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Sophimatics explores a new frontier of Artificial Intelligence that goes beyond predictive and statistical logic to seek understanding, context, and ethical awareness. Conceived by Gerardo and Giovanni Iovane, this discipline fuses philosophy, mathematics, and computer science to shape a form of computational wisdom. The book guides readers from ancient philosophy and medieval logic to modern models of mind and cognition, illustrating how AI can evolve into a context-aware and ethically guided intelligence. Sophimatics integrates complex temporality, stratified memory, and reflective ethics, proposing AI as a cultural and co-creative interlocutor in fields such as healthcare, education, creativity, research, and finance. A central focus is the Sophimatic Ethics, a paradigm of cognitive responsibility for machines. The work envisions a future where technology becomes not merely a tool, but a companion in reflection and wisdom.