Learning paths
Short interactive lessons in maths, physics, computing, history and French, from one person’s self-study. Open any topic to follow its path. Your progress stays in your own browser.
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Mathematics
The tools the rest of the tree leans on.
Exponents and logarithms2 lessonsRemedial refresher on powers and logs: what log₂ x asks, why logs of probabilities are negative, the log rules, and switching between log₂, log₁₀ and ln.
Vectors and matricesPlannedLinear algebra for physics and machine learning: vectors, dot products, matrices as transformations, eigenvectors.
Probability and informationPlannedProbability, distributions, Bayes, entropy and cross-entropy: the math under language models.
Calculus
Functions and limits3 lessonsWhat it means for a function to approach a value. The foundation for derivatives (instantaneous rate) and integrals (infinite sums). DerivativesPlannedInstantaneous rate of change: from slopes of secants to the rules that make differentiation mechanical. Prerequisite: Functions and limits. Applying derivativesPlannedOptimization, related rates, linear approximation and curve sketching. IntegralsPlannedAccumulation: areas, Riemann sums, the fundamental theorem and techniques of integration. Differential equationsPlannedEquations about rates of change: exponential growth and decay, the harmonic oscillator, and solving them numerically. Series and approximationPlannedInfinite sums and Taylor series: how calculators compute sin x and why physicists approximate everything.Computing
How the machines and models of the AI era work.
How LLMs work
Prediction, compression and intelligence3 lessonsWhy predicting the next token well requires understanding, and why compression and prediction are the same thing. The core idea behind language models. Neural networks and gradient descentPlannedNeurons, layers, loss functions and backpropagation, built with toy examples. Tokens and embeddingsPlannedHow text becomes numbers: tokenizers, embedding vectors and meaning as geometry. Attention and the transformerPlannedQueries, keys, values, multi-head attention and the transformer block. Pretraining and scaling lawsPlannedData, compute and parameters: what pretraining is and why bigger kept working. Post-training: RLHF, RL and reasoningPlannedFrom base model to assistant: fine-tuning, RLHF, constitutional methods and RL for reasoning. Sampling and inferencePlannedWhat happens when you send a prompt: sampling, temperature, KV caches, context windows and serving costs.How chips are designed
Transistors to logic gatesPlannedHow a transistor works as a switch and how switches make logic. Logic to processorsPlannedAdders, memory, clocks and how a CPU executes instructions. From RTL to tape-outPlannedHow chips are actually designed: hardware description languages, synthesis, place and route, verification. Fabs and lithographyPlannedHow chips are manufactured: wafers, photolithography, EUV, yield and why TSMC matters. GPUs and AI acceleratorsPlannedWhy GPUs won AI, what TPUs do differently, memory bandwidth and the economics of AI chips.History
Narrative history, starting with the 19th century.
The 19th century
A map of the century3 lessonsThe big picture from Waterloo to 1914: the forces and turning points the other topics zoom in on. Steam, rail and the industrial economyPlannedHow steam and railways remade economies, cities and time itself. The gold standard and the RothschildsPlannedHow money worked: the gold standard, central banks and the great banking dynasties. 1873: the first Great DepressionPlannedThe Vienna crash, the Panic of 1873 and the Long Depression, following Ahamed’s framing of how it made the modern world. Empire and the first globalizationPlannedSteamships, telegraphs, migration and the scramble for colonies. Nations made by warPlannedGerman and Italian unification and the American Civil War as one story of state-building.Languages
Language learning.
French
Reading French3 lessonsShort articles written for you at B1 level and rising, with tap-to-translate sentences, word glosses and a drill from each text. Verb conjugationPlannedSystematic drills: present, passé composé, imparfait, futur, conditionnel and the subjunctive, focused on the verbs you meet in reading. Grammar repairPlannedThe dozen grammar points that cause most mistakes: articles, pronouns, agreement, negation, prepositions.Physics
Calculus-based physics, building toward relativity and quantum mechanics.