Gödel's incompleteness theorem

Melvyn Bragg's program 'In Our Time' on Radio 4 (Thursday's 9am) is an endless source of fascination. Last week it was the story how ancient Greek manuscripts were translated into Arabic in the 900's and eventually came back to Europe 200 years later. Some of them were still used as medical texts 100 years ago. And today it was the turn of Gödel. He is more modern. A brilliant mathematician called David Hilbert and a whole team of brais were trying to prove that number theory (1+1=2 etc) was consistent. They were slaving away for 30 years when Gödel popped up and proved that they were wasting their time.

1) You cannot prove that there are no contradictions in number theory.

2) There are true statements about numbers that you can never prove are true.

Poor old Hilbert never published anything on the subject again. You can listen to the program here.

Gödel also discovered a rotating universe solution to Einstein's theory of general relativity where time travel is possible - let's hope the universe is rotating!

Comment
It all sounds very interesting, but I'm not sure I have a clue. But, mostly, I dislike Melvyn Bragg. Probaly put off then by the 1st 2 words!
Posted by: Paul | October 10, 2008 at 03:14 PM

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