No, I do not possess deep historical knowledge. I was asked a question, which I answered using facts I've gathered from my reading, with some Googling added into the mix. Disproving examples provided by an amateur does not amount to much I'm afraid.
Still, I will attempt to respond to your rebuttal using what little knowledge I have.
> There is no reason to believe that Khayyam discovered Pascal's triangle, it's much older.
A cursory glance at the article you linked shows that Khayyam was the first to formally define Pascal's triangle. However, the main issue in my view is that everyone still refers to it as Pascal's triangle, even though as you say there is evidence which proves that Pascal was not the first to discover it.
> Heliocentrism was discussed by the ancient Greeks and predates Khayyam by over 1000 years
Yes, I was aware that the Greeks tackled the issue of heliocentricity, but I added that point in the context of Copernicus. In addition, I did not state that he was the first.
> Infinite series were known to ancient Greek Archiemedes
I was not aware of Archimedes' work with infinite series'. This would have been a better reference though: https://en.wikipedia.org/wiki/Series_(mathematics)#Developme....
> the ancient Greeks already knew about some geometrical objects that we now recognise as being non-euclidean. The first to recognise non-euclidean geometry in a nearly modern form might have been Gauss
I like how you perform the same jump in time I talked about in my original comment. So essentially, when it comes to the development of non-Euclidean geometry, Greeks -> nothing -> Gauss. Are you really saying that that's how it developed?
> We must remember that almost all Greek material is lost [...]
Why did you need to write a whole paragraph on how much of the Greek's work was lost? That's irrelevant; the only thing that matters is that the Islamic scientific movement preserved Greeks works. I kind of feel you added that just to undermine your previous statement.
> I suspect that like Renaissance Europeans, medieval islamic scholars were at pains to cover up just how much they got from ancient Greece.
Regarding attribution, on the contrary, Muslim scientists were actually quite open about how extensively they based their work on that of the Greeks, especially in the field of philosophy. The same definitely cannot be said about the early Renaissance scholars.