Lectures on AGI foundations

Four chapters on the mathematical and computational foundations of general intelligence. The scope is not “will AGI arrive” or “is current AI close”, the scope is what the 20th-century logic and complexity results tell us about what any artificial general intelligence can and cannot do.

Target reader: graduate student or researcher familiar with basic logic, probability, and computability. Mathematical depth: honest about limits of our tools.

Chapter 1 · Gödel, Löb, and self-referential AI

Gödel’s first and second incompleteness theorems. Löb’s theorem and its implications for self-modifying agents (the Löbian obstacle). What the classical limitative results do say, what they do not say, and why the Penrose argument fails.

Chapter 2 · AIXI and universal intelligence

Solomonoff induction as a formalization of Occam’s razor. Hutter’s AIXI combining Solomonoff prediction with Bellman-optimal planning. The Legg-Hutter universal intelligence measure. Uncomputability and practical approximations (Monte Carlo AIXI, AIXI-tl).

Chapter 3 · World models and planning-by-imagination

Ha-Schmidhuber, DreamerV3, JEPA. The case for learning a compact internal model that supports planning by imagination. Sample efficiency evidence and its scope. LeCun’s AGI proposal and the implicit-world-model hypothesis for LLMs.

Chapter 4 · Computational irreducibility and the limits of optimization

Three deep negative results: No-Free-Lunch (Wolpert 1996), computational irreducibility (Wolfram), PAC-learnability lower bounds. What each does and does not imply for AI, and why “smarter AI” does not bypass them.

Related shorter notes covering adjacent topics are in the research notes library, including the alignment problem, multi-agent coordination, scaling hypothesis evidence, and mechanism design for AI systems.