This paper proposes a five-stage evolution framework for the development of artificial intelligence (AI). Reflecting the historical development of human cognitive technology, it argues that AI does not develop gradually but undergoes innovative changes at each stage. Similar to the development of human cognitive technology such as ancient writing, alphabets, grammar and logic, calculus, and formal logic systems, AI goes through each stage through innovative changes in its representation and reasoning abilities. This “cognitive geometry” framework goes beyond a simple metaphor and provides a systematic and integrated model that explains the past structural changes of AI from past expert systems to transformers and suggests future development paths. In particular, it emphasizes that the evolution of AI is not simply linear but self-reflective. As AI develops, the tools and insights developed by AI create a feedback loop that fundamentally restructures the basic structure of AI itself. We are currently in the midst of a “metalinguistic moment” characterized by the emergence of self-reflective capabilities (Chain-of-Thought prompting, Constitutional AI, etc.), followed by a “mathematical symbolism moment” and a “formal logic systems moment”, leading to the development of a calculus of computable thought via neural symbol architecture and program synthesis, and to provably trustworthy AI that reconstructs its own underlying representations. This paper is the methodological conclusion to a three-part series that previously explored the economic drivers of AI (“why”) and the cognitive nature (“what”), providing a theoretical foundation for the “how” and offering concrete, practical strategies for startups and developers looking to build the next generation of intelligent systems.
