Danny Arlen de Jesús
Gómez-Ramírez, Ph.D.

I study the mind through the lens of mathematics. Understanding cognition demands a truly interdisciplinary approach, and mathematics—our most precise language for the laws of nature—provides the structure and clarity this inquiry requires. My training in pure and applied mathematics allows me to build models that are both conceptually sound and practically useful for explaining the essential features of mind.

My current work spans commutative algebra, algebraic geometry, model theory, and Artificial Mathematical Intelligence (AMI)—the theoretical and practical foundations of software capable of solving mathematical problems and conjectures with human-style reasoning and explanation. In parallel, I investigate the foundations of mathematics, the interface between quantum mechanics and formal systems (e.g., ZFC), and the philosophical and formal groundwork for an experimental science of natural consciousness. I also design global intelligence tests and contribute to a general theory of mind grounded in rigorous mathematics.

A complementary line of my research focuses on effective learning and teaching methods supported by cognitive science and multidisciplinarity, with the goal of making advanced mathematical reasoning more accessible and transferable.

I enjoy doing multi-, trans-, inter- and intradisciplinary science—blending ideas from pure and applied mathematics, cognitive science, artificial (mathematical) intelligence, computer science, and the philosophy of mind and AI. My aim is to develop clear, testable models and to propose new, well-argued solutions to foundational problems, always with an emphasis on transparency, rigor, and real-world relevance.

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Research focus

• Artificial Mathematical Intelligence (AMI): cognitive-computational models, formal mechanisms (e.g., conceptual blending, functional conceptual substrata), meta-mathematical tooling, and human-style proof & explanation generation.

• Core mathematics: commutative algebra, algebraic geometry, number-theoretic structures, model theory, and categorical methods.

• Foundations & cognition: new frameworks for the science of natural consciousness, the mathematics–physics interface (e.g., quantum formalism & ZFC), and global intelligence tests.

• Applied lines: mathematical reasoning agents for science, engineering, finance, energy systems, and policy; pedagogy & cognitive training backed by formal models.