|How The Mind Creates Mathematics|
We are surrounded by numbers. Etched on credit cards or engraved on coins, printed on pay checks or aligned on computerized spread sheets, numbers rule our lives. Indeed, they lie at the heart of our technology. Without numbers, we could not send rockets roaming the solar system, nor could we build bridges, exchange goods, or pay our bills. In some sense, then, numbers are cultural inventions only comparable in importance to agriculture or to the wheel. But they might have even deeper roots. Thousands of years before Christ, Babylonian scientists used clever numerical notations to compute astronomical tables of amazing accuracy. Tens of thousands of years prior to them, Neolithic men recorded the first written numerals by engraving bones or by painting dots on cave walls. And as I shall try to convince you later on, millions of years earlier still, long before the dawn of humankind, animals of all species were already registering numbers and entering them into simple mental computations. Might numbers, then be almost as old as life itself? Might they be engraved in the very architecture of our brains? Do we all possess a "number sense," a special intuition that helps us make sense of numbers and mathematics?
Fifteen years ago, as I was training to become a mathematician, I became fascinated by the abstract objects I was taught to manipulate, and above all, by the simplest of them- numbers. Where did they come from? How was it possible for my brain to understand them? Why did it seem so difficult for most people to master them? Historians of science and philosophers of mathematics had provided some tentative answers, but to a scientifically oriented mind their speculative and contingent character was unsatisfactory. Furthermore, scores of intriguing facts about numbers and mathematics were left unanswered in the books I knew of Why did all languages have at least some number names? Why did everybody seem to find multiplications by seven, eight, or nine particularly hard to learn? Why couldn't I seem to recognize more than four objects at a glance? Why were there ten boys for one girl in the high-level mathematics classes I was attending? What tricks allowed lightning calculators to multiply two three-digit numbers in a few seconds?
As I learned increasingly more about psychology, neurophysiology, and computer science, it became obvious that the answers had to be looked for, not in history books, but in the very structure of our brains-the organ that enables us to create mathematics. It was an exciting time for a mathematician to turn to cognitive neuroscience. New experimental techniques and amazing results seemed to appear every month. Some revealed that animals could do simple arithmetic. Others asked whether babies had any notion of 1 plus 1. Functional imaging tools were also becoming available that could visualize the active circuits of the human brain as it calculates and solves arithmetical problems. Suddenly, the psychological and cerebral bases of our number sense were open to experimentation. A new field of science was emerging: mathematical cognition, or the scientific inquiry into how the human brain gives rise to mathematics. I was lucky enough to become an active participant in this quest. This book provides a first glance at this new field of research that my colleagues in Paris and several research teams throughout the world are still busy developing.
Copyright © 1996-2017 Alexander Bogomolny