Speed-learning mathematics proofs with a claude code prompts

2026-08-04

OK I am learning proofs.

Here is the substrate - three 1st year undergraduate units: MATH1011, MATH1012, MATH1014 and the book of proof by Richard Hammack.

For each unit you are given the unit handbook listing, the unit outline, and the unit reader (except 1014 -> [syllabus instead]).

MY PROBLEM

I find steps in proofs non-obvious.

YOUR SOLUTION

Here’s what I want you to do:

Write (7) proofs for EACH unit into (3) .md files + mathJAX and lyx (lyx if needded) (any appropriate tool calls allowed), Restricted to week1-week3 (week3 inclusive) content. In EACH of the proofs I want you to demonstrate useful techniques (tactics AND strategies). Strategies include overarching proof techniques such as proof by contradiction and proof by counterexample but you brainstorm appropriate strategies. Tactics are line-based and include lines such as: multiplying by conjugate, utilising an axiom mid-proof but brainstorm tactics yourself. In each of the proofs I want you to demonstrate a new tactic -> especially “non-obvious” tactics. By seeing these tactics one-by-one I can witness them and start to intuit when to use them - but I need to see it once!

The proofs are being assessed by a competent lecturer. Use minimum English and maximum mathematical symbology. Explain every mathematical symbol the first time we see it. Ensure the steps in the proof are formally expounded such that a university lecturer would grade it 100%.

Lastly, create a spaced repetition system for learning all the tactics included in the 15 proofs -> create mathJAX Anki flashcards. Two decks: One “proof tactics”: A flashcard for each tactic used. Two “proof strategies”: A flashcard for each technique/strategy used.

Success-condition/Verification

1. You have broken down the tasks and started.
2. You have read EVERY resource in this folder (just restrict reading to weeks1-3 for each unit to save yourself effort) - including the bookofproof.pdf (the orchestrating substrate) - the unit readers are supporting content.
3. You have brainstormed proof tactics and proof strategies to include to maximally enhance learning.
4. You have generated 21 proofs (7 for each MATH unit) - under each proof explain why it is beautiful <3.
5. You have formally written each 21 proofs divided into three .md +mathJAX & lyx document (labelled MATH1011.mg, MATH1012.md, MATH1014.md).
6. You have create TWO Anki spaced-repetition decks for review.

Stay tuned for an update on how I went learning proofs.