Stephen Wolfram is a crank
There is no doubt that Stephen Wolfram is extremely clever^{1}. Sadly there is also no doubt that he is a crank. He may, in fact be the best example I know of why cranks are not just stupid people who think they are clever: cranks can be – and very often are – clever people. As I wrote yesterday
cranks don't realise when they don't understand something: for cranks, there are no known unknowns, all unknowns are unknown. [...] One group of people who very often become cranks are narcissists.
If you have used Mathematica, or read any of Wolfram's books you will very quickly realise that he's a narcissist. Mathematica is, on the whole, a very good tool, but the documentation for it is just nauseatingly crowing. Its documentation mentions almost no prior art: if you read only it you would believe that Wolfram invented much more than he in fact did. At least historically Mathematica's implementation also ignored prior art. Many symbolic languages predate Mathematica and much work was done on making them fast and sorting out their syntax and semantics. Mathematica simply ignored all of this, apparently because Wolfram thought he knew better. Even today the syntax and especially the semantics of Mathematica is a huge mess.
All of this is because Wolfram simply won't, or can't, listen to anyone else: because he's a narcissist.
Then we come to A new kind of science. Wolfram apparently thinks that he alone was responsible for the discovery that simple computational systems could give rise to complex behaviour. This is simply untrue, and it is also offensive. The idea of a universal computational system dates back to the ChurchTuring thesis stated independently by Alonzo Church and Alan Turing in 1936, roughly 23 years before Wolfram was born. Anyone who has written computer programs, especially in AI, understands that very simple rules can give rise to very complex behaviour, and this was understood long ago.
I'll give him the benefit of the doubt and assume that he simply does not understand what he's claiming and that his claim is far from new.
Recently he has resurfaced with an enormous paper proposing a computational model for physics. This paper has not been peerreviewed, and Wolfram has something interesting to say about that:
I don't really believe in anonymous peer review [...] I think it’s corrupt. It’s all a giant story of somewhat corrupt gaming, I would say. I think it’s sort of inevitable that happens with these very large systems. It’s a pity.
– Stephen Wolfram, quoted here.
If that sounds like every crank you have ever dealt with fulminating against the scientific establishment who are conspiring to suppress the cranks' brilliant theory, well, that's not coincidental: Wolfram is a crank.
It's easy to see how this happened. Wolfram is extremely smart, and has a background in physics. Like many people – like me – he then got lost in computing for a couple of decades – unlike me he made a lot of money at it, not least because he's much smarter than me.
Then he decided to come back to physics. But he's now spent a couple of decades in computing. Computing is a very immature field where:
 it's possible to do great things even while ignoring the work that has already been done because, comparatively, so little has been done – even I have occasionally managed to reinvent techniques which had been previously discovered, someone as smart as Wolfram can reinvent many of them, albeit often rather badly;
 there are enormous financial rewards to be had if you construct the right product at the right time, which rewards encourage the people who receive them to believe that they are gods and to behave the way rock stars do, for exactly the same reasons;
 there is no process of peer review, but rather employees whose livelihoods depend on you and who therefore treat you as if you were a god.
It's easy to see what happens: Wolfram is already a narcissist, and he's now spent twenty years lost in computing having his ego busily stroked by the people around him. He's now completely lost sight of the notion that computing is not all there is, and still more that there might be other people who might understand physics a little better than he does. He certainly does not want to hear what they have to say about his great masterwork, or at least he does not want to hear anonymously: he wants to be able to shout at them when they are rude to him.
As so often, Freeman Dyson put it best:
There’s a tradition of scientists approaching senility to come up with grand, improbable theories. Wolfram is unusual in that he’s doing this in his 40s
– Freeman Dyson, Newsweek, 27 May 2002 p 59, in a review of A new kind of science.

I am only not using the word 'genius' because I don't really know what it means. In fact I am not sure what 'clever' and 'stupid' mean either: people who thing of themselves as 'clever' are often very willing to call other people 'stupid' (or 'less clever' if they are pretending to be polite), but human intelligence is not linearly ordered in that way. ↩