He claims that what he's shown in A New Kind of Science is revolutionary, but the revolution has yet to happen. Maybe he's the only one to really get it and he doesn't have enough time to better show "us" the way. It seems unlikely though.
OK, but that is not a mathematical claim. I thought you have a criticism of his mathematical claims.
I think NKS ist at least entertaining, more than what can be said for many other mathematicians work. And people are still wondering about the origin of life, seems to me NKS could do more to show that life is likely to emerge than many other approaches. It seems like a small thing, but maybe it is revolutionary after all, if no other approach is making any headway.
I personally don't have anything to oppose to the maths. Wolfram goes pretty deep, and nothing is obviously wrong, although some of it didn't feel right. This review, however, goes into the details:
http://www.cscs.umich.edu/~crshalizi/reviews/wolfram/
Search for "untrue" if you want to get there directly.
I enjoyed NKS as well. It's good intellectual stimulation, but the hyperbole was still annoying.
