From the reports I can read on that page, the citations refer to sentences of the form:

    CA produce complex/unpredictable results[n]

    [n] Wolfram, S. NKoS

So yes, it's referred to a lot but I don't see anything very deep.

I think the problem people have with this book is that it was hailed as the second coming before it came out and that SW had been in his basement for the past 5 years discovering CAs that ran the universe.

What it actually turned out to be was a thousand pages of examples/cataloguing CAs and the /suggestion/ that this is how the universe works rather than anything to prove it.

It also had a quite a large marketing campaign behind it.

Last I checked most objective scientific writing didn't come with a hype machine attached.

Citations seem a far more reliable positive indicator of quality than hype is a negative one.

People citing work would indicate that work's quality, but the complaint about "A New Kind Of Science" was weak citations, an indication of poor quality. I don't know much about the details. Nor do I know how much people have sited Wolfram's work since.

I think what upsets a lot of people is the attitude. But a bad attitude can still accompany good work, so I excuse Wolfram for his quirks. That acceptance is essential when dealing with people who know they are much smarter than the average person.

While at NYU, I saw Wolfram speak while on his big book tour. There were a few big brains at the Courant Institute that leveled major criticisms at the book. Unfortunately, there was another talk about nonlinear PDEs that most of the critics elected to attend in place of watching Wolfram. Wolfram started the talk by saying, "well, the important people aren't here to see this, but I suppose I'll continue anyway".

As one of the hoi polloi, I found the remark amazingly conceited, probably correct, and a bit charming at the same time.

wow that is incredibly naive. You think people in academia don't actively try to promote and position their work? Let alone the book and journal publishers, and conference organizers that have an obvious interest in all this.

Case in point: you're kovasb@wolfram.com, I'm not an academic.

Wolfram has used his business to unduly promote his research. There is a huge difference between him and a professor making the rounds.

What exactly is 'unduly' about it? Going on a book tour? Putting up a website?

That his research was funded through success in the market rather than government subsidies doesn't imply any 'unduliness' to me, but attitudes may vary.