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This book was written to establish a rigorous mathematical foundation for Self-Replicating Artificial Intelligence Machine Systems (SRAIMs) through the framework of Infinite Series with Multiple Ratios (SRMs). It develops the conceptual and formal basis of self-replicating intelligent systems, connecting deep mathematics to generative intelligence, autonomous architectures, advanced data structures, computational modeling, and long-range scientific applications. Rather than offering a purely speculative vision, the book proposes an original theoretical structure capable of supporting future research at the intersection of mathematics, artificial intelligence, and complex systems. By combining formal development with technological perspective, this volume is intended for researchers, advanced students, and professionals seeking new mathematical approaches to intelligent systems and emerging computational paradigms.
Prof. Dr. Carlos Roberto França is an Associate Professor at the Federal University of Fronteira Sul (UFFS), Brazil, and a Full Member of Sigma Xi, The Scientific Research Honor Society. Over more than three decades, he has developed original research at the intersection of mathematics, computing, and intelligent systems, with particular emphasis on his theoretical framework of Infinite Series with Multiple Ratios (SRMs) and its broader implications for artificial intelligence, data structures, computational biology, cryptography, and autonomous systems.
França is the author of the manuscript SRAIMs & SRMs: Mathematical Foundations for Self-Replicating Intelligent Systems, a work that brings together rigorous mathematical foundations, generative intelligence, and long-range technological applications. His recent publications explore mathematical challenges for generative AI, self-replicating artificial intelligence machine systems (SRAIMs), quantum-related perspectives, and computational models inspired by SRM structures.
In 2025, one of his papers, Mathematical Challenges for Generative AI in Computational Biology: Cell Proliferation and the Path to Living AI, was accepted for ICTIS 2025 at Cornell University and later published by Springer Nature in the volume ICT for Intelligent Systems. His research has also been disseminated internationally through Zenodo and other scholarly platforms, where it has attracted sustained global attention.
Throughout his career, França has worked on high-complexity mathematical models and applied technological solutions, including research related to cryptography, advanced data organization, and computational modeling. His current work is focused on establishing new bridges between deep mathematics, generative intelligence, self-replicating architectures, and future-oriented scientific challenges.