University of Connecticut

Events Calendar

Math Club
Hilbert's 2nd Problem
Damir Dzhafarov (UConn)

Wednesday, November 6, 2019
5:45pm – 6:35pm

Storrs Campus
Monteith 226

In mathematics, a proof is a sequence of logical steps that ultimately start with axioms, which are the basic mathematical "facts'' considered elementary enough to require no further justification Hilbert’s second problem asks if certain commonly accepted axioms are consistent, meaning that they do not lead to contradictory results (like proving the Pythagorean theorem is both true and not true). This problem was an earnest attempt at making sure we can be confident in mathematical results.

There is good news and bad news. The good news is that since Hilbert posed his second problem almost 120 years ago, the axioms of arithmetic have not been found to be inconsistent. The bad news is that no proof of this consistency in the form that Hilbert envisioned is known and, in a certain sense, no proof can ever exist. This follows from Goedel's 2nd incompleteness theorem, which extends beyond arithmetic to many axiomatic systems used throughout mathematics. What does it mean to prove that no proof of something can exist? For this, and pizza, come to my talk.

Note: Free pizza and drinks!


Keith Conrad

Math Club (primary), UConn Master Calendar

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