Category Archives: doing mathematics

how is it done?

The geometry of diagonal groups

Posted on 18/04/2020 by

This is an interim report on ongoing work with Rosemary Bailey, Cheryl Praeger and Csaba Schneider. We have reached a point where we have a nice theorem, even though there is still a lot more to do before the project … Continue reading →

Posted in doing mathematics, exposition | Tagged , , | 3 Comments

More on derangements

Posted on 04/04/2020 by

Francis Bacon, in The New Organon, developed a famous metaphor: Those who have handled sciences have been either men of experiment or men of dogmas. The men of experiment are like the ant, they only collect and use; the reasoners … Continue reading →

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Au revoir, GRA

Posted on 18/03/2020 by

Today (Wednesday 18 March) the Groups, Representations and Applicatons programme at the Isaac Newton Institute came to a premature end. There are still some hopes that it can be revived later, but at the moment the only certainty is that … Continue reading →

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Research trips in February

Posted on 13/03/2020 by

I don’t know how things have got so busy. I had two interesting trips in February; I worked hard, and some interesting mathematics resulted; but I don’t seem to have found the time to describe it. So here goes. This … Continue reading →

Posted in doing mathematics, exposition, geography | Tagged , , , , , | 3 Comments

Aliens Do Exist

Posted on 24/07/2019 by

The people from the planet Ade have intercepted radio transmissions from Earth, and have discovered that we know about the Petersen graph and the root system E6. One day, a flying saucer from Ade arrives on Earth and delivers an … Continue reading →

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The Hall–Paige conjecture

Posted on 18/12/2018 by

A Latin square of ordern is an n×n array of symbols from an alphabet of size n with the property that each symbol in the alphabet occurs once in each row or column. Two Latin squares L and M are … Continue reading →

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Kourovka Notebook, 19th edition

Posted on 22/04/2018 by

The latest edition (the 19th) of the Kourovka Notebook has just been released. It now has its own website, https://kourovka-notebook.org/. The Kourovka Notebook has been going for more than 50 years, longer than my life as a mathematician. It is … Continue reading →

Posted in doing mathematics, history, open problems | Tagged , , | 1 Comment

Mathematical collaboration

Posted on 08/04/2018 by

I have just spent an entire weekend at a workshop on mathematical collaboration. It blew a huge hole in the time that I had to get on with urgent work that needs to be done, but it was such a … Continue reading →

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Another Cameron–Erdős problem solved

Posted on 28/03/2018 by

In 1990, Paul Erdős and I published a paper on the topic of counting subsets of the first n natural numbers satisfying some restriction. The case we worked hardest on, and which attracted the most interest (it has its own … Continue reading →

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Integrals of groups

Posted on 28/03/2018 by

Everyone who has studied mathematics knows what the derivative and integral of a function are. The derivative measures rate of change, the integral (the inverse operation) measures area under a curve. They are inverse operations; and two functions have the … Continue reading →

Posted in doing mathematics, exposition | Tagged , , , | 2 Comments