I heard what he really said was;
"That's one small step for an American, one impossible dream for for anyone else who wants to give it a try"
What Arab Civilization?You state, "its mathematicians created the algebra and algorithms that would enable the building of computers, and the creation of encryption." The fundamental basis of modern mathematics had been laid down not hundreds but thousands of years before by Assyrians and Babylonians, who already knew of the concept of zero, of the Pythagorean Theorem, and of many, many other developments expropriated by Arabs/Muslims (see History of Babylonian Mathematics, Neugebauer).
I have a colleague from Romania who flew Migs in their Air Force and defected in the 70's. When I asked him why he wanted to be an American his memorable quote was "because the Americans are the only country on Earth who have had men $#!+ on the moon".