Steamboat Pilot & Today

Everything I say is a lie.

Is that true?

If it is true, then it also must be a lie because I told you that everything I said was a lie.

Those who follow that train of thought and find it interesting will want to attend an in-depth discussion of Gdel's Theorem on Wednesday night.

Steve Craig, a math professor at Colorado Mountain College, will explain the complex mathematical statement to interested members of the community as part of the CMC Alpine Enrichment Program.

"I thought it would be fun to tackle this proof," Craig said. "I think it will be fun to get it to a point were it's easy to swallow."

Gdel's Theorem threw the mathematical world for a loop in 1931 when mathematician Kurt Gdel proved the statement: (x) ~ Dem(x,sub(n,13,n)). Through that statement and the proof leading to that statement, he showed that within math there are many statements that cannot be proven true or false without developing a larger system full of its own unprovable statements.

Gdel's Theorem was of great interest to philosophers and to members of the religious world because of its implications outside of mathematics.

The idea to present this theorem to Steamboat Springs came while Craig was taking a philosophy class from CMC professor Bob Baker.

"He asked me to explain Gdel's Theorem to the class, and I butchered it that day," Craig said. "Since then, I've spent over 100 hours on the proof. I had to sit down, break it up and tackle it in sections."

He has been studying the proof for more than three months in preparation for his lecture.

"This theorem really burst a lot of bubbles in the scientific and mathematic community," Craig said. Of course, it was the theoretical mathematicians who were shocked. The applied mathematicians, on the other hand, were comfortable with the way math worked. It allowed them to build bridges and engines, and they saw no reason to change it.

But for those who live in the world of definitions and possibilities, Gdel's Theorem was a bomb that went off in the center of their well-structured universe.

"What it did was make people steer away from the idea that math was true," Craig said. "But what it does for me is it makes me think that math is a part of a much bigger picture. To me, math has done a better job of explaining things than religion."

Craig plans to go over the proof Wednesday and then open the room to discussion.

"I like the idea of people expanding their mind by trying to understand something they may know nothing about," Craig said.

-- To reach Autumn Phillips call 871-4210

or e-mail aphillips@steamboatpilot.com