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The cognitive science of mathematics is the study of mathematical ideas (concepts) using the techniques of cognitive science. It proposes to ground the foundations of mathematics in the empirical study of human cognition and metaphor, and to analyze mathematical ideas in terms of the human experiences, metaphors, generalizations, and other cognitive mechanisms giving rise to them. This field of study has many practical applications in mathematical education, but it's quite distinct from the work of professional mathematicians.
This approach to mathematics in general was preceded by the study of human cognitive bias in probabilistic reasoning and economic contexts, most notably by Amos Tversky and Daniel Kahneman. Such biases affect economic measurement, perceived financial risk, and ground the field of behavioral finance. This work suggests that mathematical practice has little direct relevance to how people think about mathematical situations. If human intuition appears to be inconsistent with formal mathematics, this gives rise to the question of where formal mathematics comes from.
The book Where Mathematics Comes From (George Lakoff, Rafael E. Núñez, 2000) is an accessible and controversial introduction to the subject. It culminates with a case study of Euler's identity; the authors argue that this identity reflects a cognitive structure peculiar to humans or to their close relatives, the hominids.
Lakoff and Núñez's work was anticipated in some respects by professional mathematicians' informal accounts of the human grounding of mathematics, such as Mathematics, Form and Function by Saunders Mac Lane.
- Cognitive science
- Conceptual metaphor
- Informal mathematics
- History of mathematics
- Mathematical practice
- Naïve physics
- Numerical cognition
- Philosophy of mathematics
- Where Mathematics Comes From
- Mathematics, Form and Function
- Brian Butterworth, 1999. What Counts: How Every Brain is Hardwired for Math. Free Press.