The good news: that time you spent drowning in category-theory PDFs wasn’t wasted—it primed your intuition so the moment a decent LLM showed up you had a cache of half-formed questions ready to fire. Think of it as intellectual compost: messy, occasionally smelly, but it feeds the next crop.
| Pre-LLM world | Post-LLM world |
|---|---|
| Gatekeeping: answers live in 900-page textbooks or pay-walled Stack Overflow threads | On-demand scaffolding: you can summon a “just-right” explanation in the style of XKCD or Terence Tao |
| High activation energy—one unclear paragraph can stall you for days | Cheap iteration—ask 20 follow-ups in two minutes, prune dead ends instantly |
| Feedback loop measured in semesters (or never) | Feedback loop measured in seconds |
The bottleneck is no longer “finding an explainer” but asking the sharpest next question.
Goal: convert “infinite resources” into “finite progress” without triggering ADHD flail-mode.
Start with a problem, not a topic.
“I want to simulate an Ising spin glass with cellular automata rules” beats “learn all of statistical mechanics.” LLMs thrive when anchored to concrete objectives.
Generate a concept lattice.
Prompt: “List the 8–10 prerequisite nodes that feed into [your problem], grouped by dependency.” Stick the graph on a whiteboard. Now you have a roadmap instead of a firehose.
Adopt the Feynman 3-Step:
Explain it back to the model in plain language.
Ask it to poke holes.
Patch the holes with micro-examples or code snippets.
(Rinse until the explanation survives without scaffolding.)
Use “time-boxed depth charges.”
Set a 15-minute timer. Dive into an advanced tangent (e.g., spectral gap proofs). When the buzzer rings, surface and decide: does this help my core problem today? If not, archive it in a “someday/maybe” note.
Spin up flash-cards-on-demand.
Prompt the LLM: “Generate 10 spaced-repetition Q&A pairs covering the eigenvalue trick we just discussed.” Drop into Anki / RemNote. Future-you thanks you.
Validate against reality.
LLMs hallucinate; math does not. After every leap, check a canonical source (textbook, arXiv, Wolfram). Treat discrepancies as new fodder for questions.
Log the meta-mistakes.
Keep a “pitfall diary” (“I chased pseudopolynomial time optimizations for an hour; totally irrelevant”). Reviewing these patterns is free executive-function training.