Last night I went to Oxford to talk to the Invariants, the undergraduate mathematics society.

I first arrived in Oxford in 1968; the mathematicians had fairly recently moved into the new Mathematical Institute. The letters I had received in Australia gave the address 24–29 St Giles’. Coming from a place where the numbers on each side of a street have the same parity, I did wonder if the building bridged the street; that was before I realised how wide St Giles’ is at that point.

My understanding was that, when it was built, the University asked the architects to design it so that a new floor could be added on top. However, when the need for a computer lab became obvious, the University went back to the architects, only to be told that building regulations had changed and it was no longer possible. They had to put the computer lab in the car park instead, not a popular move. At that point it was inevitable that a new building would be needed for mathematics. Now it has been built, and the Andrew Wiles Building stands in the area which used to be the Radcliffe Infirmary. As it was described to me, the entrance foyer of the new building is about the size of the old Mathematical Institute.

I was very struck by the fact that, in the room where I lectured, which is still in the basement and still called L1, they have installed what seem to be the whiteboards from the old L1, fabric boards which run around in a loop. The area available is so great that I was able to give an hour lecture without needing to erase anything. (Very unusual for me!)

I told the Invariants about the random graph. (If my memory is correct, my last talk to the Invariants, many years ago – certainly many generations of undergraduates – I also talked about the random graph; but I am not ashamed of the fact that this is my party piece.) I spent two thirds of the talk on the familiar introduction: the paradoxical Erdős–Rényi theorem, some suprising constructions, the universality and homogeneity. Then I went on to the recent result of Bodirsky, Pinsker and Pongrácz on the 42 reducts of the ordered random graph (with the obligatory reference to the ultimate question, which was probably lost on most of the audience), and the relevance of this structure to topological dynamics (the Kechris–Pestov–Todorcevic theorem).

I arrived a little early, and was able to go for a walk through the streets I used to know well. The Christmas lights were up, but in the back streets and lanes things were more or less as I remembered. Some of my colleagues in Oxford deplored the advance of electric light, preferring the soft glow of gas lamps. Maybe I have become reconciled to it now, or maybe better electric lamps are available, but the sight of light on old stone, perhaps with a few autumn leaves from an overhanging tree, seemed delightful to me.