*Membership spots not really limited!
Except the field of Mathematics could only truly flourish in an environment that was afforded by things like democracy, freedom of education and rule of law to protect the rights of individuals. That small handful of people of all skin tones aren't welcome to work on their Math in the Arab world, they do that research mostly in Europe don't they?
What did the Arabs do with their arithmetic? Did they invent mills or internal combustion machines? Did they develop manufacturing or do they just play technological catch up with other cultures who took the Arab contribution to Math and developed it's potential far beyond their wildest dreams?
i don't know where you are getting your history from, but at the time the arab mathematicians "did their thing," europe was in worse shape as far as mathematical/scientific research is concerned. there was a span of several hundred years to almost a thousand years between the arab contributions i was referring to and the industrial revolution that brought us the internal combustion engine! most people who do work in mathematics recognize the cumulative nature of mathematics and how much time and effort is really necessary for mathematics to bear fruit in the real world, especially if mass communication and public education was unavailable at the time.
you glorify the romans, but you don't acknowledge the arabs who carried the torch after the decline of the romans. the argument you wrote in your last paragraph is just silly. it would be absurd for me to write in any seriousness, "what did the romans do with their dysfunctional arithmetic? did they invent mills or internal combustion machines?" people sometimes feel like they're brilliant looking in hindsight, but looking forward is another matter. how many engineering applications of pure mathematics have you come up with given the benefit of having all of this mathematics and science from the ancient world spoonfed to you when you were in school? today, as well as in the ancient world, only a small handful of people actually make significant contributions to this body of knowledge.