Math is hard-counting is instinctive Just read The Number Sense by Stanislas Dehaene. A mathematician turned neuroscientist, Dehaene does a good job trying to be the Steven Pinker of mathematics in this book. His second book, just published this May, The Cognitive Neuroscience of Consciousness, seems broader in scope. I haven't read it, but I'll probably get to it at some point since I enjoyed this The Number Sense so much. In any case, The Number Sense is a fast engaging read and I highly recommend it to those with an interest in evolution, math and psychology (in no particular order). You get a sense you're on the cutting edge (the book was published in 1997 so a lot might have changed in a speciality like neuroscience)-the author sketches out controversies in his field just to make sure that you don't only get his perspective-though Dehaene gives the impression that he is in the mainstream. The Number Sense is reminiscent of The Language Instinct by Steven Pinker or Genome by Matt Ridley in both style and substance. Dehaene uses compelling details to launch into an exploration of the deeper issues at hand. Only in the last few chapters when the author skirts the biological and philosophical issues underlying neuroscience and veers away from the psychology of math does the book drag a bit. I believe this is because Dehaene's format of short compact chapters (about 30 pages each) simply does not serve a field as multidisciplinary as neuroscience very well. But at 250 pages of content, this book is worth an afternoon set aside-especially the first 200. Dehaene's book reinforced my perception of human mathematical capacities. Evolution has equipped us with a general suite of computational abilities, but we have gone so far beyond it to the point where our symbolic logic is simply too abstract for most (all?) human beings to conceptualize in any concrete fashion. Counting is not difficult, infants and children can instinctively understand the difference between one and three, or that three is more than one. Dehaene makes quite clear that a simple numerical processing system resides in our brains and is manifest from birth. On the other hand, babies have a more difficult time with precision and exactness, something one would not expect if they were processing numbers digitally. Like the abilities of animals human number sense is clearly fuzzy (analog). But this simple number sense serves as the foundation upon which we build the edifice of our complex mathematical systems. As the book proceeds it was obvious to me that Dehaene is strongly influenced by the evolutionary psychology of the school of Cosmides and Tooby. For instance, he asserts that the first three numbers, 1, 2 and 3 have universal significance to humans, universals being a key calling-card of politically correct evolutionary psychologists. These initial digits tend to have special distinctive characteristics (they look similar in most scripts, as in Roman numerals I, II and III or Arabic numerals 1, 2 and 3 that are actually cursive forms of horizontal lines) and even the most "primitive" of cultures have specific terms for them. Coincidentally (or not) these three numbers are the ones that young humans are most able to process in terms of differentiating without any error (the reaction time for recognition is very short). This is part of our common human heritage. And yet early on the author seems concerned about excessive emphasis on genetic determinism-wary of it leading toward the dangerous pseudo-science of the past (he uses phrenology as a cautionary tale and comes back to this example several times). Dehaene makes clear in his introduction that he does not believe that geniuses are "born," rather they have a passion for math which drives them to cultivate their abilities. More on this later. But Dehaene can not deny genetic factors absolutely and like most evolutionary psychologists of the Cosmides-Tooby school he will admit male/female differences. He is rather equivocal, and still wonders aloud whether differences might be due to cultural conditioning and implies that there is a conspiracy to keep them out of highly numerative fields like engineering. But Dehaene gives enough space to the overwhelming cross-cultural predominance of males at the highest levels of math that he feels he must posit some tentative explanation-mostly having to do with testosterone and its effect on fetal development. Once he has conceded some ground, it seems that Dehaene tries to constantly bat down any further implication of genetic determinism. Dehaene is the type that would never admit that there might group (racial) differences in mathematical abilities. He has a hard enough time admitting that some people might just naturally be better at math. Dehaene frames the debate so that environmental factors seem to be the default explanation. He presents some twin data that indicates that 50% of mathematical ability is genetic, but undermines it by wondering if common schooling might not be responsible for this (he obviously is not presenting data from twins separated at birth). The author repeatedly implies and even asserts that it is the passion for math that is the prime factor in creating genius, detailing the methods that human calculators use to achieve their amazing feats-all of which are learned rather than hard-wired. When it seems that genetic predispositions are too strong to ignore the author will bring to the fore a whole host of other reasons and declare that there are too many chicken and egg issues to resolve anything. I agree, there are multiple factors. Genes are most certainly one of them. And so is the environment. And the key is that they are intertwined and it is likely that certain genes will lead to a child seeking out a certain environment, and positive reenforcement will allow the blossoming of natural talent. This in particular applies to the "passion" factor. How do you account for passion? Dehaene does not say much about where the passion for math comes from. He seems to assume that we will assume it comes from the society or parents. And yet my personal experience with mathematically precocious children is that even if the parents are mathematicians themselves, they do not push the child into their field so much as create a role model and a conducive environment for them to pursue their natural inclinations. What I am suggesting is that there is almost certainly some sort of Lynn-Flynn Effect going on in math. This does not deny that there is a genetic predisposition to math though, it simply adds nuance to any attempt at crass determinism. Fertile soil still needs the seed. In addition I have also known many that loved math that all of a sudden encountered a ceiling to their brilliance. A student that enters college with good math SAT scores might stumble through multi-variable calculus while her friends (math majors obviously) all do fine. Similarly, another student might encounter a block in his first year graduate school seminars and switch to physics or chemistry. This sort of thing occurs in other fields, I've seen plenty of chemistry students drop out at physical chemistry, and some in organic. But this "ceiling" effect seems stronger in math than any other discipline. Why is math so difficult even for those who wish to excel in it? Dehaene makes a good case that there is no one "math module," but rather mathematical ability is the result of complex interactions between different sectors of our brain-some that specialize in mathematical processing and others that are generalized for verbal tasks. I suspect that different areas of math require cooperation in varied forms between the different regions and "ceilings" occur when a felicitous combination can not be found. For example Dehaene indicates that basic computation, addition, subtraction and multiplication (not just simple number recognition alluded to earlier) are processed separately from algebraic problems (he uses the example of a chemist who had had a brain injury and couldn't add or subtract but still could do algebra with letter variables). Dehaene mentions autistic geniuses, but doesn't note that there is some correlation of mathematical proficiency and Asperger's Syndrome, a form of autism that is genetically inherited. The areas of the brain that allow visual-spatial and mathematical virtuosity in these individuals do not seem to suffer from the lack of social ability or possible verbal shortcomings of suffer's from this form of autism. A genius requires many factors to develop no doubt. Family, culture, chance and yes, genes. None of these are exclusive, nor they do not inhabit separate discrete spheres. It seems reasonable to assert that if one's parents are mathematicians, one is more likely to become one for both environmental and genetic reasons. I also think it reasonable that if one is adopted by novelists and one's biological parents were mathematicians-one is more likely to become a mathematician than if one's biological parents were field workers. To be a great mathematician, there are both genetic and environmental prerequisites . On one point I totally agree with Dehaene-children should not be molded by the preconceptions of adults on how they should learn math. Just as I believe children will learn language without being taught grammar by adults, they should learn math through basic examples rather than formal axioms. Dehaene recounts with horror the French government's experiments with the instruction of elementary school students of math through axioms and proofs. The problem is that children are not a blank slate-they have an intuitive understanding of "1" or "3" (they go for twice the number of M&M's every time!). Teaching them math from the ground up is like teaching children language from the ground up-you simply confuse them with abstractions when the basics are pre-programmed into their brain (I can recognize grammatical mistakes, but couldn't tell you much about adverbs or prepositions). Granted, higher levels of math do require an understanding of proofs and axioms, but most students will never get beyond algebra and trigonometry. Lastly, I found it interesting that Dehaene indicates that Asian children (in particular Chinese) have an easier time with basic math because the names for their numbers are smaller! It seems that the human brain has a specific number of sounds it can easily store in the brain before it drips out of the memory bucket. English and other European languages have rather long names for basic numbers compared to Chinese. So while American children can store seven numbers in random sequence in their brains, Chinese children can store ten! The differences between the languages are deeper than this, but you can read the book to find out how-it makes me wonder a bit whether Asians really do have greater mathematical abilities than Europeans (I don't know whether the names for numbers are very long in African languages of course, and Dehaene would never touch such a subject). Let me leave you with an amusing test from the book: Answer the following questions as fast as you can: -2+2 -4+4 -8+8 -16+16 Now quick! Pick a number between 12 and 5 Click here to find out what you should have picked