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  • Artificial Hydrogen Molecule in vertically stacked Ga_{1-x}Al_xA_s Nanoscale Rings: Structural and

External Probes Effects in their Quantum Levels. Joint with J. D. Castrillón, M. R. Fulla, I. E. Rivera, Y. A. Suaza and J. H. Marin (submitted CompletePreprint). Physika E: Low-dimensional Systems and Nanostructures, 117, 113765 (2020) (to appear).

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  • A General Version of the Nullstellensatz for Arbitrary Fields. Joint with Edisson Gallego

and Juan D. Vélez. Open Mathematics 17, 556-558. Preprint 2018.

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  • Functional Conceptual Substratum as a New Cognitive Mechanism for Mathematical Creation.

Joint with Stefan Hetzl. (to appear), PreprintArxiv 2019.

 

  • ​​​Category-Based Co-Generation of Seminal Concepts and Results in Algebra and Number Theory:

Containment-Division and Goldbach Rings. Joint with Marlon Fulla, Ismael Rivera, Juan D. Vélez and Edißon Gallego. To be published in JP Journal of Algebra, Number Theory and Applications, 2018.

 

  • Towards a General Many-sorted Formal Framework for Describing Certain kinds of

Legal Statues. Joint with Egil Nordqvist. Under review, Preprint 2017.

 

  • Towards an Homological Generalization of the Direct Summand Theorem. Joint with

Juan D. Vélez. Under review, PreprintArxiv 2017.

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  • Artificial Co-Creative Generation of the Notion of Topological Group based on the Categorical 

Conceptual Blending. Joint with Yoe A. Herrera-Jaramillo and Florian Geismann. (Under Review), Preprint.

 

  • A New Multiple-Intelligences Test for Artificial General Intelligence. Joint with Judith Kieninger, 

Stephan Schneider and Nico Potyka. Under review. Preprint

 

  • Containment-Division Rings and New Characterizations of Dedekind Domains.

Joint with Edisson Gallego and Juan D. Vélez, PreprintArxiv 2017.

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  • On Preservation Properties and an Algebraic Characterization of Some Stronger

Forms of the Noetherian Condition. Joint with Edisson Gallego and Juan D. Vélez. Under review, Preprint 2017.

 

  • Towards an Experimental Science of Natural Consciousness. Joint with F. Becker and R. Garita, Preprint 2017.

 

  • Theory Blending: Extended Algorithmic Aspects of Examples. Joint with M. Martinez,

A. M. H. Abdel-Fattah, U. Krumnack, A. Smail, T. Besold, A. Pease, M. Schmidt, M. Guhe and K.-U.

Kuehnberger. Annals of Mathematics and Artificial Intelligence, pp. 1-25, 2016. pdf-link

 

  • Normality and Related Properties of Forcing Algebras. Joint with Holger Brenner. Com-

munications in Algebra. Volume 44, Issue 11, pp. 4769-4793, 2016. pdf

 

  • The Direct Summand Conjecture for some bi-generated extensions and an asymptotic

Version of Koh’s Conjecture. Joint with Edisson Gallego and Juan D. Velez. Beitraege zur Algebra und Geometrie (Contributions in Algebra and Geometry) pp. 1-16. 2016. OfficialPdfLink 

 

  • Towards a Computational Framework for Function-Driven Concept Invention. Joint with

N. Potyka, D. and K.-U. Kuehnberger. In Lecture Notes in Artificial Intelligence 9782, Steunebrink et al. (Eds.). Springer International Publishing Switzerland. 2016. pdf

 

  • The Role of Blending in mathematical invention. Joint with F. Bou, M. Schorlemmer, J.

Corneli, E. Maclein and A. Smaill and A Pease. Proceedings of the Sixth International Conference on Computational Creativity (ICCC). S. Colton et al., eds. Park City, Utah, June 29-July 2, 2015. Publisher: Brigham Young University, Provo, Utah. pp. 55-62. 2015. pdf

 

  • Conceptual Blending as a meta-generator of mathematical concepts: Prime Ideals

and Dedekind Domains as a Blend. In T. Besold, K.-U. Kuehnberger, M. Schorlemmer and Alan Smaill (eds.). Kuehnberger K.-U., Koenig P. and Walter, S. (series eds.). Proceedings of the workshop on Computational Creativity, Concept Invention, and General Intelligence 2015, C3GI. Institute of Cognitive Sciences. Publications of the Institute of Cognitive Sciences, Osnabrueck, PICS series Vol. 2, 2015. pdf

Complete Volume pdf​.

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  • On the Connectedness of the Spectrum of Forcing Algebras. Joint with Holger Brenner,

Revista Colombiana de Matematicas. Vol 48(2014)1, Pag. 1-19. pdf

LATEST ARTICLES AND PREPRINTS

“Truth is ever to be found in the simplicity, and not in the multiplicity and confusion of things”

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-Issac Newton-

PUBLICATIONS AND TALKS

“The most incomprehensible thing about the universe is that it is comprehensible”

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-Albert Einstein-

BOOK CHAPTERS

 

 

  • General Introduction to the Artificial Mathematical Intelligence Program. In Artificial Mathematical

Intelligence: Cognitive, Metamathematical, Physical and Philosophical Foundations. Danny A. J. Gomez-Ramirez. Series 'Mathematics in Mind', Springer-Verlag. To appear. 

 

  • General Considerations for the New Cognitive Foundations' Program.  In Artificial Mathematical

Intelligence: Cognitive, Metamathematical, Physical and Philosophical Foundations. Danny A. J. Gomez-Ramirez. Series 'Mathematics in Mind', Springer-Verlag. To appear. 

 

  • Towards the (Cognitive) Reality of Mathematics and the Mathematics of (Cognitive) Reality. In

Artificial Mathematical Intelligence: Cognitive, Metamathematical, Physical and Philosophical Foundations. Danny A. J. Gomez-Ramirez. Series 'Mathematics in Mind', Springer-Verlag. To appear. 

 

  • The Physical Numbers.  In Artificial Mathematical Intelligence: Cognitive, Metamathematical,

Physical and Philosophical Foundations. Danny A. J. Gomez-Ramirez. Series 'Mathematics in Mind', Springer-Verlag. To appear. 

 

  • Dathematics. In Artificial Mathematical Intelligence: Cognitive, Metamathematical, Physical and

Philosophical Foundations. Danny A. J. Gomez-Ramirez. Series 'Mathematics in Mind', Springer-Verlag. To appear. ArxivPreprint

 

  • Conceptual Blending in Mathematical Creation/Invention. In Artificial Mathematical Intelligence:

Cognitive, Metamathematical, Physical and Philosophical Foundations. Danny A. J. Gomez-Ramirez. Series 'Mathematics in Mind', Springer-Verlag. To appear. 

 

  • Formal Analogical Reasoning in Concrete Mathematical Research. In Artificial Mathematical

Intelligence: Cognitive, Metamathematical, Physical and Philosophical Foundations. Danny A. J. Gomez-Ramirez. Series 'Mathematics in Mind', Springer-Verlag. To appear. 

 

  • Conceptual Substratum. In Artificial Mathematical Intelligence: Cognitive, Metamathematical,

Physical and Philosophical Foundations. Danny A. J. Gomez-Ramirez. Series 'Mathematics in Mind', Springer-Verlag. To appear. 

 

  • Global Taxonomy of the most Fundamental Cognitive Mechanisms used in Mathematical

Creation/Invention. In Artificial Mathematical Intelligence: Cognitive, Metamathematical, Physical and Philosophical Foundations. Danny A. J. Gomez-Ramirez. Series 'Mathematics in Mind', Springer-Verlag. To appear. 

 

  • Meta-Modeling of Classic and Modern Mathematical Proofs and Concepts. In Artificial

Mathematical Intelligence: Cognitive, Metamathematical, Physical and Philosophical Foundations. Danny A. J. Gomez-Ramirez. Series 'Mathematics in Mind', Springer-Verlag. To appear. 

 

  • The most Outstanding Challenges towards Global AMI and its Plausible Extensions. In Artificial

Mathematical Intelligence: Cognitive, Metamathematical, Physical and Philosophical Foundations. Danny A. J. Gomez-Ramirez. Series 'Mathematics in Mind', Springer-Verlag. To appear. 

 

  • Formal Conceptual Blending in the (Co-)Invention of (Pure) Mathematics. Joint with Alan

Smaill. In Confalonieri R., Pease A., Schorlemmer M. eds. Concept Invention: Foundations, Implementations, Social Aspects, and Applications. In Cognitive Technologies (Series). Springer, 2018. Link.

 

  • Concept Invention in DOL: Evaluating Consistency and Conflict Resolution. Joint with

M. Codescu, F. Neuhaus, T. Mossakoski and O. Kutz. In Confalonieri R., Pease A., Schorlemmer M. eds. Concept Invention: Foundations, Implementations, Social Aspects, and Applications. In Cognitive Technologies (Series). Springer, 2018. Link.

 

BOOKS & MONOGRAPHS

 

  • Artificial Mathematical Intelligence: Cognitive, Metamathematical, Physical and Philosophical

Foundations. Springer-Verlag. Cham, 2020. 

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  • Cuantum Mechanics, Cuantum Computing and Heat Computing: An Introduction.

 'Joint work with J.D. Vélez and J. P. Hernandez. First Initial Preprint. 

 

  • A Modern View of Relativity: A Rigorous Introduction to Mathematicians. Joint with J. D. Vélez,

C. Arias and A. Quintero  2019 PreprintLastVersion. Initial Online Preprint.

 

  • The Prime Number Theorem and some Equivalences. Diplom's Monograph, National

University of Colombia, September 2004. In Spanish. pdf

 

  • Hilbert's Tenth Problem and some related Questions. Master's Monograph, National

University of Colombia, September 2007. In Spanish. pdf

 

  • Homological Conjectures, Closure Operations, Forcing Algebras and Vector Bundles.

Thesis, National University of Colombia in association with the University of Osnabrueck, September 2013. pdf

SELECTED SCIENTIFIC TALKS

  • "Fundamental Pillars of the Creation of Artificial  Co-Creative Mathematical Agents of Artificial Mathematical Intelligence". Talk given at the Colloquium of the University of Antioquia. May 24, 2018.

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  • "Dathematics: a Meta-Isomorphic Version of Classic Mathematics based on Proper

Classes". Talk given at the Logic Colloquium (Annual European summer meeting of the Association of Symbolic Logic). Stockholm, Sweden. August 14, 2017.

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  • "Cognitively-inspired Formal Models of Scientific Creation". J6’ Spring School for Studies

on Intelligence and Cognition. The Joint Exploratory Society for Interdisciplinary and

Cognitive Studies (JESICS). Cairo, Egypt. March 30, 2017.

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  • “Towards a General Taxonomy and Meta-Formalitazion of the Seminal Cognitive Me-

chanisms used in Mathematical Concept Invention”. Talk given at the Collouium of the Theory and Logic Group of the Faculty of Informatics of the Vienna University of Technology. Vienna, Austria. November 23, 2016.

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  • “A cognitively-Inspired Reformulation of Meta-Mathematics”. Zif Workshop From Compu-

tational Creativity To Creativity Science. ZIF Center for Interdisciplinary Research (Bielefeld) in Coo- peration with the University of Osnabrueck, Germany. September 22, 2016.

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  • “Towards a Cognitively Inspired Physical Philosophy of Nature”. Talk at the Institute of Phi-

losophy of the University of Antioquia, Medellın, Colombia. September 9 of 2016.

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  • “Logic-Categorical Meta-Models of the Conceptual Creation in Mathematics” (Original

Title: Meta-Modelos Logico-Categoricos de la Creacion Conceptual en Matematicas). Talk given at the Logic Seminar of the University of Los Andes. Bogota, Colombia. September 25 of 2016.

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  • “Towards the Classification of the Metagenerators of Mathematical Theories: Formal

Conceptual Blending”. Seminar of Logic and Computation. EAFIT University. Medellin. December 16 of 2016.

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  • “The Reality of Mathematics and the Mathematics of Reality” (Original title: La realidad de

las matematicas y las matematicas de la realidad). Public Library Piloto BPP. Conference open to the general public in Medellın. August 24 of 2015.

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  • “Conceptual Blending as a meta-generator of mathematical concepts: Prime Ideals

and Dedekind Domains as a Blend”. Contributing speaker at the 5-th World Congress on Universal Logic, UNILOG’15. Istanbul, Turkey. Juni 26 of 2015.

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  • Main Speaker and Organizer of the 1-day Workshop ”Toward the Fundamental Princi-

ciples of Mathematical Creativity: A Cognitive Perspective” (Original Title: Hacia los Principios Funda-

mentales de la Creatividad Matem ́atica: Un Enfoque Cognitivo). National University of Colombia in Medellin. December 12 of 2014.

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  • “Toward a Meta-mathematization of Mathematical Creation”. Speaker and co-organizer of

 the 1-day workshop ”Toward the Main Formal Pinciples of Mathematical Creativity”, University of Osnabrueck, October 11 of 2014.

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  • “A Normality Criterion for Forcing Algebras over the Ring of Polynomials”. Gradurierte

Kollege Kombinatorische Strukturen in Algebra und Topologie. University of Osnabrueck, December 18 of 2012.

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  • “On the Connectedness of Forcing Schemes”. Algebra and Geometry Seminar. University of

Basel. Juni 1 of 2012.

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