Interactive guides,
built from scratch.
267 parts across 16 long-form guides to AI, vision and math. Every part is interactive — you drag the point along the curve, run the training loop, and watch the solver converge. Nothing here is a static diagram.
Est. 1950 Compiled by Denim Patel Guides & interactive notes Last updated Sep 2026
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Six interactive guides to how a language model is trained, how one is served at scale, how to build with LLMs, how agents act in the world, and how models are made to see, hear and generate media.
Three long interactive guides built around running examples you can drag: the geometry that turns images into 3D structure, the nonlinear least-squares machinery that makes it converge, and the Lie groups and Lie algebras that let rotations and poses be estimated at all.
The machinery every other subject assumes, built from pictures first: a 22-part interactive guide to linear algebra, two interactive calculus volumes that build single- and multivariable calculus from local linearity up to the gradients, Jacobians, backprop and Lie-group updates the AI and vision guides consume, two interactive probability volumes that go from what a probability means to the filters, samplers and estimators those guides run on, and an interactive guide to statistics that starts at a sample you can redraw and ends at Kalman filters and causal inference.
Built from scratch, step by step
16 guides, 267 parts. Each is built around one running example carried from the first part to the last.
AI
Next-token prediction, autoregressive generation, and why OLMo is the running example for this series.
Why generating one token costs a full sweep of the weights through HBM, and why that single fact shapes everything that follows.
The model is a stateless text function; every 'memory' is your code resending text, and the context window is the budget that governs it.
The five workflow patterns, the complexity/value/viability/cost-of-error gate, and why most 'agents' should be workflows.
Sampling from a distribution you never see: a 2D dataset you draw yourself, and the line between memorising it and modelling it.
Patching an image into a sequence, position embeddings and the class token, and what a vision transformer gives up against a convolution.
Vision & Geometry
The projective plane, homogeneous coordinates, the congruence symbol, and the point/line duality every later part depends on.
Gradient descent, Newton's method, Gauss-Newton and Levenberg-Marquardt, built around one running example: a robot figuring out where it is.
Average two compass headings, add two sets of Euler angles, sum two rotation matrices - and watch each one fail in a way that points at the same missing idea.
A minimal page proving the new subject-neutral guide kit renders: guide.css styling, a Guide.drawBars() canvas demo driven by a slider, and a GuideMath helper call.
Math
An arrow, a list of numbers, and an abstract object you can add and scale — and why they are the same thing.
The whole subject in one idea: almost every function is locally linear, and a derivative is just the slope you find when you zoom in far enough.
A particle-flow canvas you edit by hand: arrows at every point, streamlines through them, and the two numbers that describe how a field changes.
Relative frequency settling into a limit, a belief you can bet on, and the three axioms both pictures have to obey.
Drag the parameter and watch the log-likelihood surface move with the fitted curve — and see why a likelihood is not a probability over θ.
A hidden population, one sample, and an estimate that moves every time you redraw it while the truth stays put.