Outbound aeroplanes good with a two at Worcester Park and a three at Earlsfield. Viewing conditions at Earlsfield were very good, with only the carriage roof in the way. Unusually, the first two of the three turned sharply into the flight path from the north while the last turned in from the south.
Too late for the goat, but I took my warfarin at the feet of Faraday.
It seems that, despite being disabled by illness through what should have been a busy time in his life, Nash was a truly great mathematician. A genius who knew it, who would only take on difficult problems which would bring him respect and renown. But despite his faults, he was a wow at subcontracting out great chunks of his work to others, to specialists, this despite the fact that at the time it was normal for mathematical papers to have just one author, whereas these days a more explicitly collaborationist tone is expected.
There was a splendid bit in a film clip made at about the same time as the film proper, with Nash peeing myopically at some large portrait hung up in the hall of his old college - Harvard or somewhere like that - and managed a splendidly dismissive 'physicist' as he turned away. Rather different was his knocking on the door of what had been his room there, many years before, to find some bright young thing who had not got a clue who he was and was not in the least bit impressed. Sic transit gloria mundi.
One of his papers was about the fact that any reasonable metric space can be isometrically embedded in a Euclidean space, if you allow enough dimensions in this last. You can trade complexity for high dimensionality, so making geometry a small world, in the sense that there is just the one world, the Euclidean world.
Villani, as well as being a very good lecturer, was also good with questions, with a nice touch at the end of question time when he made a point of taking a question from a youngster, there with mum or dad. The audience held its breath a bit to see how he would do, and clapped when he did rather well for someone of tender years - and despite the privately educated, precocious treble. I wondered whether he had spent quality time beforehand dreaming up a suitable question - with the one he in fact asked not being particularly keyed to the subject matter. In any event, clearly a rising star.
Audience a little more dowdy than usual, but perhaps that was all the mathematicians. One very flashily dressed female - I wondered whether she was a luvvie from the film - and one rather odd chap with a shambly manner and a lot of luggage (given the nature of the seating). No highness on this occasion.
There was another geometry discourse back in 2014 (see reference 2) and I did not heed the admonition to myself not to delve, as I bought the good book illustrated, read very little of it - but now turn it up again in the wake of Villani on Nash. I think I now know what sort of a metric space is good for geometry, with the lines and angles one had at school. I was reminded that I had done no geometry since I left school; not something that cropped up in my university days at all, topology being all the rage at that time. Geometry old hat, something that school boys and ancient Greeks went on about. Topology far more general, far more deep and profound...
Also reminded, not for the first time, of all the interesting things there are in the mathematical world which I never got around to when the brain was still fit for such activity. I shall have to be consoled by the remark of a lecturer at the time: 'you can't expect to do everything' - perhaps more comforting when you have in fact done something. If one has one's monument.
Three threes while I waited for my train at Wimbledon closed the proceedings.
Reference 1: http://psmv3.blogspot.co.uk/2016/04/a-diversion.html.
Reference 2: http://psmv2.blogspot.co.uk/2014/12/memory-lane.html.
Reference 3: https://en.wikipedia.org/wiki/Nash_embedding_theorem.
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