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... and zero mathematicians.
I don't have much faith in their selection process. Their list of economists includes the man who guided Russian economy into a 40% GDP drop.

>Yegor Gaidar, Russia, Economist, politician

>Gaidar was Boris Yeltsin’s acting prime minister from June 15 to December 14, 1992 and a proponent of “shock therapy” for the Russian economy.

You left out:

>He is a contributing editor to FP.

That should make clear both the quality and the nature of this publication.

So, who are some computer scientists (and mathematicians) that should be on the list? That is a loaded but honest question.
Grothendieck, Knuth, Paul Cohen, Terence Tao, Shing-Tung Yao.

In my opinion Godel was the greatest mathematician of the 20th century, but he's dead.

How can you possibly think that Grothendieck should be on a list of public intellectuals?
I'm not nominating anyone. I don't think being named to the list of "100 random names, compiled over a round of beers at a Foreign Policy office party, that make you sound sophisticated when you drop them" is a very high honor.
That's an interesting question. I think that the software world (distinct from CS or Math) does have "public intellectuals", though they are rarely known outside software. I'd say that Eric Raymond, David Heinemeier Hansson, Paul Graham, Joel Spolsky, Kathy Sierra, and Linus Torvalds are "public intellectuals" within this space. Many of these folks have impressive tech accomplishments, but people know who they are largely because they've read their writings/essays about software (ie., I'm distinguishing people who are known purely on the basis of code). It's very difficult to become a software public intellectual without reasonably impressive technical achievements, though I'd probably say Lawrence Lessig is in the club.
IMHO: Linus, Alan Kay, Alan Turing
I'm pretty sure that Alan Turing is dead...
ouch! That was stupid, thanks for the correction.
Marvin Minsky, John McCarthy and Donald E. Knuth,
There are two biologists, one physicist, one neuroscientist, and one medical scientist. The list is dominated by individuals with careers in politics, religion, literature, philosophy, and history.
I agree, a list of the Top 100 Intellectuals would be dominated by mathematicians, scientists, engineers, and probably a hacker or to, but this list is titled The Top 100 PUBLIC Intellectuals, i.e. public policy, so I wasn't expecting any different.
The title of the list is a gross misnomer. Half of the people on the list are political activists of some sort.

Take Barenboim. Why is he an intellectual? He is a fantastic pianist, a (IMHO) mediocre conductor and an activist for peace in the middle east.

Take Ayaan Hirsi Ali. She is a Dutch politician who build her entire career upon the fact that she has suffered a lot being raised as a female Muslim. She is definitely not what I would call an intellectual.

IMHO Mandelbrot, Prigogine, Mccarthy and Minsky should be on that list and by the way Baremboin was born in Argentina.
For better or for worse, the modern connotation of an intellectual is heavily slanted towards the matters of humanities and arts. I've had the pleasure of studying under some great computer scientists, but unfortunately, although geniuses in their field, very few of them could be considered an "intellectual" in the current form of its meaning.
Note that the list is of public intellectuals -- intellectuals who play a prominent role in public discourse. Most great computer scientists tend to stay out of the public realm, for the most part -- and perhaps with good reason.
The emphasis is obviously on the "public" more than the "intellectual." Witness Thomas Friedman's place on the list!
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I find it very hard to believe that Slavoj Zizek is better known, or more influential, than, say, Linus, RMS, PG, Joel, ESR or many others in our field.

Silly, vague, badly defined list.