What a bizarre framing. Of course the Abbasids were influenced by other cultures, including Hellenic ones — they couldn't have helped it, since they were a Hellenistic culture themselves after Alexander the Great took over. Much of the "Golden Age" work was indeed dedicated to the translation of foreign texts (not only Greek, but Hindu as well) into Arabic so that they could be analyzed, commented upon, built-upon. Unlike, say, the Byzantines, the Abbasid scholars substantially enlarged and developed these ideas, and added their own in as well: they were not merely translating or maintaining, but were also building-upon and innovating.

Your instructor seems to have a strange view of what it means to be original. Under this guideline, literally nothing is original unless it somehow emerged out of a total vacuum (which nothing generally does). The Greeks themselves were very willing to credit their own philosophy and mathematical interests as emerging out of Egyptian and Babylonian advances, and credited many of the pre-Socratic innovators (Pythagoras, Thales, etc.) with having visited these regions of the world for their inspiration and learning.

Would your instructor also say that the Renaissance was "unoriginal" because it was based upon rediscovery of Greek and Arabic sources? It is hard to avoid feeling that this is some kind of weird denigration of Abbasid work, to state it in such terms. God forbid such an approach was applied to art, music, political thinking, or anything else.

There were some aspects of the Abbasid work that were definitely "extensions" of Greek ideas; there are others that are innovative and very un-Greek in their appearance. We should not waste time trying to separate out what was "original" from what was "derivative" — it is a pointless enterprise in such cases, and probably impossible in most. We can speak of influences, we can speak of cross-cultural communication, and we can speak of areas where significant impacts appear to have been made.

I can comment on Arabic philosophy, at any rate.

Scholars categorize medieval philosophy in different ways: Latin and Arabic, Christian and Islamic, etc. For the purposes of answering this question, we can talk about Arabic philosophy before Al-Ghazali (1058-1111) and after.

Before Al-Ghazali, the main Arabic philosopher was Avicenna (980-1037). Of course, there were others, such as al-Farabi and al-Razi, but Avicenna is typical of the approach during this period. Every single thing a philosopher believed in this period would have been inflected by Greek philosophy. This gives the impression that Arabic philosophy was not "original" and was an "extension" of Greek philosophy.

This impression is incorrect -- for a few reasons.

First, Arabic philosophers did not have complete works of ancient Greek philosophy. For instance, even much later in Arabic philosophy, Averroes (1126-1198) wanted to write a commentary on Aristotle's Politics. He was unable to even find a copy. Then, he settled for a commentary on Plato's Republic. He was unable to find a copy. Finally, he ended up writing a commentary on Galen's paraphrase of the Republic. This meant that Arabic philosophers were simply unable to be replicate ancient Greek philosophy -- even if they had wanted to.

Second, Arabic philosophers were often wrong about the authors of ancient Greek texts. The most important example of this is that they attributed to Aristotle a text by the Neoplatonist philosopher Plotinus. Plotinus often criticizes Aristotle. This led to some of the most important innovations in Arabic philosophy. Being prompted to synthesize Aristotle with someone who disagreed with him led to al-Farabi and Avicenna, for instance, inventing some of the most recognizable Arabic medieval doctrines -- all the while thinking that they are faithfully working out Aristotle's thoughts.

The most important difference between ancient Greek philosophy and Arabic philosophy is the introduction of Islam. Islam changes the intellectual climate of philosophy profoundly. God's omniscience, the resurrection of the dead, and the creation of the world in time are three ideas that ancient Greek philosophers, especially Aristotelians/Peripatetics, would not have been able to countenance.

And before al-Ghazali, Arabic philosophers didn't countenance them either. Avicenna, famously, denies God's omniscience -- which is something attested-to in the Quran. That being said, Avicenna qualifies all his claims in order to ensure that he gives the appearance of being consistent with Islam.

Al-Ghazali later pushes back on Avicenna and others, whom he saw as going too far in their endorsement of classical Greek ideas. Ghazali is a masterful philosopher and he wrote The Incoherence of the Philosophers, arguing that, for instance, God is the only true cause in the cosmos. This idea is an important innovation in the history of philosophy, and it would re-surface later in the European modern period.

The debate between al-Ghazali and his predecessors reveals a vibrant intellectual exchange that continues after his death. Averroes tries to pick up on Avicenna's ideas, and he wrote a reply to Ghazali called The Incoherence of the Incoherence. The fact that Avicenna then wrote significant commentaries on Aristotle's text shows the continuity of the themes discussed above, but the drastically different context -- now that there is pushback from different, pro-Islamic, and even pro-mystical corners -- shows that Arabic philosophy could not have been a mere extension of Greek philosophy, although it was influenced by it, partly because, as I've said, the Arabic understanding of Greek philosophy was so different from the reality of classical Greece more than a millennium earlier.

Sources and suggested reading:

M. Campanini, An Introduction to Islamic Philosophy (Edinburgh: 2008).

M. Fakhry, A History of Islamic Philosophy (New York: 1983).

S.H. Nasr and O. Leaman (eds), History of Islamic Philosophy (London: 1995)