Emphasis on Language Precision
A standout section compares everyday English vs. mathematical statements:
As the student types, the linter checks for:
Before we add extra resources, let’s establish the foundational pillars of 18.090. Emphasis on Language Precision A standout section compares
The Mistake: Assuming the negation of the conclusion but never deriving a contradiction—instead, you derive the original premise and call it a day (which is actually a direct proof). Extra Quality Fix: Explicitly write "We assume ( \lnot B )" at the start and "This contradicts ( A ) because..." at the end. If you cannot name the contradiction, you haven't finished.
The official 18.090 problem sets are notoriously challenging. But to get extra quality, you need additional sources. As the student types, the linter checks for:
1. The "Gold Standard" Problems from the Harvard Math 23a Archive Harvard’s equivalent (Math 23a) offers problem sets that focus on writing quality. Try this one:
"Prove that ( \sqrt2 + \sqrt3 ) is irrational." (Hint: Square it, then use the rational root theorem—a connection to algebra often missed.) "Prove that ( \sqrt2 + \sqrt3 ) is irrational
2. The MIT PRIMES Problem-Solving Database MIT’s PRIMES (Program for Research in Mathematics, Engineering, and Science) has a public archive of "proof readiness" problems. These are short, elegant, and brutal.
3. Generating Your Own Proofs with AI (Ethically) An extra quality modern technique: Use a large language model (like GPT-4) not to solve the problem, but to critique your proof.
The Proof Linter is an in-browser, AI‑assisted tool that analyzes student-written proofs (in a structured natural language + symbolic notation) and provides line‑by‑line feedback on logical validity, clarity, and common reasoning errors — without giving away full solutions.