Meta-Modeling of Classic and Modern Mathematical Proofs and Concepts

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 11 in Artificial Mathematical Intelligence, 2020, pp 201-249 from Springer

Abstract: Abstract Based on the global taxonomy of fundamental cognitive (metamathematical) mechanisms developed within the artificial mathematical intelligence research program, specific cognitive meta-generations (or pseudo-pre-code) of dozens of (mathematical) concepts and proofs are presented. In particular, two classic proofs in elementary geometry and number theory are meta-generated. Moreover, around 30 fundamental notions are constructed belonging to several mathematical sub-disciplines like set theory, abstract algebra, topology, category theory, commutative algebra, and (classic and modern) algebraic geometry. All of these concepts vary enormously in their degree of sophistication. Nonetheless, the initial mathematical structures used as basic conceptual “bricks” are elementary in nature and essentially involve simple constructions done using the standard numerical systems (e.g., the natural, integer, and real numbers). The most sophisticated notion that is generated (only by space constrains in the presentation) is the one of (mathematical) schemes in modern algebraic geometry.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-50273-7_11

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DOI: 10.1007/978-3-030-50273-7_11

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