The Best Prompt Template
Copy and paste this template, filling in the bracketed [ ] sections.
Prompt:
Act as an expert in mathematical exposition and communication. I am writing a [blog post/paper/statement] about [Your Topic, e.g., "the concept of a continuous function," "the difference between countable and uncountable sets," "the idea behind group theory"].
My primary goal is mathematical rigor. Every statement, definition, and logical step must be 100% correct, precise, and unambiguous from a pure mathematics standpoint.
_> My second, equally important goal is clarity and accessibility. I want to strictly avoid complex mathematical notation (e.To, $\forall$, $\exists$, $\in$, $\subset$, $\sum$, $\lim$, etc.) wherever possible.
Please [help me draft/review and rewrite] the following concept.
My Draft/Concept:
[Paste your draft, your notes, or the formal symbolic definition you want to translate here. For example: "∀ϵ>0,∃δ>0 s.t. 0<∣x−c∣<δ⟹∣f(x)−L∣<ϵ"]
Your Task:
Translate: Rewrite my concept using clear, precise natural language (English).
Ensure Rigor: Do not simplify the meaning. The logical structure must be perfectly preserved. Point out and fix any logical gaps or ambiguities in my original text.
Define Terms: If a technical term (like "arbitrarily small" or "one-to-one correspondence") is absolutely necessary, define it in simple terms first.
Use Analogies (Sparingly): You may use a simple analogy or example only if it clarifies the concept without sacrificing any rigor. State clearly where the analogy might break down.
Target Audience: The final text must be understandable to [Your Target Audience, e.g., "an intelligent high school student," "an undergraduate in a non-STEM field," "a curious layperson"].
Why This Prompt Works
Sets a Clear Role: "Act as an expert in mathematical exposition" tells the AI to focus on explaining, not just solving.
States the Conflict: It explicitly highlights your two main goals: "mathematical rigor" and "clarity and accessibility" (avoiding notation). This forces the AI to balance them.
Provides Your "Work": The
[My Draft/Concept]section gives the AI the raw material to work with.-
Gives Specific Instructions: The numbered "Your Task" list breaks down how to achieve your goals.
"Translate" focuses on language.
"Ensure Rigor" prioritizes correctness.
"Define Terms" prevents jargon.
"Target Audience" is crucial. "A high school student" will get a different explanation than "a physics graduate."
A Simpler Version (For Quick Checks)
If you just have one short statement you want to check and rephrase, you can use this:
Prompt:
Please rewrite the following mathematical statement. You must preserve its exact rigorous meaning but use zero formal notation (or as close to zero as possible). The final version should be clear to someone who has never taken a university-level math class.
Statement: [Your statement here, e.g., "A function is continuous if the preimage of every open set is open."]
This prompt is faster and works well for self-contained definitions or theorems.