## Hypergame! or I Stubbed my Toe on the Foundations of Mathematics |

**William S. Zwicker**

Union College

November 8, 2007

4:00 pm

Bailey Hall 201

Refreshments will be served at 3:45 in Bailey 204

In the early 1980s I was working on a test for a Gen. Ed. mathematics course I was teaching at the time, when a truly wicked idea for a bonus problem came to me. In fact, the more I thought about the idea, the nastier it got – I had stumbled across a new paradox in the theory of games. In my undergraduate logic courses I had learned about the fundamental importance of Russell’s Paradox (1903), which badly shook up researchers interested in the foundations of mathematics. Also, I had noticed some connections between Russell’s Paradox and proofs of two important results in mathematics: the set of real numbers is uncountable (Cantor) and the halting problem is unsolvable (Turing). So, I knew that paradoxes were more than just curiosities. But the feeling of being really confused by this new paradox was very different from that of reading about an old controversy. It was frustrating . . . and energizing at the same time. You may also feel a bit dazed and annoyed when you try to figure out this paradox. But that’s OK!

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