Alex's Adventures in Numberland - Alex Bellos [2]
Entering the world of maths as an adult was very different from entering it as a child, where the requirement work onass exams means that often the really engrossing stuff is passed over. Now I was free to wander down avenues just because they sounded curious and interesting. I learned about ‘ethnomathematics’, the study of how different cultures approach maths, and about how maths was shaped by religion. I became intrigued by recent work in behavioural psychology and neuroscience that is piecing together exactly why and how the brain thinks of numbers.
I realized that I was behaving just like a foreign correspondent on assignment, except the country I was visiting was an abstract one – ‘Numberland’.
My journey soon became geographical, since I wanted to experience mathematics in the real world. So, I flew to India to learn how the country invented ‘zero’, one of the greatest intellectual breakthroughs in human history. I booked myself into a mega-casino in Reno to see probability in action. And in Japan, I met the world’s most numerate chimpanzee.
As my research progressed, I found myself being in the strange position of being both an expert and a non-specialist at the same time. Relearning school maths was like reacquainting myself with old friends, but there were many friends of friends I had never met back then and there are also a lot of new kids on the block. Before I wrote this book, for example, I was unaware that for hundreds of years there have been campaigns to introduce two new numbers to our ten-number system. I didn’t know why Britain was the first nation to mint a heptagonal coin. And I had no idea of the maths behind Sudoku (because it hadn’t been invented).
I was led to unexpected places, such as Braintree, Essex, and Scottsdale, Arizona, and to unexpected shelves on the library. I spent a memorable day reading a book on the history of rituals surrounding plants to understand why Pythagoras was a notoriously fussy eater.
The book starts at Chapter Zero, since I wanted to emphasize that the subject discussed here is pre-mathematics. This chapter is about how numbers emerged. At the beginning of Chapter One numbers have indeed emerged and we can get down to business. Between that point and the end of Chapter Eleven the book covers arithmetic, algebra, geometry, statistics and as many other fields as I could squeeze into 400-ish pages. I have tried to keep the technical material to a minimum, although sometimes there was no way out and I had to spell out equations and proofs. If you feel your brain hurting, skip to the beginning of the next section and it will get easier again. Each chapter is self-contained, meaning that to understand it one does not have to have read the previous chapters. You can read the chapters in any order, although I hope you read them from the first to the last since they follow a rough chronology of ideas and I occasionally refer back to points made earlier. I have aimed the book at the reader with no mathematical knowledge, and it covers material from primary school level to concepts that are taught only at the end of an undergraduate degree.
I have included a fair bit of historical material, since maths is the history of maths. Unlike the humanities, which are in a permanent state of reinvention, as new ideas or fashions replace old ones, and unlike applied science, where theories are undergoing continual refinement, mathematics does not age. The theorems of Pythagoras and Euclid are as valid now as they always were – which is why Pythagoras and Euclid are the oldest names we study at school. The GCSE syllabus contains almost no maths beyond what was already known in the mid seventeenth century, and likewise A-level with the mid eighteenth century. (In my degree the most