Godel's Theorem

[WoodenPupa]

Can anyone summarize Godel's incompleteness theorems in something that resembles layman's terms? I'm not formally educated in mathematical theory so I am somewhat limited as far as what I can comprehend when gaggles of math jargon are used. However I do enjoy the subject and I can figure out some of the stuff with enough effort. Godel's theorem however has really eluded me; so far I haven't encountered an explanation with enough meat---it's way too abstract.

It seems to indicate something along the lines of, for any given mathematical language, there will always be a statement within it that cannot be proven or disproven. That's about all I can decipher. Can anyone help with this?

 

[Witling]

I can't explain Godel's theorem but, I commend the book Godel, Bach, & Escher to your attention. I think it's as close to a non-technical explanation as you're going to get.

 

[WoodenPupa]

I was afraid this would be the case. Thanks for the book recommendation. I'll check that out.