Study / Structure, proof & computation
Mathematics.
From a visible pattern to a precise statement—and the argument it needs.
Learning notebookMathematics begins to feel tangible when a definition becomes something you can manipulate. Two angles can trace a torus. A derivative can describe a local slope. An iterative rule can turn that slope into a sequence of guesses.
The optimization experiments compare multi-start gradient descent with a convex-model starting point. They keep evaluation budgets and original-objective measurements visible. A lower bound can help assess a candidate, while a flat convergence curve alone does not establish a global optimum.
The Goldbach workspace studies the statement that every even integer greater than two is a sum of two primes. Its notes separate exact identities, conditional arguments, numerical checks, and missing proof obligations. The workspace claims no proof or counterexample. A finite computation establishes what happened in its checked range; a universal claim needs an argument covering every case.
Questions to explore
Geometry from parameters
Use two parameters to describe a surface, then distinguish changing the geometry from changing its projection.
Optimization with evidence
Compare methods with reproducible starting points, disclosed budgets, and values measured on the same objective.
Proof & computation
Track exactly which claims a calculation supports and which step still needs a general argument.