Numerous studies have been done trying to assess the degree to which mathematical ability is inborn or learned. Especially since the era of brain imaging made neurological enquiry realistic.

For example, in a 2011 study, Melissa Libertus, a psychologist at Johns Hopkins University, displayed briefly flashing groups of blue and yellow dots on a computer screen to 200 four-year-old children. The children had to estimate which group of dots was larger (in number). They also were given a standard test of early mathematical ability that measures numbering skills (counting items on a page), numeral literacy (reading numbers), and elementary calculation skills. These researches found that the precision of their estimations of the relative numbers of blue and yellow dots correlated quite strongly with the other measures of budding mathematical ability.

But such studies still beg the question as to what degree humans have an hard-wired sense of number, and where in the brain such facility is located. Now a recent study may reveal some answers.

In a 2013 Science article, researchers from Utrecht University in the Netherlands have identified a small area in the brain which represents numbers along a continuous “map” of sorts. In other words, our visualization of numbers along a mental number line may have a physical representation in the brain.

This research was done by wiring some test participants with functional magnetic resonance imaging, then analyzing the signals as participants viewed different numbers of items on a computer screen. From these tests, the scientists identified a small region (a few centimeters in size) that appears to be the site of numeration. Indeed, one side of this region of the brain shows activity for small numbers, its adjacent region shows activity for moderate-sized numbers, and larger numbers score on the other end.

The response of the individuals was not identical — the number map represented relative quantities, but the specific values at specific points varied from participant to participant. Also, the responses were only seen when different numbers of dots were shown; digits on the screen did not elicit the same response.

The researchers note that their results are restricted to number representation, not more abstract mathematical skills. At least one previous study, for instance, showed that arithmetic functions are language-dependent, and activate different regions of the brain. Nonetheless, this finding raises the possibility that the brain contains maps for other types of basic information.

This is all generally consistent with the work of Stanislas Dehaene on *number sense*, with that of Nobel economist Daniel Kahneman on *exact and approximate reasoning*, and indeed with the work of Lakoff and Nunez on *embodied cognition* in Mathematics. Lakoff and Nunez, for instance, found that human arithmetic can be see as a combination of metaphorical operations (e.g., object collection, using a measuring stick, etc.).

Along this line, in November 2013 neuroscientists at the University of California, Irvine found that the brain has not one, but two different internal clocks that sense elapsed time. Other studies have also illuminated the mechanisms and physical locations of how the brain processes memories.

For additional details, see the very nice Scientific American article summarizing these results by Emilie Reas.