How many colours in a rainbow? More than 100:  Think Like A Mathematician by Junaid Mubeen

Doing jigsaws with Junaid Mubeen doesn’t sound like much fun. Mubeen insists on sorting the pieces according to three characteristics: colour, number of tabs (pointy bits) and size.

He uses three trays – one for each size – and creates grids on them, with each row representing a colour and each column a number. His brother-in-law, with whom he does jigsaws, prefers to just fish pieces out of a messy jumble.

Mubeen is a mathematician. He believes that understanding mathematical concepts will help us think more clearly about everyday issues. And he’s not just talking about ‘applied’ maths that helps us construct bridges or check our bank statements. He means ‘pure’ maths, which is more abstract and usually has no obvious utility.

‘Pure mathematicians often take pride in the apparent uselessness of their work, even deriding the supposed need for their subject to bring practical benefits,’ Mubeen writes. ‘“Here’s to pure mathematics”, starts one toast, “may it never be of use to anyone.”’

Across ten chapters he covers topics such as ‘dimensionality’, ‘sets’, ‘axioms’ and ‘fractals’. He’s good at leading readers through unfamiliar concepts and most of it is pretty interesting stuff.

For example, everyone knows that the rainbow has seven colours, right? At school, we all learned ‘Red, orange, yellow, green, blue, indigo, violet’. But that number is arbitrary. In his chapter on ‘the continuum’, Mubeen points out that: ‘Those colours represent specific wavelengths (in increasing order) but we could just as well reference ten colours, or a hundred, or indeed any number between the two extremes of red and violet. Isaac Newton, whose experiments led to the discovery of the visible light spectrum, attached mystical significance to the number seven, which is probably why he settled on that many markers.’

This leads into a discussion about numbers that can’t be accurately expressed as fractions – irrational numbers, such as pi – and then to a description of ‘calculus’ and, for the first time, I, a non-mathematician, felt as though I understood what the latter is.

But his efforts to show how this knowledge can map on to everyday issues are less successful. The jigsaw story comes in the chapter on ‘dimensionality’, in which he attempts to relate the mathematical concept of spaces with many more dimensions than three to the notion that there are lots of different types of intelligence. An understanding of multi-dimensional spaces doesn’t add much to the idea that intelligence is a complex attribute.

Elsewhere he writes that just as the limitations of our senses mean our perception of the world is a distortion of the reality, so the sort of mathematical concepts with which we are most familiar do not truly reflect the subject. Then he compares that with the way we provide only a selective view of our lives on social media.

The analogy is reasonable but we don’t need an understanding of complex mathematical ideas to get the measure of Instagram.

I think I might be with those who celebrate pure mathematics for its lack of applications.