Is mathematics an emergent property of sociality? I posed this intriguing question to a mathematician colleague, who is also an evolutionary biologist, and he said yes. The question came up because I have argued that rules are actually a social construct; a solitary species needs few or no rules governing its interactions with other individuals of its species, because other than mating or occasional territorial conflict, it has almost none. Individuals in social species, by contrast, are completely dependent on rules to survive and reproduce, because interactions with other members of the species are constant, and determine standing within a social group, and thus generally reproductive success.
Most evolutionary arguments applied to humans are tenuous, because of cultural complexities that overly our basic biology. Complicating the picture further, aberrant behavior (that which does not comply to a given social norm) is also probably more common among humans than among other social animals, because 1) we have chemical treatments that suppress some symptoms of such conditions, 2) we have easy access to addictive products which our brains did not evolve to cope with, such as drugs, junk food, slot machines, etc., and use of these can lead to self-destructive behavior, and 3) many aberrant people are smart enough to overcome or disguise their problems enough to fit in somewhat. So, there are many ways in which humans seem to get away with behaving in socially maladaptive ways, without suffering reproductive consequences, as other social primates probably would.
However, we did evolve as a social species, and much of our behavior is indeed a legacy of that evolutionary history. The playing of games is an example. Games are all about rules. Kids love learning new games, because their brains are wired to learn rules — particularly rules for navigating in real society, but an artificial society with artificial rules will do. Whether it is sports or war games or pin-the-tail-on-the-donkey, humans love games. Games with complex rules are more fun to learn for many of us, but those with fairly simple rules but complex strategy, such as Go or hearts or chess, usually capture the most active minds. It is our love of rules that make us despise the referee who makes a bad call. In our minds, if a rule is broken, the entire game should be void.
It seems that mathematics is universal, a truth that existed before humans and that they discovered. But to humans at least, mathematics is also all about rules, and perhaps the way that we perceive mathematics is filtered through our obsession with rules. We all learned them at the beginning of every school year for a decade. “Addition and multiplication are commutative. The transitive property says that if a=b and b=c, then a=c. The distributive property says that a * (b + c) = a * b + a * c” and so on. If you take higher level math classes in college, you discover that there are other mathematical systems with different rules; for instance, matrix multiplication is not commutative. So math is indeed a world of many rules that apply one way in one context but another way in a different context, very much like the rules of social interactions — for example, it is inappropriate to wear a bikini at the opera, but just fine at the beach.
Although many would protest the truth of the statement, humans are wired for math. (If you hate math, it is not that you are “no good” at it; it is because the way it was taught to you made it painful and boring. This is a persistent problem that will likely never be corrected on a large scale, because of the vicious cycle of elementary school teachers who dislike math and barely get through it in college, go on to teach it poorly, cause their students to dislike it, and so on.) The interesting question is, would, or could, an intelligent solitary species have developed math? Some would say the question is completely moot because only a social species would have evolved brains as large as ours, because sociality requires a larger brain to navigate the intricacies of social interactions, in addition to the basic needs of finding food and mates and defending oneself. It is perhaps a chicken-and-egg question. But what is no question is that complex rules govern sociality, human brains are therefore wired to learn and use rules, and mathematics is a system of rules. Mathematics, very much like religion, is likely a byproduct of our success as a social species.