(Initial) Global Taxonomy of the Most Fundamental Cognitive (Metamathematical) Mechanisms Used in Mathematical Creation/Invention

Danny A. J. Gómez Ramírez
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Danny A. J. Gómez Ramírez: Instituto Tecnológico Metropolitano (ITM), Research’s Labs Center Parque i

Chapter Chapter 10 in Artificial Mathematical Intelligence, 2020, pp 165-198 from Springer

Abstract: Abstract A general taxonomy of the most fundamental cognitive (metamathematical) mechanisms used during mathematical creation/invention is presented. Additionally, formalizations of each of them are described in a conceptual setting broad enough to include virtually any classic mathematical sub-discipline which possesses a sufficiently “robust” logic. All of this is grounded in general formalizations of the notions of mathematical concept and mathematical structure that take into account domain-specific symbolic aspects. The explicit list consists of (meta-)exemplification and generic exemplification, syntactic and conceptual strengthening and weakening, formal metaphorical reasoning, generalization and particularization (on symbolic units), conceptual comparison, replacement, identification and duplication, (un-)conscious conjunctive combination, (generic) conceptual blending, analogical reasoning, conceptual substratum, conceptual lining, conceptual complement and counterfactual (contradictory) affirmation.

Date: 2020
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DOI: 10.1007/978-3-030-50273-7_10

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