Cognitive science of mathematics

The cognitive science of mathematics is the study of mathematical ideas using the techniques of cognitive science. Specifically, it is the search for foundations of mathematics in human cognition.

This approach was long preceded by the study, in cognitive sciences proper, of human cognitive bias, especially in statistical thinking, most notably by Amos Tversky and Daniel Kahneman, including theories of measurement, risk and behavioral finance from these and other authors. These studies suggested that mathematical practice and perhaps even mathematics proper had little direct relevance to how people think about mathematical concepts. It seemed useful to ask where, if not from intuition, formal mathematics came from.

The most accessible, famous, and infamous book on the subject is Where Mathematics Comes From (George Lakoff, Rafael E. Núñez, 2000). This book culminates with a case study on Euler's Identity; the authors argue that Euler's Identity is a concept that reflects a cognitive structure unique to humans, or less specifically to a narrow range of beings similar to humans, e.g. hominids.

Topics

 * innate math: subitizing
 * naïve math
 * conceptual metaphor
 * Where Mathematics Comes From