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# Category Archives: doing mathematics

## The random graph and anti-foundation

Last year, Bea Adam-Day, one of my undergraduate project students, settled a question that had been bugging me for years. According to the downward Löwenheim–Skolem Theorem of first-order logic (a consequence of the proof of Gödel’s Completeness Theorem), if a … Continue reading

Posted in doing mathematics, exposition
Tagged Anti-foundation Axiom, Bea Adam-Day, random loopy graph, ZFA
3 Comments

## Mathematical diversity

Don’t worry, this post is not about factors irrelevant to mathematics such as gender, ethnicity and sexual orientation. Nor is it about important factors, highlighted in the 2011 International Review of UK Mathematics although largely ignored by the research council … Continue reading

## Automorphism groups of transformation semigroups

I have been in the transformation semigroups game for nearly ten years now, but I still feel that I am finding my feet. Here is apparently a huge difference between permutation groups and transformation semigroups, one which is still not … Continue reading

Posted in doing mathematics, open problems, Uncategorized
Tagged automorphism, primitive groups, synchronization
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## Prospects in Mathematics, 2

I didn’t say anything about my own talk at the Prospects in Mathematics meeting. But soon afterwards I was re-reading Lee Smolin’s 2006 book The Trouble with Physics, and it resonated with some of the things I said. My topic … Continue reading

Posted in doing mathematics, events
Tagged CFSG, Classification of Finite Simple Groups, Lee Smolin, string theory
7 Comments

## Perth, week 1

The first week of the visit is over. The weather has been quite cold, but it is likely to improve as time goes on. The best day so far was yesterday, when we went to Yanchep National Park and had … Continue reading

Posted in doing mathematics, exposition
Tagged derangements, H. Zantema, Jordan's theorem
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## More groups

The title reminds me of the occasion when my academic grandfather lectured to the London Mathematical Society on “Moore graphs”. Unfortunately, someone got it wrong, and his lecture was billed as “More graphs”. But here I really do mean what … Continue reading

## 12160

12160 is an interesting number; but I didn’t know that until last night. As part of the work on semigroups, we are looking at the following problem. Given n and k, with n ≥ 2k, suppose that G is a k-homogeneous subgroup … Continue reading

Posted in doing mathematics, exposition
Tagged 4-homogeneous, permutation groups, semigroups
3 Comments