Category Archives: doing mathematics

how is it done?

Digraphs on groups

Posted on 27/03/2026 by Peter Cameron

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 … Continue reading →

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Positive news about AI

Posted on 16/03/2026 by Peter Cameron

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 … Continue reading →

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A counting problem

Posted on 08/03/2026 by Peter Cameron

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, … Continue reading →

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Publication and Erdős–Bacon number

Posted on 02/03/2026 by Peter Cameron

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 →

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Discovered or invented?

Posted on 13/02/2026 by Peter Cameron

Last night, I took part in a debate organised by the students’ Debating Society and Mathematics Society jointly. The proposition before the house was This House Believes That Mathematics Is a Human Invention Rather Than a Discovery. When I was … Continue reading →

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Why transformation monoids are harder than permutation groups

Posted on 26/11/2025 by Peter Cameron

For permutation groups (or transformation monoids), we don’t need to assume the associative law, since composition of functions is always associative. So a permtation group is a set of mappings satisfying the identity, inverse and closure axioms. This implies that … Continue reading →

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Graphs defined on algebras

Posted on 17/11/2025 by Peter Cameron

Next February, I will be speaking at AAA108 (Arbeitstagung Allgemeine Algebra) in Vienna. I thought this might be a chance to take some of the work about graphs defined on groups, and see whether it can be extended to arbitrary … Continue reading →

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Retirement party

Posted on 14/08/2025 by Peter Cameron

Our retirement party was last Tuesday. We had two very nice talks from people we had taught, and whose careers had perhaps been influenced by our teaching: Mia Tackney, who applies Rosemary’s methods for design of experiments (including Hasse diagrams) … Continue reading →

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Mathematical family

Posted on 08/08/2025 by Peter Cameron

Officially, I retired (or strictly speaking, was made redundant) on 28 February. But I was still teaching and directing a student project until the end of May, as well as fighting against various problems caused by different parts of the … Continue reading →

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When is a group not a group?

Posted on 18/07/2025 by Peter Cameron

Open any algebra textbook, and you will be told that a group consists of a set of elements with a binary function defined on it and satisfying a few axioms. But if you assume that is always the case, you … Continue reading →

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