On the Power of Proof: Characterizing the Gap Between Provability and Truth
OTHER MATHEMATICS DEPARTMENT EVENTS: MATH TABLE
When: April 30, 2025
4:30 pm - 5:30 pm
Where: Science Center 507
Address:
1 Oxford Street, Cambridge, MA 02138, United States
Speaker: Ava Zinman - Harvard
This talk seeks to distinguish between mathematical terms that provide a strong characterization of correctness; namely, proof and truth. We first formalize our motivating question, the Henkin Problem, and subsequently answer it by proof of Löb’s Theorem. Gödel’s 2nd Incompleteness Theorem, a corollary to Löb’s result, inspires the use of forcing to model ZFC-provability. We ultimately conclude that mathematical uncertainty stems from the inaccessibility of “natural” truth, which must be resolved by use of intuition.