Without numbers, modern civilization would not exist. But until now, no one has explained where numbers exist in the mind, how they got there, or how we use them. In What Counts, Brian Butterworth combines his unique expertise in cognitive neuroscience with his broad knowledge of mathematics to offer a completely original picture of how our brains do math.
Butterworth’s pioneering research into the behavior and genetics of mathematical ability has led him to discover that we all possess a fundamental number sense which he calls “numerosity.” This inherent ability is even more basic to human nature than languages. Numbers do not exist inside our heads the way words do; they are a separate kind of intelligence with their own brain module. This module, located in in the left parietal lobe, is where math happens.
We all know that some of us are good at math and some of us are not. But, as Butterworth shows, the reason a person falters at math is usually not because of the wrong gene or “engine part” in the left parietal lobe, but because he or she has not fully developed the sense we are all born with. The left parietal lobe is also where fingers are registered in our brain – a fact that Butterworth demonstrates is an important clue to the evolution of our sense of numerosity – and, interestingly, it’s the reason we count on our fingers. The nonlinguistic nature of math explains why cultures that have no words for numbers have still managed to develop market economies throughout history with all the counting that buying and selling require. Butterworth argues that counting is so basic a facet of our biology that, with practice, most people could become mathematical prodigies.
Butterworth illustrates his cognitive model of math with enlightening examples from the history of mathematics and its many anomalies. He shows us the numerical world of the Neanderthals, Cro-Magnons, and Stone Age peoples. He recounts the case of the Italian woman who suffered a stroke that left her unable to count beyond four, as well as the extraordinary story of zero. He describes how the great math prodigy Ramanujan emerged from a childhood of poverty and astonished the world with his brilliance. He presents surprising research demonstrating that infants can add and subtract even when they are only a few weeks old, and that people afflicted with Alzheimer’s have unexpected numerical abilities.
The implications of Butterworth’s advances and fundamental concepts of mathematical thinking are profound – for our understanding of how minds work, how we can lead our children into a deeper understanding of mathematics, and even how formal education could be better structured on the basis of what counting really is. What Counts is the first book to provide a complete picture of how and why our mathematical brain evolved and what this new knowledge means in our everyday lives. No one who reads it will ever think about math in the same way again.
Brian Butterworth is Professor of Cognitive Neuropsychology in the Institute of Cognitive Neuroscience at University College in London. In 1993 he launched the scientific journal Mathematical Cognition, which publishes studies on the psychology and neuropsychology of numbers. He lives in London.