Programming is the construction of languages for thought. This series begins inside ordinary Python, where a useful program grows awkward as its requirements multiply. Instead of adding more branches, parameters, and callbacks, we find the domain's primitives, define how they …

Calculus is a handful of big ideas and one theorem that ties them together, and almost every other playlist on this channel quietly stands on it. A limit makes "approaching" precise. The derivative reads that as a rate of change, and the chain rule extends it to quantities built …

Most courses drown differential equations in closed-form solution techniques. This playlist skips almost all of that. A differential equation says how something changes given where it is now, and the interesting question is what trajectory that produces. We answer it two ways …

Illustrated books from Alex Towell: complete narrated works paired with purpose-built visual storytelling.

Every learner that generalizes is making a bet about the world, and the bet is the bias. This playlist opens with the theory that makes assumptions mandatory (no free lunch, sample efficiency, and the price paid out of distribution) and then reads each major neural architecture …

Information theory is a theory of distinguishability under a model. A source creates alternatives. Binary questions and codewords separate them, an observation changes which remain plausible, a wrong model misprices them, noise makes them overlap, channel coding separates them …

One function connects maximum likelihood, Bayesian updating, confidence procedures, regression losses, incomplete observations, and language-model pretraining. This playlist builds that function from a coin flip and follows it to modern statistical learning. It treats likelihood …

Videos that explore mathematical ideas through concrete examples, visual intuition, and rigorous reasoning. Some episodes test famous conjectures; others build the models and geometry that help us understand what data can and cannot tell us.

The mechanics pair to the inductive-biases playlist: that series asks what an architecture assumes; this one builds the machine that does the assuming, in pure Python with no NumPy and no autograd, on the scratchnn library (which exists to be read). One idea built up in three …

Newton's second law is not a complete theory of nature, and it is not a physics engine by itself. It is the update rule at the center of one: choose a state, add the forces and constraints that act on it, and follow how its velocity and position change. This playlist builds that …

A 13-episode build-it-yourself series that constructs a statevector quantum simulator from first principles in NumPy, then uses it to understand Grover's search, the Quantum Fourier Transform, Shor's algorithm, density matrices, noise models, and quantum error correction. Every …

Given a sequence, predict the next symbol. The theoretically optimal solution is Solomonoff induction, which is incomputable. Every practical algorithm is an approximation encoding assumptions about what patterns are likely. This playlist traces the arc from the formal problem …

Alexander Stepanov's central insight is that the algebraic structure of a type determines which algorithms apply to it. Declare that your type is a monoid and you get power-by-squaring, parallel reduction, and fold for free. Declare a semiring and the same matrix-power code gives …