I've written about this in a past thread here about the Mongols impact on Islamic society and intellectual "openness" that might be of interest to you.

For the wider answer that takes you from around 1258 and the sack of Baghdad to our 20-year-rule-limited 1996 end-date...it's complicated.

For one thing I would step away from "most progressive" and "pro-science&math". The modern progressive movement is self-consciously oriented towards achieving their conception of "progress." Historically, for the early 20th century "progressives" that included all kinds of things that we now regard as being morally suspect like eugenics and racial purity, but the point is that they were enacting a positive program to achieve their aims along these lines.

That's not really what was going on in Islam. Tolerance might be a better word for what they practiced, and even that has to be couched in terms of tolerance within the Islamic legal and the dominant Arab social framework of late antiquity and the early medieval period. But the result is that, yes, from a modern perspective, and in contrast what was being done to perceived heretics in Europe, or the persecution of Jews, the treatment of minorities in late antique or medieval Islamdom looks a lot more tolerant of religious and to a certain extent intellectual diversity than what you would find in the equivalent time period in Europe.

But the reason why I don't think that line of analysis is particularly useful is because if you were to compare the status of religious minorities in Islam in, say, the year 800 to what existed in the Ottoman Empire in, say, 1800, it wouldn't look profoundly different. Admittedly I'm by no means an expert in the intricacies of the Ottoman millet system (which allowed for an individual's religion to determine the personal law that applied to him) but conceptually not a whole lot changed).

Rather, it's that Europe moved on to a profoundly different framework for judging the treatment and status of minority groups. Liberty, egality and fraternity are potent standards of judging ones "freedom" that frankly the Islamic intellectual elite, when Napoleon first showed up in Egypt in 1798, just didn't agree with.

In terms of science and math it's an interesting point and I think it has to be discussed in relation to a few things:

A: The fact that most of the Middle East was colonized by people who did not prioritize the education and advancement of colonized peoples. This includes the Ottomans who, despite having printing presses of their own in Istanbul, did not allow an Arabic printing press in their Arab territories. This would not be introduced until Napoleon. The situation arguably gets worse when Europeans start actively taking over the region, particularly in comparison with how Europeans treated and funded their own domestic educational systems.

B: Even if these territories failed to adapt to intellectual and technological developments, I think you would be hard pressed to say that that was a result of being anti science and math. After Napoleon's withdrawal from Egypt in 1801 the Ottoman empire and the soon-to-be pseudo-independent Egypt under Muhammad Ali Pasha basically enacted crash modernization programs with European advisors and efforts at governmental, administrative and technical reforms. In Egypt I would argue that these were quite successful until the country's near bankruptcy and subsequent occupation by Britain in 1882. Khedive Ismail was not being absurd when in 1879 he said "My country is no longer in Africa; we are now part of Europe." And he had the railways and urban boulevards and slick western suits to show for it.

C: The combination of A and B is that I don't think there's really a point where you can point to where the Islamic world sort "stopped doing science" or something. It's just that the pace of change in parts of Europe started accelerating quite profoundly.

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So that's quite a slapdash run through of about 1000 years of Islamic intellectual history, but I think if I had to sum up it would be that I would hesitate to say that the pace of intellectual or technological life in the Middle East "stagnated" or even "plateaued" but rather that Europe was just really unusual in that that pace started to accelerate. And then under Ottoman and European imperialist efforts in the region you actually have active efforts to prevent the development of an educated populace. That's inevitably going to slow the development of economic progress in a world where development is largely predicated on education and literacy, even among the working class.

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As a separate discussion on 20th century Islamism, because I think this is incredibly misunderstood, I'd also want to separate out western notions of progressive social life from being connected with acceptance of science and mathematics. That's just not how the ideology of Islamism works. When Hassan al-Banna founded the Muslim Brotherhood he did so, yes, as a society of conservative religious revival, but also to promote mass education and to found schools, which remained a major activity of the Brotherhood's charitable efforts throughout its history. Support for the Brotherhood has always been strongest, not among the uneducated, but among the professional classes, including a very large number of scientists. The same is true even for certain extremist groups. I don't think I'm breaking the 20 year rule in pointing out that, in 1996, what would eventually become known as the Hamburg Cell of al-Qaeda were enrolled as engineering students in the Technical University of Hamburg. Ayman al-Zawahiri has a masters degree in Surgery. Osama bin Laden had a degree in Engineering. etc. etc.

While I think many Western commentators would argue that without intellectual and social freedom you will inevitably stunt societies educational and scientific advancement, and that may be a valid concern, it does not mean that people who are opposed to Western notions of social freedom are, ipso facto, opposed to the latest scientific and technological advances.

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Sources: Whew boy how do I provide sources to describe about 1000 years of societal development? I should first mention what I left out, which is, my God, everything. I haven't touched on Arab nationalism and its results on attitudes towards religious and ethnic minorities. I alluded to but did not directly discuss the role of women in modern middle eastern societies. I haven't talked about non-Middle Eastern Islamic societies like Indonesia or India and as such I should caveat this by saying that the above applies more specifically to Islamic societies in the Middle East rather than to Islam as a whole. I would personally argue that it has almost no bearing on individual muslims given the success of muslims as a group in Western European and American societies. Nor did I discuss whether it's entirely valid to assess religions or cultures in this way, and although you didn't mention it in your question its that much of these assumptions are based on Europe's power to use technology and science to militarily dominate societies less martially advanced and whether that's valid. There's a lot more I've left out. It's a very complicated question as I said at the top.

That being said, some books that I think might be useful:

I've been reading John Darwin's After Tamerlane lately which I think offers a very good discussion of the relative geo-political positions of European and non-European societies from the 15th century to the 20th. It does quite a good job in dispelling absolute notions of European superiority in science and technology, or at least insofar as that was able to be applied for imperial power.

Timothy Mitchell's Colonizing Egypt for a discussion on colonial policy in that country.

I don't often recommend this book because I disagree with many of its conclusions but your question is very much one where a familiarity with Edward Said's Orientalism would be useful.

The best one-volume modern history of the region I've come across and that I recommend here often is Eugene Rogan's The Arabs: A History.

For modern Middle Eastern intellectual thought see Albert Hourani's Arabic Thought in the Liberal Age: 1798-1939.

For the Muslim Brotherhood's ideology and early history see Richard Mitchell's The Society of Muslim Brothers.

For Islamism more generally, and its relationship on western conventions and society, much of his work leans towards contemporary politics but Shadi Hamid does better work on this anyone I've come across. I haven't finished it, but his book Temptations of Power: Islamists and Illiberal Democracy in New Middle East is very much on-point from the portions I've read.

For the older medieval stuff I would look at my previous thread, as well as Marshall Hodgson's three volume The Venture of Islam.