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Encyclopedia > 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. Mathematics is the study of quantity, structure, space and change. ... Cognitive science is usually defined as the scientific study either of mind or of intelligence (e. ... The term foundations of mathematics is sometimes used for certain fields of mathematics itself, namely for mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory. ... Look up Cognition in Wiktionary, the free dictionary The term cognition is used in several different loosely related ways. ...


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. Cognitive bias is any of a wide range of observer effects identified in cognitive science, including very basic statistical and memory errors that are common to all human beings (first identified by Amos Tversky and Daniel Kahneman) and drastically skew the reliability of anecdotal and legal evidence. ... Amos Tversky (March 16, 1937 - June 2, 1996) was a pioneer of cognitive science, a longtime collaborator of Daniel Kahneman, and a key figure in the discovery of systematic human cognitive bias and handling of risk. ... Daniel Kahneman (born 1934 in Tel Aviv, Israel) is a key pioneer and theorist of behavioral finance, which integrates economics and cognitive science to explain seemingly irrational risk management behavior in human beings. ... In classical physics and engineering, measurement is the the result of comparing physical quantities of objects, relations (e. ... Risk is the potential harm that may arise from some present process or from some future event. ... Bank of Sweden Prize in Economic Sciences winner Daniel Kahneman, was an important figure in the development of behavioral finance and economics and continues to write extensively in the field. ... The term mathematical practice arose in the philosophy of mathematics to distinguish actual practices of working mathematicians (choices of theorems to prove, informal notations to persuade themselves and others that various steps in the final proof are formalizable, refereeing and publication) from the final result: proven and published theorems. ...


One central claim that justifies a cognitive science of mathematics is that Euler's Identity reflects a cognitive structure unique to humans, or less specifically to a narrow range of beings similar to humans, e.g. hominids. This claim may or may not be necessary or central to the overall study of the subject, and there are other approaches that might come to be included as part of the study of the relationship between human cognition and formal modern mathematics. In mathematics, Eulers identity is the following equation: where: is the base of the natural logarithm, is the imaginary unit, the complex number whose square is negative one, and is Archimedes constant, the ratio of the circumference of a circle to its diameter. ... Genera Subfamily Ponginae Pongo - Orangutans Gigantopithecus (extinct) Sivapithecus (extinct) Subfamily Homininae Gorilla - Gorillas Pan - Chimpanzees Homo - Humans Paranthropus (extinct) Australopithecus (extinct) Sahelanthropus (extinct) Ardipithecus (extinct) Kenyanthropus (extinct) Pierolapithecus (extinct) (tentative) The Hominids (Hominidae) are a biological family which includes humans, extinct species of humanlike creatures and the other great apes...


The most accessible, famous, and infamous book on the subject is Where Mathematics Comes From (George Lakoff, Rafael E. Núñez, 2000). Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being is a book by cognitive linguist George Lakoff and psychologist Rafael E. Núñez. ... George P. Lakoff (Pronounced: lay-koff) is a professor of linguistics (in particular, cognitive linguistics) at the University of California, Berkeley where he has taught since 1972. ... Rafael E. Núñez is a professor of Cognitive science at the University of California, San Diego and is well known for promoting the idea of embodied cognition. ...


Topics

  • innate math: subitizing
  • naïve math
  • conceptual metaphor

Introduction Kaufman et al. ...

See also

cognitive science, conceptual metaphor, folk mathematics, Michel Foucault, history of mathematics, mathematical practice, naïve physics, philosophy of mathematics, Platonism, socially constructed reality, sociology of knowledge Cognitive science is usually defined as the scientific study either of mind or of intelligence (e. ... Conceptual metaphor: In cognitive linguistics metaphor is defined as understanding one conceptual domain in terms of another conceptual domain, e. ... As the term is understood by mathematicians, folk mathematics or mathematical folklore means theorems, definitions, proofs, or mathematical facts or techniques that circulate among mathematicians by word-of-mouth but have not appeared in print, either in books or in scholarly journals. ... Michel Foucault Michel Foucault (October 15, 1926 – June 26, 1984) was a French philosopher and held a chair at the Collège de France, a chair to which he gave the title The History of Systems of Thought. His writings have had an enormous impact on other scholarly work: Foucault... The word mathematics comes from the Greek μάθημα (máthema) which means science, knowledge, or learning; μαθηματικός (mathematikós) means fond of learning. Today, the term refers to a specific body of knowledge - the rigorous, deductive study of numbers, shapes, patterns, and change. ... The term mathematical practice arose in the philosophy of mathematics to distinguish actual practices of working mathematicians (choices of theorems to prove, informal notations to persuade themselves and others that various steps in the final proof are formalizable, refereeing and publication) from the final result: proven and published theorems. ... Naïve physics or folk physics is the untrained human perception of basic physical phenomena. ... Philosophy of mathematics is that branch of philosophy which attempts to answer questions such as: why is mathematics useful in describing nature?, in which sense(s), if any, do mathematical entities such as numbers exist? and why and how are mathematical statements true?. Various approaches to answering these questions will... Platonic idealism is the theory that the substantive reality around us is only a reflection of a higher truth. ... Socially constructed reality forms a concept within the sociology of knowledge and the social constructionist strand of postmodernism. ... The sociology of knowledge is the study of the social origins of ideas, and of the effects that prevailing ideas have on societies. ...


 
 

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