"Let the author speak for himself. From page 7, "Gödel's 1931 work on incompleteness, Turing's 1936 work on uncomputability, and my own work on the role of information, randomness and complexity have shown increasingly emphatically that the role that Hilbert envisioned for formalism in mathematics is best served by computer programming languages[.]"

Imagine if a working composer wrote, "Bach's preludes and fugues, Beethoven's symphonies, and my own string quartets have shown increasingly emphatically..." This man's reputation in his declared field is nowhere near his apparent stature in his own mind. The ideas discussed in this book are worthy of late-night musings over a nice brandy, or maybe a Scientific American article, but only after extensive revision. They are not ready for publication in a monograph. "

I might even recommend Schneier as the poster-boy of healthy entrepreneurial self-promotion.

Really? He is one of the coinventors of Kolmogorov complexity, and Kolmogorov complexity certainly does shed a lot of light on the relationship between information, randomness, and complexity. While he is clearly a big ego and a shameless self-promoter, I think it's also fair to say that he is among the foremost experts on K-complexity and related topics.

Here's Chaitin's layman's description of his theory:

http://plus.maths.org/issue37/features/omega/feat.pdf

His book about getting there:

http://arxiv.org/PS_cache/math/pdf/0404/0404335v7.pdf

And the halting problem thrown in for good measure:

http://en.wikipedia.org/wiki/Halting_problem

BTW, if someone wants karma, I haven't submitted any of the other Chaitin links. The book, at least, would probably be worth something.

I am pretty much mathematically illiterate but I am still enjoying his book immensely.

http://www.umcs.maine.edu/~chaitin/unknowable/ch6.html

EDIT

The definition of randomness he uses is the same as Kolmogorov's, something that has a description as complex (containing as many bits) as itself. So, when Chaitin says math is random, he means the basic truths of math cannot be reduced to a simpler system. Godel said such truths exist, Chaitin says they permeate all of math.

A Theory of Everything was meant in the physical sense. One that fully describes the nature of spacetime (or what appears to us as spacetime).

Obviously the above can't be true. You can't have a consistent and complete theory, come on, that's Godel already.

This is exactly what I'm saying. Chaitin might have a clue to what he's talking about, but obviously the author has nought. I rest my case for people to stop upmodding the article. You may not know it's sensationalist and innacurate, so I'm just letting you know.

I thought we wanted to avoid articles like this on HN?

EDIT: Parent edited his comment.

EDIT2: What basic truths? The only "basic truth" is first-order predicate logic. After that you assume some axioms (ZFC), and then it's not basic anymore. If you had used different axioms, you'd end up with a different mathematics, .e.g.

http://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Bernays%E2%...

Anyways, here's what I gather the article is saying:

Pysics depends on maths. Godel's incompleteness theorem (GIT) doesn't necessarily impact physics because physics can just use the untouched part of maths. However, Chaitin says his Omega number impacts all of maths with the same kind of consequence as GIT. Therefore, physics and the TEO is in trouble no matter what part of maths it uses.

He shattered mathematics with a single number. And that was just for starters, says Marcus Chown.

Certainly reading about uncomputable numbers like Chaitin's constant is interesting reading, but my case is that this article is not the right start.

Anyways, foundations and information theory isn't my area of research, so I'll leave it at that.

Anyways, they are saying different things from what I can tell, as mentioned in the edit. So, I'm not seeing the case that the article is innacurate.