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# Category Archives: exposition

## Synchronization and all that, 2

The story I told in the last post is not over. The recent development is that we spotted a mistake in the paper. An easy mistake to make: we had simply used the symbol n in two different places with … Continue reading

Posted in doing mathematics, exposition
Tagged association scheme, large sets, ovoid, Philippe Delsarte, quadric, spread, Steiner systems, synchronization, triality
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## EKR, Steiner systems, association schemes, and all that

A great number of mathematical problems amount to looking in a large but highly structured graph, and finding a complete or null subgraph of largest possible size there. For a simple example, consider Latin squares of order n. One of … Continue reading

## p-values, 2

In this sequel, I want to tell a story which perhaps indicates that the philosophical positions of scientists and statisticians have less influence on what really goes on than much more practical things like publication policies of journals. This story … Continue reading

## 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

## Outer automorphisms

I have just put on the arXiv a paper I wrote with Sam Tarzi ten years ago. I want to say here something about the context, the contents of the paper, and the reason for posting it now. Outer automorphisms … Continue reading

## Wiles and Langlands

One of the best things that pops regularly into my pigeonhole is the European Mathematical Society Newsletter. The current issue, number 104, is particularly rich in interesting articles. For example, there is the transcript of a talk by Christian Krattenthaler … Continue reading

Posted in exposition, mathematics and ..., Uncategorized
Tagged Diophantine equations, Galois representations, Langlands, Wiles
2 Comments

## Infinity and Foundation

After the reviving effect of a week’s holiday, I have been thinking about Zermelo–Fraenkel set theory, inspired by a very nice student project I supervised (about which I hope to say something here sometime soonish). I have come across a … Continue reading