Can’t Decide? Undecide!

I nmymathematical youth, when I first learned of Gödel’s Theorem and computational undecidability, I was at once fascinated and strangely reassured of our limited place in the grand universe: incredibly, mathematics itself establishes limits on mathematical knowledge. At the same time, as one digs into the formalisms, this area can seem remote from most areas of mathematics and irrelevant to the efforts of most workaday mathematicians. But that’s just not so! Undecidable problems surround us, everywhere, even in recreational mathematics!