ai_math
AI, Algorithms & Math
Modern AI meets classical math. Intuition before formalism.
The Spectral Gap and How Markov Chains Forget
— Eigenvalues decide the queue
The Johnson–Lindenstrauss Lemma, Proven Two Ways
— Gaussians or coin flips, geometry stays put
p-values, carefully
— Calibrated, modest, and easily abused
How retrieval actually works: BM25, dense vectors, hybrid, and the art of re-ranking
— search first, then let the model talk
Markov's Inequality and Its Children
— One inequality, an entire dynasty
The Bootstrap is Two CLTs Glued by Glivenko–Cantelli
— Trust the staircase, then the bell
Spin first, quantize later: how TurboQuant gets nearly-optimal vector compression for free
— spinning the basis until the math gets easy
The Central Limit Theorem, Three Proofs
— bell curves are a fixed point of arithmetic
Galois Connections: The Algebra Behind Sound Static Analysis
— Adjoint thinking, computable answers
From a Token to a Generation: Every Part
— written in the dark, recovered in the morning
Persistent Homology for Noisy Data
— Loops survive; jitter doesn't
Bayes' Theorem as Hypothesis Arithmetic
— Count the evidence in decibans
The PCP Theorem at the Intuition Level
— Three bits, and the whole edifice stands
Matrix Exponentiation for Linear Recurrences
— companion matrix; Cayley–Hamilton does the rest
Entropy as the Price of Ignorance
— the wall is real, and asymptotically it is sharp