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The '''cognitive science of mathematics''' is the study of [[mathematics|mathematical]] ideas using the techniques of [[cognitive science]]. Specifically, it is the search for [[foundations of mathematics]] in human [[cognition]].
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{{Mathematicalpsychology}}
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The '''cognitive science of mathematics''' is the study of [[mathematics|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 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.
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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 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. [[Hominidae|hominid]]s.
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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 [[hominidae|hominid]]s.
   
== Topics ==
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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]].
* innate math: [[subitizing]]
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* naïve math
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[[Brian Rotman]] is also notable for his research on the [[semiotics]] of mathematics.
* conceptual metaphor
 
*''[[Where Mathematics Comes From]]''
 
   
 
== See also ==
 
== See also ==
* [[cognitive science]]
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* [[Cognitive science]]
* [[conceptual metaphor]]
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* [[Conceptual metaphor]]
* [[folk mathematics]]
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* [[Informal mathematics]]
* [[history of mathematics]]
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* [[Mathematical practice]]
* [[mathematical practice]]
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* [[Numerical cognition]]
* [[naïve physics]]
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* [[Philosophy of mathematics]]
* [[philosophy of mathematics]]
 
 
* [[Platonism]]
 
* [[Platonism]]
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==References==
 
==References==
*[[Brian Butterworth]], 1999. ''What Counts: How Every Brain is Hardwire for Math''. Free Press.
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*[[Brian Butterworth]], 1999. ''What Counts: How Every Brain is Hardwired for Math''. Free Press.
*([[George Lakoff]], and [[Rafael E. Núñez]], 2000. ''[[Where Mathematics Comes From]]'' Basic Books.
 
   
 
[[Category:Cognitive science|Mathematics]]
 
[[Category:Cognitive science|Mathematics]]
[[Category:Mathematics]]
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[[Category:Philosophy of mathematics]]
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[[Category:Mathematics education]]
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[[Category
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Latest revision as of 11:55, January 2, 2010

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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.

Brian Rotman is also notable for his research on the semiotics of mathematics.

See also Edit


ReferencesEdit

  • Brian Butterworth, 1999. What Counts: How Every Brain is Hardwired for Math. Free Press.[[Category
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