Category-Based Co-Generation of Seminal Concepts and Results in Algebra and Number Theory: Containment-Division and Goldbach Rings

Gomez-Ramirez, Danny A. J.; Fulla, M.R.; Rivera, Ismael; Vélez, Juan D.; Gallego, Edisson

doi:10.17654/nt040050887

Cited by 3 publications

(2 citation statements)

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“…Latest advances in computational creativity, cognitive and computer science continue enhancing our understanding about the way in which our minds create mathematics at high levels of sophistication [11]. In particular, more precise formalization of fundamental cognitive mechanisms for conceptual creation has been developed and tested in several mathematical domains [29,12,34,10]. Among those basic cognitive abilities conceptual blending has shown to be not only one of the most powerful, but also one of the most omnipresent among mathematics [1,6].…”

Section: Introductionmentioning

confidence: 99%

“…Among those basic cognitive abilities conceptual blending has shown to be not only one of the most powerful, but also one of the most omnipresent among mathematics [1,6]. For instance, seminal notions of (algebraic) number theory, Fields and Galois theory and commutative algebra have been conceptually meta-generated (with a computational basis) in terms of a categorical formalization of conceptual blending [12,4,10,3].…”

Section: Introductionmentioning

confidence: 99%

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Artificial Cognitively-inspired Generation of the Notion of Topological Group in the Context of Artificial Mathematical Intelligence

Gomez-Ramirez¹,

Herrera-Jaramillo²,

Geismann³

2021

Preprint

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The new computational paradigm of conceptual computation has been introduced in the research program of Artificial Mathematical Intelligence. We provide the explicit artificial generation (or conceptual computation) for the fundamental mathematical notion of topological groups. Specifically, we start with two basic notions belonging to topology and abstract algebra, and we describe recursively formal specifications in the Common Algebraic Specification Language (CASL). The notion of conceptual blending between such conceptual spaces can be materialized computationally in the Heterogeneous Tool Set (HETS). The fundamental notion of topological groups is explicitly generated through three different artificial specifications based on conceptual blending and conceptual identification, starting with the concepts of continuous functions and mathematical groups (described with minimal set-theoretical conditions). This constitutes in additional heuristic evidence for the third pillar of Artificial Mathematical Intelligence.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%