Development of the human species' mathematical ability

PLoS biology has an incredible interesting article up on the study of the Evolutionary and Developmental Foundations of Mathematics by Michael J. Beran.

Understanding the evolutionary precursors of human mathematical ability is a highly active area of research in psychology and biology with a rich and interesting history. At one time, numerical abilities, like language, tool use, and culture, were thought to be uniquely human. However, at the turn of the 20th century, scientists showed more interest in the numerical abilities of animals. The earliest research was focused on whether animals could count in any way that approximated the counting skills of humans [1,2], though many early studies lacked the necessary scientific controls to truly prove numerical abilities in animals. In addition, both the public and many in the scientific community too readily accepted cases of “genius” animals, including those that performed amazing mathematical feats. One such animal still lends its name to the phenomenon of inadvertent cuing of animals by humans: Clever Hans. Hans was a horse that seemed to calculate solutions to all types of numerical problems. In reality, the horse was highly attuned to the subtle and inadvertent bodily movements that people would make when Hans had reached the correct answer (by tapping his hoof) and should have stopped responding [3]. One consequence of this embarrassing realization was a backlash for the better part of the 20th century against the idea that animals could grasp numerical concepts. The second, more positive consequence, however, was that future researchers would include appropriate controls to account for such cues.

Beran goes on to explain how the current research shows that animals operate on approximations, rather than concrete numbers, much the same way that humans do when prevented from counting while comparing two sets of items. What's more interesting, in my opinion, is how much our symbolic representation of numbers actually mean for our math ability. Not only on the grand scale, but also on smaller problems.

Human mathematical abilities, of course, are highly dependent on symbolic representations of number. A recent paper by Diester and Nieder published in PLoS Biology shows that brain areas critical to processing symbolic and analogue numerosities in humans also support numerical processing in monkeys [38]. After monkeys learned to associate Arabic numerals with specific numbers of items, the researchers recorded from single neurons in the PFC and IPS when monkeys judged whether two successive analog arrays were the same in number or whether an analog array matched a numeral in a pairing. PFC neurons were selectively responsive to given numerical values, presented in either analog or symbolic formats. In other words, the PFC in monkeys seems to be involved in the association between symbols and numerical concepts, and it builds upon the capacities of the IPS to encode approximate numerical information early in quantity processing. By four years of age, the IPS in human children is already responsive to changes in the numerosity of visual arrays [39], but the parietal cortex shows a more protracted developmental trajectory for the representation of symbolic numbers. Specifically, children who have not yet become proficient with numerals show elevated PFC activity in response to numerals, whereas parietal areas seemingly take over as proficiency with symbols emerges [40,41]. In adult humans, representation of numerical information across many formats (numerals, analog stimuli, number words) relies substantially on parietal areas [42].

So while our brains are hardwired to math, we can only utilize it fully when using symbolic representations.