Julian Havil on surprises in maths, 20 October 2016; and Vicky Neale on number theory, 3 October 2016


Julian Havil ran a session about how maths produces surprises at CoLA on 20 October 2016. We also welcomed students and teachers from CoLA Hackney.

A central thing about maths, but one that it’s often hard to pick up from school maths, is that it enables us to prove that things that seemed more or less impossible are true, and that other things that seemed obviously true are in fact false.

Julian Havil was a maths teacher at Winchester College and retired early to write books. There are many excellent books published recently about maths: what is different and unusual about Julian Havil’s books is that they are, as one reviewer put it, books of maths, but written so as to be accessible to readers with only school-maths knowledge.

Julian’s session covered Benford’s Law and the Simpson Paradox
(see also here.)


Vicky Neale from Oxford University (above) ran a session on number theory on 3 OƧtober. Although maths at school is mostly about calculations with numbers, in the real world most of maths is about concepts rather than calculations, and a lot of time doesn’t use numbers very much.

“Number theory” is the branch of maths to do with the patterns and structures in the arithmetic of the whole numbers, 0, 1, 2, 3, and so on. These days it has huge practical applications, in encryption for example. Every time you use an ATM, the technology to keep your transaction secure depends on number theory.

Vicky’s lecture covered ground similar to her talk on “Seven Things You Need To Know About Prime Numbers, and then she ran an interactive session on which numbers can be written as the sum of two squares (maybe including 02) (1 can, 2 can, 3 can’t, 5 can, 6 can’t, 7 can’t, 8 can, 9 can, 10 can… how does the pattern continue?)