The origins and organization of numerical information in the mind and brain

Thirty-thousand years ago, humans kept track of numerical quantities by carving slashes on fragments of bone. It took approximately twenty-five thousand years for the first iconic written numerals to emerge among human cultures (e.g., Sumerian cuneiform). Now, children acquire the meanings of verbal counting words, Arabic numerals, written number words, and the procedures of basic arithmetic operations such as addition and subtraction in just six years (between ages 2 and 8). What cognitive abilities enabled our ancestors to record tallies in the first place? And, what cognitive abilities allow children to rapidly acquire the formal mathematics knowledge that took our ancestors many millennia to invent? Our research aims to discover the origins and organization of numerical information in humans using clues from child development, the organization of the human brain, and animal cognition.

This essay traces the origins of numerical processing from "primitive" numerical abilities to math IQ. Pre-verbal children and non-human animals possess the ability to appreciate quantities, such as the approximate number of objects in a set, without counting them verbally. Instead of counting, children and animals can mentally represent quantities approximately in an analog format, akin to the way in which a machine represents intensities in currents or voltages (1). We have shown that humans and non-human primates share cognitive algorithms for encoding numerical values as analogs, comparing numerical values, and arithmetic. Further, my colleagues and I have shown that the brain regions recruited to perform these tasks are also shared by adult humans, non-human primates, and 4-year-old children who cannot yet count to 30. Recently, we have found that neural regions involved in analog numerical processing are important for the development of math IQ (and not verbal IQ). Taken together, the data implicate a degree of continuity in numerical abilities ranging from primitive approximation to complex and sophisticated math.

Although there is general agreement that nonsymbolic, analog numerical estimation is a cognitive antecedent of formal (symbolic) mathematical knowledge, there is considerable debate over how numerical information is organized in the mind. The debate can be distilled down to three main issues. The first issue concerns the role of general-