--- title: "Writing a Proof Someone Else Can Check" description: "A written proof is a claim about what a reader can verify, not a record of how it was found. Announced structure, named hypotheses and explicit quantifiers are what make it checkable." canonical: https://lightmysky.com/learn/mathematics/writing-a-proof-someone-else-can-check-mt_nZ-zMzj18N source: https://lightmysky.com/learn/mathematics/writing-a-proof-someone-else-can-check-mt_nZ-zMzj18N.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Writing a Proof Someone Else Can Check A written proof is a claim about what a reader can verify, not a record of how it was found. Announced structure, named hypotheses and explicit quantifiers are what make it checkable. Subject: Mathematics · Area: Mathematical Thinking · Ages 22 to 23 Page: https://lightmysky.com/learn/mathematics/writing-a-proof-someone-else-can-check-mt_nZ-zMzj18N ## Ready when they can - Write a proof whose structure is announced in the first line - Name the hypothesis at the step where it is used, not in a preamble - Rewrite an argument that hides a quantifier so the order is explicit ## Lesson: Writing proofs a stranger can verify A written proof is a claim about what a reader can verify, not a record of how it was found. Announce the structure in the first line: name the method, such as direct, contradiction, or induction, and state the claim. Theo opens well: we prove by contradiction that root 2 is irrational, and suppose root 2 is rational. The reader knows the plan before any deduction starts. **Example.** Name each hypothesis at the step where it is used, not only in a preamble. To conclude n is odd from n being prime above 2, write: since n is prime larger than 2, n is odd. A preamble list alone lets uses hide. Likewise write: taking limits, by continuity of f at c, f(xn) converges to f(c). The reader can then check that exact step on the spot. Make every quantifier explicit and keep its order. Over the integers, for every x there is a y with y above x is true, with y equals x plus 1 as witness. Reversing the order claims one single y above every integer, which is false. If X then Y says X suffices for Y and Y is necessary for X: mixing the directions breaks proofs, especially in if and only if arguments. **Tip.** State which direction each step proves, and revise by reading the draft cold. Check that each line uses only named facts: a definition, a hypothesis, or an earlier line. When a step feels obvious, spell it out, since obvious to the writer is where readers get lost. A proof that hides a quantifier should be rewritten so the order is explicit. **Recap.** Announce the plan up front, cite each hypothesis where used, and write quantifiers in order. ## Practice 14 questions on this page, each with its working shown. ## Needs first - [Reading a Mathematics Paper](https://lightmysky.com/learn/mathematics/reading-a-mathematics-paper-mt_pTF-HzLWE6) - [Statements, Quantifiers and Negation](https://lightmysky.com/learn/mathematics/statements-quantifiers-and-negation-mt_S5NvyPxEZ_) ## Opens up - [Definitions as Design Decisions](https://lightmysky.com/learn/mathematics/definitions-as-design-decisions-mt_b6ip8eP0-d)