Math Foundations
open in notion ↗Logic, computation, and the limits of formal systems.
Pure intuition-building via 3Blue1Brown's visual series and Colah's Visual Information Theory — no intellectual-history context needed. The Essence of Linear Algebra series is the single most leveraged math investment you can make.
The foundations crisis of formal reasoning: Cantor's different sizes of infinity, Russell's paradox, Hilbert's formalist program, and Gödel's 1931 proof that the program is impossible. Leibniz dreamed of a formal language that could decide any question by calculation — Gödel killed that dream, and this unit is about that story.
Turing's 1936 "On Computable Numbers" as the computational twin of Gödel's incompleteness theorems: what a machine can compute, the undecidable halting problem, P vs NP, and the Kolmogorov/Chaitin/Solomonoff development of algorithmic information theory.
Optional unit on how proofs work and why they matter — what proof actually is as a cognitive activity. Take it if Unit 1 leaves you wanting to read math at a technical level or write proofs rather than read summaries; skip otherwise.
The minimum viable math for quantum foundations — linear algebra, probability, and complex numbers — enough fluency to recognize what's happening when Bell or Norsen writes down a two-qubit state or a unitary operator. That's weeks, not years.
The payoff where computation meets quantum: Feynman's 1982 proposal of quantum computation, Deutsch's 1985 universal quantum computer, and quantum information recasting quantum mechanics as a theory of a different kind of information. This is where the page fuses with the Quantum and Information pages.