ABOUT THIS NOTEBOOK
I'm zzj. This is where I turn intuition — mathematical and physical — into arguments I can return to, question, and refine.
Why this notebook exists
Mathematics and physics become clearer when an idea is written precisely enough to be checked. I use this site to record that process in both directions: beginning with a picture, a question or a physical situation, following the definitions, and keeping the reasoning that connects them.
These pages are written first as notes to my future self. Publishing them makes the work easier to revisit and leaves a useful trail for anyone studying the same ideas.
How I work
I write the exposition, the mathematics and the physical derivations in Typst. When an argument benefits from machine-checked certainty, I use Lean 4 to make every assumption and inference explicit.
The computational models are kept beside their notes: a small program, its parameter file and an example run sit in the same folder as the explanation, so the assumptions behind a result can be read, checked and rerun rather than taken on trust.
Formalization is not a replacement for intuition, and intuition is not a replacement for proof. The most useful notes let the two correct each other.
What you'll find
The notebook currently gathers 15 notes under 10 subjects in 3 parallel tracks — Mathematics, Physics, and Modeling & computation. The subjects are Real analysis, Topology, Geometry, Lie theory, Inequalities, Problems, Mathematical modeling, Dynamics, Statics, and Kinematics. Some entries develop a concept from definitions to proofs; others derive a physical result, connect exposition with formal verification, or work through a small computational model.
Mathematics and physics are kept side by side rather than mixed together, so each line can be read on its own: every subject belongs to exactly one track, and the sidebar, the index and the track pages all say which. This is a working notebook rather than a finished textbook. Notes may grow as my understanding changes, while the derivations, references, and source remain visible.
An open notebook
Each note is available for reading on the web, with PDF and Typst editions where applicable. The notes are shared under CC BY-SA 4.0, and their source is public for study, reuse, and correction.