A *norm* is a general notion of distance that applies to vectors (most people have typically met vectors in two or three dimensions at school, for instance during GCSE maths). Several areas of mathematics arise out of the idea of a norm, such as *Banach spaces* and *Banach algebras*, the two areas I used to research as a PhD student and PostDoc.

Though mathematicians are stereotypically seen as bad communicators, it isn’t universally true. While mathematicians may on average be more socially awkward than, say, hairdressers, as in any walk of life there’s plenty of extroverts. It’s not even true of those at the top of the subject. Continue reading