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AI Trajectories (May 2026)

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 Silicon Empires On the Future of AI Evolution Trajectories through 2023 Business Trajectories Tao on Trajectory Tracing AI AI trajectories describe both the developmental pathways of artificial intelligence (technology, compute scaling) and the internal decision-making sequences of AI agents . Understanding these paths is critical for forecasting how rapid automation, tool use, and machine reasoning will impact enterprise, policy, and daily productivity. [ 1 , 2 , 3 ] Macro-Level AI Trajectories The broad evolution of artificial intelligence is shifting from static, rule-based systems toward dynamic and autonomous capabilities. [ 1 , 2 ] Generative & Agentic AI: Moving from static text and image generation toward multi-step, action-oriented systems that utilize tools, access files, and make independent decisions. Domain-Specific Superintelligence (DSS): A paradigm shift proposing smaller, highly specialized models built on structured symbolic abstractions (e.g., knowledge gr...
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An AI Solution to the Unit Distance Problem Conjecture

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Latent Space arxiv: Remarks Silicon Reckoner Marcus on AI  
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Universal Prediction

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Universal Approximation Universal Prediction Universal Prediction Universal Prediction Universal Prediction
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Math Capabilities of LLMs

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Math Capabilities of LLMs Struggle AI on Computation versus Memorizaton as Defined by Stephen Wolfram n the context of mathematics and Large Language Models (LLMs), Stephen Wolfram defines memorization as the probabilistic retrieval of text sequences, while computation is the use of deterministic, logical steps. LLMs excel at extrapolation when blending intuitive understanding with computational power, making specialized tooling essential for reliable math. [ 1 , 2 , 3 ] The Mechanism of LLMs Probabilistic Pattern Matching: LLMs predict tokens based on statistics rather than mathematical logic. When an LLM solves a math problem, it draws from the structure of previous proofs and examples it was trained on. Hallucinations vs. Reality: Because LLMs lack the ability to truly compute, they are prone to mathematical hallucinations—convincingly formatted text that contains faulty logic or invented numbers. [ 1 , 2 , 3 ] The Limits of Extrapolation via Memorization In-Context Extrapolati...
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