EA. The Limits of Computation
One of the great discoveries of the twentieth century is that mathematics can describe the limits of mathematical thought! We’ll discuss some of these ideas from time to time in coming weeks. In this segment, we consider Alan Turing’s insightful question:
Can the answer to any mathematical question be computed?
We’ve also prepared a more comprehensive, much more subtle discussion here.
Of course we misspoke in the podcast when we said that Goldbach conjectured that every even number is the sum of two primes &emdash; 2 itself is not!
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dfollett76 said,
June 20, 2008 at 2:35 pm
I had the opportunity to teach my students some geometric proof this year. I told them that a postulate is accepted without proof and a theorem can be proved from postulates or other theorems. Therefore, a “theorem that can not be proved” is a contradiction. Did I teach them wrong or did Chaim mis-state Goudel? I look forward to hearing the next episode.
dfollett76 said,
June 20, 2008 at 2:44 pm
We know that Shaquille O’Neal would agree:
“Our offense is like the pythagorean theorem: There is no answer!”