AI RNG: Practical Systems That Ship
Scratch work is honest. It shows the real path you took: the false starts, the simplifications that only worked after you made a clever substitution, the moment you realized a sign error, and the quick sanity check that saved you from a wrong conclusion.
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Notes are different. Notes are meant to be read later, possibly by someone else, and the goal is not to preserve the struggle. The goal is to preserve the structure: the definitions, the key steps, the dependencies, and the final reasoning.
AI can help you convert scratch into LaTeX quickly, but only if you keep control of the mathematics and enforce consistency in notation. The workflow below turns a messy page into a clean document you can trust.
Start with a notation table before you typeset anything
Most LaTeX notes fail because notation drifts. You use x for one thing early and for something else later. You change conventions silently. You forget whether an inner product is linear in the first argument or the second. The fix is to write a short notation table first.
Include:
- Symbols and their meaning
- Domain and codomain for maps
- Standing assumptions on parameters
- Any conventions that differ from common defaults
Even if you do not publish the notation table, building it forces consistency.
Extract the logical spine from the scratch
Your scratch contains many lines that were useful while thinking but do not belong in the final narrative. What belongs is the spine: the minimal chain of claims that leads to the conclusion.
A helpful way to extract the spine is to rewrite your work as a sequence of labeled claims.
- Claim A: the reduction step that reframes the problem
- Claim B: the key lemma or inequality that does the heavy lifting
- Claim C: the final computation or argument that closes the loop
AI can assist by turning your scratch into a list of claims, but you should insist that it does not invent steps. Give it the scratch and ask it to produce only what is explicitly present, with gaps marked as gaps.
Choose a LaTeX structure that matches the mathematics
Some notes are best as a sequence of short propositions. Others are best as a narrative with examples. The structure should serve the reader.
Common structures that stay readable:
- Definitions, then lemmas, then the main result
- A theorem with a proof, followed by remarks and examples
- A workflow page: problem statement, plan, proof outline, then details
A small structure map helps:
| Content | Best format | Why it works |
|---|---|---|
| A single theorem with dependencies | Lemmas + theorem | Makes the dependency chain visible |
| A computation-heavy derivation | Sections with checkpoints | Lets the reader verify step by step |
| A concept explanation | Definition → example → remark | Builds intuition without losing precision |
| A collection of exercises | Problem/solution blocks | Keeps each item self-contained |
Standard LaTeX moves that make scratch readable
Even when the math is correct, readability often fails because the typesetting hides the structure. A few standard moves fix most of that.
| Goal | LaTeX choice | Reader benefit |
|---|---|---|
| Show a multi-step derivation | aligned equations | The reader sees where each line comes from |
| Split into cases | cases format | The reader knows which branch they are in |
| Emphasize a key identity | display with a short sentence | The spine becomes visible |
| Separate lemma from proof | lemma + proof blocks | Dependencies become clear |
| Track assumptions | a short “Assumptions” paragraph | No hidden constraints |
AI can format these quickly, but you still check that the symbols are unchanged.
Make the mathematics KaTeX-friendly by default
If your notes will be rendered on the web, prefer LaTeX that is widely supported. Avoid relying on custom packages unless you know the renderer supports them.
In practice:
- Use standard environments like align, cases, and simple matrices
- Prefer clear notation over exotic macros
- Keep custom commands minimal, and define them explicitly
AI is good at rewriting equations into standard environments, but review the output carefully because small formatting changes can hide a mathematical change.
Use AI as a typesetting assistant, not as a proof generator
The safest use of AI in this context is mechanical:
- Turn handwritten steps into LaTeX with the same symbols
- Format aligned equations cleanly
- Rewrite paragraphs for clarity without changing meaning
- Normalize notation to match your notation table
Risky use is asking AI to fill missing reasoning. If you have a missing step, treat it as a separate proof obligation. Either prove it yourself or write it as a lemma that is explicitly assumed.
Add verification notes that future-you will thank you for
A small “verification” paragraph near the end of a derivation prevents future confusion.
Include:
- What checks you ran and what they confirmed
- Any boundary cases that require attention
- Any steps that depend on a specific hypothesis
This turns your notes from a polished story into a dependable reference.
A repeatable conversion routine
When you want speed without losing accuracy, use the same routine each time:
- Notation table
- Logical spine as labeled claims
- Typeset the spine first
- Insert supporting computations only where needed
- Add examples and remarks
- Add verification notes
With practice, you will find that the LaTeX notes are not just prettier. They are clearer, more reusable, and far easier to build on when you return to the topic later.
Keep Exploring AI Systems for Engineering Outcomes
• AI Proof Writing Workflow That Stays Correct
https://ai-rng.com/ai-proof-writing-workflow-that-stays-correct/
• Proof Outlines with AI: Lemmas and Dependencies
https://ai-rng.com/proof-outlines-with-ai-lemmas-and-dependencies/
• Writing Clear Definitions with AI
https://ai-rng.com/writing-clear-definitions-with-ai/
• Lean Workflow for Beginners Using AI
https://ai-rng.com/lean-workflow-for-beginners-using-ai/
• The LaTeX Notebook That Teaches You Back
https://ai-rng.com/the-latex-notebook-that-teaches-you-back/
Books by Drew Higgins
