When does learning from data work (math starting from basic probability)

# Summary The article explains when machine learning models trained on sample data generalize to unseen data, answering this through the Fundamental Theorem of Statistical Learning: a hypothesis class is learnable if and only if it has finite VC dimension. The post builds up the mathematical foundations from basic probability—including concentration inequalities, the union bound, and VC dimension—to prove both directions of this equivalence and establish when empirical risk minimization reliably works.