Peter Cameron's Blog

In the last two hours, the following three news items have appeared on the BBC website: Be very afraid!

I have not been well for a while; my brain has turned to gamgee, and I find it difficult to concentrate on hard mathematics. So let me try to get things working by an easier warm-up exercise. There has been … Continue reading →

Not THE famous ABC conjecture, but a conjecture of mine with Mohammed Aljohani and John Bamberg. A simple counting argument shows that, in any vertex-transitive graph, the product of the clique number and the independence number is at most the … Continue reading →

I am now retired, and nearly 80. My brain does not work at the same clock speed that it used to, and I am no longer paid for things which were part of the job sucuh as refereeing, conference attendance … Continue reading →

The latest newsletter from the International Mathematical Union urges mathematicians to attend this year’s ICM in Philadelphia. It will help our beleaguered collleagues in the USA by showing support, and the organisers guarantee our personal safety. Well, I will not be there. But after moral pressure like that, I feel called on to justify my decision. So here goes. - I believe I do a certain amou…

I believe Eugene Plotkin has died. I read this on the AGTA website but I have no details. I met him for the first and only time at Daniela Nikolova’s birthday conference in Deerfield Beach, Florida, four years ago. We got on very well. Outside of mathematics, one of his hobbies is finding beautiful “works of art” in natural stones; he sent me some of the extraordinary videos he had produced.

I have spent a lot of time recently thinking about graphs on groups. To recall the rules: the vertex set must be the group (in general, but not here, I allow an automorphism-invariant subset or the quotient by an automorphism-invariant equivalence relation); the graph must be defined in terms of the group structure with no arbitrary choices; so the automorphism group of the group acts as automorp…

I have been, and remain, sceptical about AI. At best, it is saiad to be good at writing programs, and finding specific facts; but it has a tendency to lie, to invent, and to tell you what it thinks you want to hear, so you have to check very carefully everything it tells you. But I was sent a manuscript by Donald Knuth where he claims that Anthropic’s robot Claude (named after Claude Shannon, the…

As the tagline for this blog says, I like counting things. Reading my Iran diary reminded me of a counting problem I solved then, of which I am quite proud. But like all good problems, it leaves a loose end, which you might like to try. THe problem came from Charles Johnson, one offour pairs of my coauthhors with the same surname. He was interested in properties of a matrix which are at least par…

Last month I was in Vienna, at AAA108. This was the 108th meeting of the Arbeitsgruppe Allgemeine Algebra (or Workshop on General Algebra), which has been going since 1971, with usually two meetings a year. The meetings are held at weekends, to maximise the chance that people can attend without disrupting their lecturing schedules too much (Friday, Saturday and Sunday morning). It was founded by …

The set Q of rational numbers is obviously an interesting topological space. In 1920, Waclaw Sierpiński gave a lovely characterisation of it. The simplest way to state it is to say that a countable, metrisable, space without isolated points is homeomorphic to Q. (Sierpiński also gave a purely topological characterisation: a countable, second countable, 0-dimensional, T1 topological space without …

Two brief topics. My resolution to publish in diamond open-access journals is already in tatters. I assumed this would happen because I had coauthors who were compelled to publish in certain journals. But the other plausible reason for it to … Continue reading →