Lemma

Lemma opens PDFs of mathematics, statistics and computer science papers and textbooks, and makes their references navigable. Hover a theorem, equation or citation to preview it, or click to open it beside the line you are reading. It shows an outline of definitions, theorems and proofs, lets you fold proofs so you can try them first, and checks derivations you write in LaTeX. Notes and highlights stay tied to the passage, and can be exported to Markdown, Anki or Jupyter. It suits students and researchers who read dense technical books. The README says the app has no account and no analytics, and goes online only for actions you choose, such as downloading a free book or searching arXiv.

It requires macOS 15 or later, on Apple silicon or Intel. The README says this build is not yet notarized by Apple, so the first launch needs Done, then Open Anyway under System Settings, Privacy & Security; you do this once. Asking an assistant sends the selected passage to that service (ChatGPT, Codex, Claude Code, or an API provider) using your own account or key.