I thought about this after writing, "Where Did All The Cool Black People Go". I'm doing this completely free of research. I will research it later, but for now I want to write about it from my impressions at this moment. Perhaps many of you will get the same impression?
 
Personally, I can't think of one cool Arab Muslim person? Muhammad Ali was cool but  a Black American. Nope not a one that fits the bill?

So lets take it from a cultural point of view.

Literature
The Koran- not cool.
The ancient Arabic history  of their literature reveals they had a huge library of literature. Most of it was done by the Persians (now in Iran) who are not Arab at all. Regardless, within our cultural sphere it appears to be pretty sparse.

Fashion
Burka for women white robe for men. The rich Arabs get  have gold encrusted cuffs and an Arab hat with a gold woven rope around it. Golds cool, but not necessarily the man.

Movies
Lawrence of Arabia was a classic film. It starred Omar Sharif, very cool, but he was French-Arabic and a Roman Catholic. Can't think of anyone else except that guy from Lost. Ah shit, he was born in the UK and is actually of Indian origin.

Music
They did develop some fairly good music and their musical scales are interesting, however they learned it from the Greeks. They do have a rich musical history but I can't think of one cool song or person that is both Arabic and Muslim.

Religion
Definitely not cool.

Sports
 Definitely some cool American Muslims involved with sport. I can't think of one that is Arabic as well though.

Art and Architecture
Wow! Loaded with splendid art superb architecture. I can't think of anyone recently however, and near my home they are building a Mosque that resembles a huge prison. The thing is  twelve inch concrete all around with tiny little windows. I get the impression it's more of a terrorist training camp than a place of worship. I was invited to a smaller one a few years back to do an estimate. I wasn't allowed to wear shoes. My contact brought me to the class rooms, on the walls were pictures of their war heroes sporting automatic weapons. Maybe the kids there think they are cool Arab men?

Science and Math
They did contribute quite substantially to the sciences. They gave us algebra. Some science is very cool, but algebra? No.

Socially
I know at least here in Canada there is a problem with assimilation. The Muslims I have dealt with are very polite. I encourage my children to play with the Muslim boys up the road as they are very well mannered. Their parents send us cakes after their religious events. Very nice people actually. Then there are the ones I don't deal with, they are rude in stores, show blatant disregard for authority and let their kids run wild. These are usually the black Muslims from Somalia. There are others who have a penchant for crime. Perhaps these ones are giving Muslims a bad rap? I've received some death stares from some Arabic looking dudes. They just look at me like I deserve to die. Could be considered cool in some circles. I don't know if they were Muslim though. 

Obviously, I have demonstrated my ignorance regarding cool Arab Muslim people. I know they must be out there, but I can't for the life of me think of one. Considering all that is happening in the Middle East and the wars we are engaged in I think it is about time we learn "who is the enemy?"
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This is pretty cool