Category Archives: doing mathematics

how is it done?

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 →

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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 →

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A counting problem

Posted on 16/03/2018 by

I quite often get questions by email. Mostly I can’t answer them, but sometimes I can, and sometimes the answers might be of more general interest. Suppose that we have m boxes and a supply of identical balls. In how … Continue reading →

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Summer research into print

Posted on 01/03/2018 by

I described here the outcome of a summer research project in 2016 with St Andrews undergraduates Horacio Guerra and Šimon Jurina, on power graphs of torsion-free groups. (It took us a while to write it up, for various reasons.) The … Continue reading →

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