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!

2 Comments »

  1. 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.

  2. 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!”

RSS feed for comments on this post · TrackBack URL

Leave a Comment

You must be logged in to post a comment.

The Math Factor Podcast Website


Quality Math Talk Since 2004, on the web and on KUAF 91.3 FM


A production of the University of Arkansas, Fayetteville, Ark USA


Download a great math factor poster to print and share!

Got an idea? Want to do a guest post? Tell us about it!

Heya! Do us a favor and link here from your site!