Mathematical Foundation of Artificial Intelligence: Geometric, Physical, Causal, and Autonomous AI

Mathematical Foundations of Artificial Intelligence: Geometric, Physical, Causal, and Autonomous AI is the second volume in a two-part series.The first volume, Mathematical Foundations of Artificial Intelligence: Basics of Manifold Theory (CRC Press, 2026), developed the geometric language needed to think rigorously about differential manifolds, metrics, curvature, and related structures of intelligence.That volume established the vocabulary. This volume asks what follows when that language is used to reconstruct artificial intelligence from the ground up around four foundational themes: geometry, physics, causality, and autonomy. Artificial intelligence is moving beyond pretraining alone toward the mechanisms of intelligence.Many branches of AI that appear separate can be understood as different aspects of one broader mathematical program.In this program, intelligence is not treated merely as disembodied symbol manipulation or statistical pattern matching.It is modeled as motion and a