that Oxford was a good place to hold the meeting. Once again the IMA was involved, and in due course they published the proceedings. Although we had originally planned to have a small meeting, it soon became clear that the word was out, and a number of people wrote from abroad asking to attend. The future shape of these conferences was clearly becoming an issue, and a meeting was held one evening in Oxford to decide how to proceed. The outcome was that there should be a regular British Combinatorial Conference (BCC), starting in 1973, and continuing every two years thereafter. It would be open to all-comers, although we still thought in terms of small numbers, perhaps thirty or so from Britain and the same number from abroad. An organising committee was set up and under its guidance, meetings were arranged for Aberystwyth (1973) and Aberdeen (1975).

Woodall was also responsible for another important innovation. In 1971-72 he compiled the first British Combinatorial Information Sheet, listing the combinatorial mathematicians in Britain and the papers they had written or published in the previous year. He continued to produce this publication single-handedly for the next four years.

Crispin Nash-Williams decided to advertise the Aberdeen conference as the Fifth BCC, which resulted in the BCC achieving classic status almost overnight. Partly for this reason the Aberdeen conference was larger than the previous ones. Another factor was that the Science Research Council (as it was then) sponsored a week-long workshop which took place immediately before the conference, so that a number of people attended both events. The growth in size meant that the burden of organisation was becoming non-trivial. In fact, Nash-Williams moved to Reading in January 1975, and John Sheehan took over the task of making the local arrangements in Aberdeen.

Aberdeen marked an important step forward in the story of Combinatorics in the UK. But it was also memorable for other reasons, as several colleagues have pointed out. There was the 'glass-in-cornflakes' incident, resulting in the precautionary hospitalisation of Gian-Carlo Rota and Dominic Welsh. There was the conferment of an honorary degree on Frank Harary. There was the outing to Balmoral, when the coach carrying Paul Erdős broke down; after a long delay a replacement appeared but he refused to board it, preferring instead to join a returning coach, so that he never saw the Queen's holiday home. I was on another coach, which was subject only to a minor delay caused by Béla and Gaby Bollobás buying an extremely large copper object in a back-street antique shop. All in all it was an eventful time. Many consider that John Sheehan's greatest feat was to arrange the programme for the Conference Dinner so that there was no opportunity for after-dinner speeches of the unscheduled kind.

The informal organising committee met one evening in Aberdeen, and agreed to hold the 1977 conference at Royal Holloway College. Peter Rado and I joined the committee at that time. There were no rules of procedure, and I found myself effectively responsible for everything to do with the committee. One immediate problem was that Douglas Woodall wished to give up compiling the Information Sheet, but luckily Ian Anderson and Stuart Hoggar agreed to do it in Glasgow, with financial support from the committee. The 1975-76 edition was the first to appear under their editorship, and the first to bear the name British Combinatorial Bulletin.

Another problem was that the conferences were tending to become dominated by Graph Theory. For this reason we invited James Hirschfeld to join the committee. He had already organised a very successful meeting on Finite Geometries and Designs, and he was able to advise about good speakers in that area for the 1977 conference.

Around the beginning of the 1975-76 session, Crispin Nash-Williams told me that the Aberdeen conference had made a healthy profit, and that in due course I could expect to receive a balance of around £700. At that time this was quite a large sum, and I began to feel that a slightly more formal basis for the committee and its activities would be desirable. I put a note to that effect in the 1975-76 Bulletin, and asked for comments. The response was not exactly enthusiastic. However, the idea of a framework for our activities seemed even more attractive when, perhaps inevitably, some contentious matters had to be settled. Such problems could only be decided by a group of people who were, in some way, representatives of the community. I therefore drew up a 'draft constitution', which set out the aims and objectives of the Committee. Its first priority would be to ensure the continuity of the series of Conferences, but it would be able to use any incidental profits to support other activities, such as the Bulletin and one-day colloquia. The plan was to put the matter to a vote at a general meeting of the participants at the 1977 Conference, and elect a new committee at that time.

The existing informal committee approved the plan at a meeting held during the British Mathematical Colloquium in Edinburgh in April 1977. We realised that the new committee would need a distinguished Chairman, and naturally our first thought was to invite Richard Rado. But his son Peter, who was present, pointed out that his father had recently retired, and might not wish to take on the administrative burden. Accordingly, we agreed to approach Sir Edward Wright. I wrote to him soon afterwards, and he accepted our invitation. I also took it upon myself to look for a Secretary for the new committee, and I was delighted when Donald Keedwell said that he would be willing to do the job (if elected).

A couple of days before the 6th BCC was due to start, I received a call from Sir Edward Wright, telling me that he was unable for health reasons to attend the conference, and that in the circumstances he thought it proper to stand down as our Chairman-elect. It was clear what had to be done, and much to our relief Richard Rado agreed to take it on. The fact that there was a willing Secretary in the offing was an important factor in our pleading.

The 1977 conference had over 200 participants, a significant contrast with the 1971 RHC meeting. For some time we had talked about the possibility of getting the talks of the major participants printed and published so that a 'conference volume' could be ready at the start of the meeting. I discussed this with a friendly publisher, Anthony Watkinson (at that time with Academic Press), and he agreed to try it. Peter Cameron was persuaded to be the Editor, and he succeeded in extracting typescripts from the speakers so that the book was indeed ready on time.

The Business Meeting and elections all went as planned, and the new committee members met for the first time on 13 July 1977. They were asked to fulfil their aims and functions 'with the consent and goodwill of the community of Combinatorial Mathematicians, and subject to the general consensus of opinion as expressed at Business Meetings of the Conferences'. In my view, they and their successors have discharged that responsibility with distinction.