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Travels, 5 | Peter Cameron's Blog
It was a great relief to see someone waving to us as we came out of the baggage hall in Kochi Airport, compared to the rather frightening difficulties I had last time here on the three occasions I was at the airport. Aparna Lakshmanan and her student had come to collect us. It was a…
Travels, 4 | Peter Cameron's Blog
As we went out of the terminal building past the armed guard with the taxi despatcher, two people materialised from the crowd, colleagues from IIT Madras, including Arun Kumar, the organiser of our talks there. After discussion they decided to stick to the plan we had made; Arun would come with us to the hotel…
Travels, 3 | Peter Cameron's Blog
A terrible journey, but not in the way I expected. We caught an earlyish train which had a very intermittent journey to Heathrow, with several long pauses at red signals. But we still managed to arrive before check-in opened. So we had a quarter of an hour's pause before the next tsunami hit We had…
Travels, 2 | Peter Cameron's Blog
Today is the day it really starts. The long flight will be an ordeal, but at least my cold is a little better than it was. We had allowed ourselves two quiet days in London to prepare. Inevitably, the outside world intervenes. An email from Leandro Vendramin about bad things happening in Argentina with respect…
Travels, 1 | Peter Cameron's Blog
Off on a long and complicated trip. But I don't think I am a good traveller. On Friday I started the day with the symptoms of a really awful cold, and unable to take any prophylactic medicine for quite some time. Saturday was our train journey down to London at the start of the adventure;…
Shocking news | Peter Cameron's Blog
I just learned from Misha Klin that Misha Volkov "has suddenly lost his job and has been placed under a travel ban". At the same time he has serious health issues. What is going on? I have no idea of the reason and cannot imagine that this great mathematician and gentle person could have offended…
A class of interesting permutation groups | Peter Cameron's Blog
This is the class of primitive groups having an imprimitive subgroup of index 2. Let us make them almost simple as well. For a boring name, I will call this class (P). So I begin with two questions for specialists: Have you met this class before? In what context? What do you think are the…
Is mathematics useful? | Peter Cameron's Blog
This morning I picked up two small books from the sofa, to take upstairs to the bookshelves. They were G. H. Hardy's A Mathematician's Apology, and Kenneth Falconer's Fractals: A Very Short Introduction. These two authors take very different views about the usefulness of mathematics. Hardy says, There are then two mathematics. There is the…
Hold the date! | Peter Cameron's Blog
The date: 12 August 2025, afternoon. The place: St Andrews, Mathematical Institute, Lecture Theatre C The event: A little do to celebrate Rosemary's and my retirement. We are very fortunate to have two former St Andrews students both now making their way in the academic world, who were taught by us as undergraduates here: Scott…
Gender and collaboration | Peter Cameron's Blog
Recently I was browsing Jerry Grossman's beautiful Erdős Number Project website, when I came across an article by Kirsten Menger-Anderson. She begins by attempting to determine the gender of all mathematicians who have Erdős number 1. I was a bit surprised at first. I have quite a few coauthors (261 by my count, though not…
An ADElphabet | Peter Cameron's Blog
Some things involved in the ADE affair. A is for asymptotically locally Euclidean spaceB is for binary polyhedral groupC is for Clifford algebra, or cluster algebraD is for Du Val singularityE is for eigenvalue, or exceptional Lie algebraF is for Fischer groupG is for generalized line graphH is for Hurwitz unitsI is for icosahedral groupJ…
Ruin and desolation | Peter Cameron's Blog
A description of the ruins of Rome by Poggius, in the reign of Pope Eugenius IV (first half of the 15th century), quoted by Edward Gibbon in the final chapter of his Decline and Fall of the Roman Empire: Her primeval state, such as she might appear in a remote age, when Evander entertained the…
AIprl Fool | Peter Cameron's Blog
In Private Eye this morning, I read about a nice April Fool joke perpetrated by Tim Gowers. He claimed on X that he had succeeded in getting Grok to solve the "well-known Dubnovy Blazen problem" in graph theory. The clue is apparently in the facts that this was posted on 1 April, and that "dubnovy…
Support for Harvard | Peter Cameron's Blog
… let us recall the well-known statement of a university professor in the Republic of the Massagetes: "Not the faculty but His Excellency the General can properly determine the sum of two and two." Hermann Hesse It is only the last and wildest kind of courage that can stand on a tower before ten thousand…
The Shrikhande graph | Peter Cameron's Blog
In 1993, Derek Holton and John Sheehan published a book on the Petersen graph. This object is probably the most famous finite graph, and is an example or counterexample to many conjectures. (It was originally introduced by Petersen to debunk a proposed proof of the Four-Colour Conjecture by Tait, who had shown the equivalence of…
Memories of CFSG | Peter Cameron's Blog
Rebecca Waldecker is collecting material for a history of the Classification of Finite Simple Groups (CFSG). Prompted by this, I wrote down a few thoughts. Although I was never involved in any project which fed directly into CFSG, I was on the edge of it for a good part of my career. What follows are…
Weeping Atlas cedars | Peter Cameron's Blog
"Why is a raven like a writing-desk?", the Hatter asked Alice. When she couldn't guess and asked him the answer, he said, "I haven't the slightest idea." So here is another riddle. Why are greedy leaders like weeping Atlas cedars? This occurs in the George Harrison song "Beware of darkness"; at least, all the Internet…
Defend research against government censorship | Peter Cameron's Blog
How sad, and almost unbelievable, that we need this! The Declaration to Defend Research against Government Censorship has four goals: Support instances of resistance to U.S. government censorship; Promote venues for scholars to share, safeguard, and preserve their work, beyond the reach of censorship; Participate in efforts to track and record instances of U.S. government…
Compactness | Peter Cameron's Blog
As almost the last thing in almost my last lecture a week or so ago, one of the highlights was the Compactness Theorem for first-order logic together with some of its consequences (sucuh as the upward Löwenheim–Skolem theorem). Some of the students who had met complactness in the Topology module were interested to know how…
Retirement day | Peter Cameron's Blog
Today is my official last day, after 50 years, as a University lecturer, made up of half a year at the University of Michigan; a year and a bit at Bedford College, London; eleven years at Merton College, Oxford; 26 years at what began as Queen Mary College, University of London, and ended up dropping…
Mathematics at Cardiff | Peter Cameron's Blog
I'm afraid this is the sort of news I have to report all too often. The University of Cardiff, one of the leading universities in Wales, is in financial trouble. They are proposing re-structuring, which will involve merging mathematics with computer science and "data science" and making half of the mathematics staff redundant. I have…
Second Simon Norton memorial lecture | Peter Cameron's Blog
I went to London on Wednesday for the second in the series of Simon Norton memorial lectures, endowed by his family in memory of this remarkable mathematician. The lecture was given by Leonard Soicher; I gave the first in the series last year. Here are the first two lecturers, with Yang He, the organiser of…
ADE: the book of the series | Peter Cameron's Blog
The ADE book now has a webpage where you can pre-order it, though it won't actually be published until August. The ISBN for the paperback version is 9781009335980 and the link is https://www.cambridge.org/9781009335980. You will see that it contains much more than just what I discussed in the ADE series of posts.
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…
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…
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…
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…