ProofGPT-AI-powered proof assistant

Example

A user attempting to write a proof of the Intermediate Value Theorem might be unsure how to structure their argument. ProofGPT would suggest starting with a clear statement of the theorem, defining necessary terms like 'continuous' and 'interval,' and guiding the user through the steps to demonstrate the existence of a solution between given bounds.

Scenario

In real analysis courses, students often struggle with structuring their proofs. ProofGPT can help by clarifying the logical order of assumptions, conclusions, and intermediate steps, ensuring a clear and precise progression.

Example

A student faced with proving a number-theoretic result, such as Fermat’s Little Theorem, might be stuck on devising an approach. ProofGPT can apply Pólya’s problem-solving techniques, such as breaking the problem into smaller parts or working backwards from the desired conclusion.

Scenario

ProofGPT is particularly useful in heuristic problem solving, guiding users to identify auxiliary problems, spot patterns, or apply known theorems in new contexts—skills that are essential in fields like combinatorics, algebra, and number theory.

Example

When tasked with proving that a certain sequence converges, a user might be unsure whether to use a direct proof, proof by contradiction, or another technique. ProofGPT analyzes the problem and advises on the most effective technique based on the type of statement (e.g., a universally quantified implication).

Scenario

In advanced mathematics courses, such as topology or cryptography, students must choose the right proof strategy. ProofGPT helps by offering context-specific suggestions on which proof method to apply, whether it's a direct, contrapositive, or contradiction-based approach.