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A prediction | Peter Cameron's Blog
From Chuang Tzu, as quoted by Aldous Huxley: The ruler of the Southern Ocean was Shu, the ruler of the Northern Ocean was Hu, and the ruler of the Centre was Chaos. Shu and Hu were continually meeting in the land of Chaos, who treated them very well. They consulted together how they might repay…
Lecturing fee | Peter Cameron's Blog
In her memoir about her father André, the famous mathematician, and her aunt Simone, the even more famous saint, Sophie Weil says the following: My father often said that Jews could be divided into two categories: merchants or rabbis. Naturally he classified himself, along with his sister, in the latter category, shich did not keep…
Happy (20+25)*(20+25) | Peter Cameron's Blog
Happy new year! 2025 is the square of a triangular number, somethiing that won't happen again for a thousand years (literally). Indeed, the square of the triangle is an interesting graph, being one of only two finite homogeneous graphs (the other is the pentagon). Indeed, I don't have to say whether I mean the Cartesian…
Problem solving | Peter Cameron's Blog
Mathematicians' perspective on problem solving is not unique to us. The following is from At home in the world by Vietnamese monk Thich Nhat Hanh: "One day when I was a child, I looked into the large clay water jar in the front yard that we used for collecting water and I saw a very…
A dream problem | Peter Cameron's Blog
Not infrequently I dream that I am thinking about a mathematical problem. Usually it turns out that the problem is worthless; occasionally it is interesting but tough. A few days ago I had the unusual experience of a simple but meaningful problem. Problem: Is there a 5-digit number, with all digits different, so that its…
Finite groups and discrete mathematics | Peter Cameron's Blog
Recently I had a paper rejected by a journal including the words "discrete mathematics" in its title. The paper was sent back unrefereed, the editor explaining that in their judgment it was group theory not discrete mathematics. In fact the editor was wrong on several counts, which I will come to. A lot of my…
St Bernard on collaboration | Peter Cameron's Blog
I found the answer to the annoying bureaucrats who ask what percentage of the work on a publication was done by each of its authors, in the writings of St Bernard. He said, Grace is necessary to salvation, free will equally so—but grace in order to give salvation, free will in order to receive it.…
Location parameters and twin vertices | Peter Cameron's Blog
It is a pleasant experience when two previous interests suddenly reappear and combine to give something new. This happened to me yesterday, and to add to the pleasure, the two previous interests were things I had first worked on with former students: location parameters and twin vertices in graphs. Location parameters If you are lost,…
Singing mathematics | Peter Cameron's Blog
Yesterday we had a fascinating colloquium talk about the Kerala school of mathematics, given by Aditya Kolachana from IIT Madras (where, by a remarkable coincidence, I am giving a remote talk next week). I knew a bit about this subject, since when I visited Kerala in 2010, I was given a book about the Kerala…
Worrying news | Peter Cameron's Blog
From the International Mathematical Union newsletter: Paper mills and predatory journals have strongly professionalised their activities in the past 10 years and are now creating a substantial revenue. There is a growing parallel universe of fake mathematical science that undermines the trust in science and devaluates the classical selection criteria for scientific excellence based on…
Cluster detection and error correction | Peter Cameron's Blog
A thought, possibly worthless, but I will record it anyway. Today I heard a talk by Brian Franczak from MacEwan University. It was on cluster detection in data, a big topic in artificial intelligence now. The new feature was that he and his colleagues were detecting clusters in data where there is missing or corrupted…
Paul Halmos and Tom Blyth | Peter Cameron's Blog
Tom Blyth, a long-term member of the Mathematics department in St Andrews, died in May this year at the age of 85. Last week, I spotted the Head of Department talking to a woman carrying a big heavy bag. We learned later that it was Abigail, Tom's daughter, who had brought his mathematics books to…
Between transitive and primitive, 2: results | Peter Cameron's Blog
Partitions and the partition lattice The partitions of a set Ω are partially ordered by refinement: Π1 is below Π2 if every part of Π1 is contained in a part of Π2. With this order, they form a lattice; the infimum or meet of two partitions is the partition whose parts are all non-empty intersections…
Between transitive and primitive, I: history | Peter Cameron's Blog
I do enjoy being able to describe some mathematics to you. In this post and the next, it is the somewhat neglected class of transitive but imprimitive finite permutation groups. The paper is on the arXiv, 2409.10461. The official history In the late 1960s, combinatorial methods seriously entered permutation group theory. If a permutation group…
New open access journal? | Peter Cameron's Blog
A message from Ross Kang. Dear colleagues, On behalf of MathOA, we are excited to open a call for proposals for a new startup fund, intended to stimulate the founding of new high-quality Diamond OA mathematics journals: https://www.mathoa.org/diamond-open-access-stimulus-fund/ The call closes December 15, 2024.
The end (or not?) | Peter Cameron's Blog
Rosemary and I have been in St Andrews for nearly twelve years, on temporary contracts. The current contract expires at the end of February 2025, and there is no money to renew it. So we will technically be retiring (or being made redundant) on that date. However, we will not immediately disappear, and it seems…
Simplicial complexes on groups | Peter Cameron's Blog
At the recent UMI/AMS joint meeting in Palermo, I had some brief discussions with somebody about this topic. But I didn't get contact details. If it is you, and you happen to be reading this, please get in touch! I have been thinking about this, and there are some interesting things to say and some…
New BCC website | Peter Cameron's Blog
The British Combinatorial Committee has a new website: www.britishcombinatorics.org.uk/ Take a look, and pass on any comments! My personal thanks to Julia Wolf. The WordPress site I maintained for several years will now be decommissioned. And on the subject of announcements, the next British Combinatorial Conference will be in Cardiff, 6-10 July 2026.
Two conferences, two mysteries | Peter Cameron's Blog
Two conferences in recent days. Time permitting, I would say more about each. I just want to point to two mysteries and some synergy. Last week I was at the British Mathematical Colloquium in Manchester. The last plenary speaker at the first was Nina Snaith, who talked about one of the most striking recent mysteries,…
Dominic Welsh memorial service | Peter Cameron's Blog
To Oxford last Saturday for the memorial service for Dominic Welsh. I wrote about Dominic here; the picture was taken at Geoff Whittle's conference in Wellington in December 2015, if my memory serves. Many people's lives were touched by Dominic, and it was good to see so many able to make it for the service.…
My first doctoral student | Peter Cameron's Blog
One of the hardest things for a supervisor of a new doctoral student is to choose a research topic. It should be one which is not trivially easy or impossibly difficult. But of course it is impossible to say in advance whether a problem will fall into one of these categories. It is especially difficult…
A talk on discrete mathematics | Peter Cameron's Blog
The Academy for Discrete Mathematics and Applications is an Indian organisation founded in 2005 to foster and support interest in discrete mathematics. The current president, Ambat Vijayakumar, has started up a Colloquium Lecture seres, and honoured me by asking me to give the first lecture. I decided that, rather than up-to-the-minute new research, a more…
Graphs and groups, designs and dynamics | Peter Cameron's Blog
Four and a half year ago there was a conference and summer school on the four topics of the title (part of the G2 series of conferences, whose hiistory you can read here) at the Three Gorges Mathematics Center in Yichang, China. Now a book containing the notes from four lecture courses on the four…
British Combinatorial Conference | Peter Cameron's Blog
The British Combinatorial Conference returns to Queen Mary Univesity of London in the first week of July. The web page is here. Last time when the conference was there, and I was one of the organisers, the insttution was called "Queen Mary and Westfield College". We had 319 delegates, a record which has never been…
A talk by Gareth Jones | Peter Cameron's Blog
Today I attended (remotely) a nice talk by Gareth Jones in the Ural Workshop on Group Theory and Combinatorics, about prime powers in permutation group theory and polynomials taking prime values in number theory. I will give just one example result from the first part. For a prime p, a p-complement in a group G…
Ischia group theory conference 2024 | Peter Cameron's Blog
The island of Ischia, about a 45-minute hydrofoil ride from Napoli, is rich in history. The museum has a Homeric drinking cup with an inscription in ancient Greek from the 8th century BCE. At the other end of history, the British composer Sir William Walton and his Argentine wife Susana bought a desolate hilltop producing…
West Virginia University | Peter Cameron's Blog
Anthony Hilton, my former colleague at Queen Mary, spent some time as an Eberly Professor at West Virginia University. Now he has passed on to me the news that the University has decided to close down Pure Mathematics research and put the money into "computer related activities", whatever that means. One of the last mathematicians…
Cauchy numbers: job done | Peter Cameron's Blog
After recruiting Scott Harper to the team, we have finished the job of determining all the Cauchy numbers (these are the positive integers n for which there exists a finite list F of finite groups so that a finite group has order divisible by n if and only if some member of F is embeddable…
Anatoly Vershik | Peter Cameron's Blog
Anatoly Vershik died the day before yesterday. As I have told here, he was the person who told me about the Urysohn space. I had given a talk at the ECM in Barcelona on the countable random graph, and after it he approached me and asked "Do you know about the Urysohn space?" We wrote…
Richard Parker | Peter Cameron's Blog
Richard Parker died last month. Now only two of the authors of the ATLAS of finite groups remain, the two Robs. I knew Richard, but perhaps not well enough to write anything appropriate as a tribute. But I recommend you take a look at Rob Wilson's account on his blog.
More on Cauchy numbers | Peter Cameron's Blog
Following on from the earlier post, the new version of the paper has just gone on the arXiv: 2311.15652 (version 2). If we say that n is a Cauchy number if there is a finite set F of finite groups, all with orders divisible by n, such that every group with order divisible by n…
Cauchy’s theorem for the prime 6 | Peter Cameron's Blog
Before you think I have gone totally crackers: Cauchy's theorem says that a finite group whose order is divisible by a prime number p contains a subgroup which is cyclic of order p. My co-authors and I have proved some similar results, of which the one referred to in the title is the following: A…
Simon Norton lecture | Peter Cameron's Blog
I have been honoured by an invitation to give the inaugural Simon Norton lecture at the London Institute for Mathematical Sciences on 12 February. The webpage is here. Of course there are other people who knew Simon better than I did. Nevertheless, I think I have something to say. It was a paper of mine,…
New Year | Peter Cameron's Blog
The youth could not help breaking a rule of courtesy towards this heavily burdened and yet, as he felt, noble man by asking: "But tell me, I beseech you, why do you carry on such wars on your star? Who is to blame for them? Are you yourself in part responsible?" The King seemed angered…
Programming and typesetting | Peter Cameron's Blog
Is computer typesetting a kind of programming? One of the pioneers, Donald Knuth, clearly thought so. In The TeXBook, he gives TeX code for computing and typesetting the first thirty primes; apart from anything else, this demonstrates that TeX has the capacity to act as an all-purpose program. But there is a rather significant difference.…
Dominic Welsh | Peter Cameron's Blog
Dominic Welsh died late last week. Dominic and I were tutors at Merton College, Oxford for nearly eleven years. I was the pure maths tutor and he was the applied maths tutor. But there was no other Oxford college where the mathematical interests of the pure and applied maths tutors were closer. College lunches are…
Covers of groups | Peter Cameron's Blog
Here is the second of these discussions of elementary problems on finite groups with unexpected ramifications. This topic was suggested to me by Hamid Reza Dorbidi form Jiroft, Iran. Let F be a finite set of finite groups. A finite group G is a cover of F if every group in F is isomorphic to…