Mathematics Atlas

Mathematics Atlas is a learning application that rebuilds mathematics from the axioms. Its principle is traceability: every term, every symbol, every theorem, every operation and every activity it presents points back, through a registry, to the notion where it was established. Four peaks organise the path: general relativity, quantum field theory, machine learning and quantum computing. The project is under construction.

The Atlas is a map of dependencies between notions. The Ledger, the learner’s personal register, records what they have earned, and a node unlocks only by passing an assessment. No word before its turn: a teaching text cannot use a term absent from its Ledger, and a closure compiler checks it at writing time. Only the map can name a destination still locked, as a preview.

Activities must embody the mathematical operation rather than have it recited, and each notion offers a moment where you can violate an axiom to see the precise failure that results. A depth dial sets the level of formalism, from gesture to expert. The specifications are validated data, an engine in pure TypeScript derives the state of the nodes from them, and a React interface plugs into it. A companion publication in several volumes follows the same map.

The project starts from a principle: you must be able to trace any term back to the axioms it comes from, and no word is used before it has been earned. It extends my scientific interests, the mathematical foundations of quantum physics first among them. Mathematical exactness comes before simplification there, and the rewards are the traces themselves, with no points or day streaks, a bet on values that I own.