Alex Bellos on Maths

Your first choice is in Portuguese.

A fascinating property of maths is that it is totally international and never goes out of date. So if you write a maths classic it is a classic for ever, everywhere. This Brazilian book links my past life in Brazil with maths. The literal translation of the Portuguese title is ‘The Man Who Calculated’ but the English version is called The Man Who Counted. There are editions in many other languages too.

The author Malba Tahan is a fictional character, the pen name of Júlio César de Mello e Sousa, and the book is set in Arabia as a mixture of One Thousand and One Nights and a maths book – it’s coming out of the most populous Catholic country in the world and yet it’s as much a love story to Arab culture as to maths itself. There were lots of Arab immigrants in Brazil and they love Arab culture – one of the most popular fast food chains is called Habib’s. The story here is presented as if the author, whom I believe only went to Lisbon once and virtually never left Brazil, has just stumbled upon or discovered this Arab text.

A bit like the Rubaiyat of Omar Khayyam?

Exactly. It is composed of lovely little stories and, with each chapter of a few pages, it introduces a mathematical idea along with a story about travelling through the Arab world. For example, one chapter shows you how to make every number between one and ten just using four fours because the narrator meets someone who shows him this trick.

This is also a brilliant piece of international cultural history because Brazil is a country in which very few people read books, in which everyone is obsessed with sport. Yet when this book came out in the 1950s, Malba Tahan, which is a pen name, became as famous as any of the footballers. He was huge. So in Brazil when I told friends, ‘I’m now working on maths,’ they all said, ‘Oh, you must read Malba Tahan.’ And friends who were kids during that era said, ‘Oh, I remember my parents reading it to me’ – it’s almost like Alice in Wonderland in that it is one of the things that makes people feel nostalgic about their childhood. My Brazilian copy is the 74th edition.

It’s easy and it’s fun but any adult would love it. An international classic.

Your other choices are not fictional though.

My next book is by Georges Ifrah, who you could say is the real ‘man who counted’. The French have what is probably the best tradition of popular maths in the world: they love their science, their maths, their engineering and philosophy. And from 1650 to 1850 probably the largest percentage of the great mathematicians were French: Pascal, Fermat, Laplace, Lagrange and the rest.

Ifrah was a schoolteacher who kept being asked by his pupils, ‘Where do numbers come from?’ He began to research it and – weirdly – it turned out no one had bothered to ask this question in the same way. He’s not an academic, nor is he a writer: he’s a massively obsessed schoolteacher on a mission. So the book is a bit sprawling and doesn’t have much of a narrative but it is absolutely incredible. He goes through each culture and describes why they thought of numbers and how they counted. So we have it explained here exactly how the Maya counted, the Sumerians, Hebrews, exactly how the ancient Chinese counted, all different types of tally systems, hand systems, how the abacus works.

Then halfway through it changes and becomes largely about India because Ifrah realises that our own number system really originated in India. Our number system being what we call Arabic numerals and which are really Indian numerals. What you realise from reading The Universal History of Numbers is that everything before India is just a curiosity really.

The three things that define our number system are: only ten digits, zero to nine; a place value system, which isn’t true of Roman numerals; and the use of zero, because with a zero it enables easy multiplication and it then becomes feasible for the lay person to calculate, which wasn’t really possible with Roman numerals.

So the book then becomes an encyclopaedia of all things Indian – a bit eccentric, but so full of information that when I was writing my book this was on my desk at all times to refer to. It’s the bible of counting and where numbers came from.

It’s an enormous, rectangular format.

Well worth having in among any other awkwardly shaped books you might have. Ifrah has never really done anything since, and he’s described here as ‘an independent scholar’ who was ‘the despair of his own maths teacher’. He funded his research around the world on the ten-year project by doing jobs as a waiter and taxi driver.

Your next choice looks less unusual, although it’s an unusual subject, zero.

Unlike Ifrah, Charles Seife is a brilliant popular science writer who has here has written the ‘biography’ of zero. And even though he doesn’t talk that much about India, it works well as a handbook to Ifrah’s sections on India. Because Seife talks about how zero is mathematically very close to the idea of infinity, which is another mathematical idea that the Indians thought about differently. Seife gives you the context and it explains why, really, without zero, you can’t do anything. The difficulty of understanding zero is similar to the difficulty of understanding infinity.