MATH WITHOUT NUMBERS

MILO BECKMAN

Allen Lane, 205pp, £20

Milo Beckman, a maths prodigy who went to Harvard at 15, offers a calculation-free guide ‘through the sort of fascinating mathematics we didn’t get taught at school’, according to Manjit Kumar in the

Times. Beckman shows how many of our intuitions – what a shape might be, or what might be more than infinity – are either wrong, or under-considered: ‘mathematicians tend to overthink things that the rest of us take for granted’. And here he explains this thinking with imaginative and intuitive examples that won’t require the reader to reach for a calculator.

‘For instance, how many shapes are there? “Lots” simply won’t cut the mathematical mustard for Beckman [...] Starting with the simplest shape, a line, Beckman introduces the concept of mathematical proof as he elegantly proves, in less than half a page, that there is an infinite number of shapes using only words and a simple drawing.’

Likewise, Beckman explains the concept of infinity – or different infinities – by imagining a hotel with an infinite number of rooms along a corridor; and doesn’t forget to include ‘light relief from some mind-blowing maths’ by including ‘fun factoids such as six circles fit around any circle of the same size; that one cannot cross every bridge in Old Konigsberg without crossing a bridge twice.’

Ranging into the extreme abstraction of high-level algebra, Beckman shows us how ‘Some things are just provably unprovable’ – the sort of result, says Kumar, that led even Einstein to marvel: ‘The eternal mystery of the world is its comprehensibility.’

Kirkus shared Kumar’s admiration for the project, saying that in this ‘pleasant, amusing look at mathematics’ Beckman maintains that ‘everything –“plants, love, music, everything” – can be understood in terms of math and proceeds to explain how mathematicians try.’