It puzzles me that the Romans had such a fruitful intellectual platform to build on with their conquest of the Greeks, but there were very few (that I can think of) willing to further develop on the ideas of Archimedes, Euclid, Hippocrates, Aristotle etc.
Of course, I could be completely wrong as there may be Roman pioneers who don't have the luxury of being household names. But they did have some famous regressive mathematical schemes, including architecture based on the premise that pi = 4.
All answers appreciated!
Ultimately the reason is that you're comparing the achievements of a single city (Rome) to those of the entirety of the central and eastern Mediterranean. Hippocrates, Eudoxos, and Aristarchos were Greek, and Aristotle was arguably Greek; but Archimedes was Sicilian; Hipparchos, Apollonios, and Galen came from Turkey; Eratosthenes came from Libya; Euclid, Diophantos, and Ptolemy came from Egypt.
Usually it's not unreasonable to think of them as Greek, because they wrote in Greek, and they were for the most part of Greek ethnicity, at least sort of. But for the purposes of a question like this, comparing "Greece" and "Rome" using them as examples, it'd be way too misleading. It'd be a bit like having a list of "British" scientists that included people like Richard Feynman, Edwin Hubble, and Ernest Rutherford, on the grounds that they all wrote in English and their home countries were settled by British colonists. That way madness lies.
So a large part of the reason for Greek dominance is: Greek was simply the lingua franca of the Mediterranean world. And the blame/credit for that is split between Greek colonisation and Alexander the Great. Even some intellectuals who were Roman or who operated in Rome wrote in Greek, like Krates and Sextus Empiricus, because writing in any other language would be like publishing a modern physics article in a language other than English. Sure, it happens, but not nearly as many people will read it.
That doesn't tell the whole story, of course: there were plenty of places in the Roman Empire away from the Mediterranean coast where Greek was not the lingua franca, and philosophers/biologists/mathematicians are thin on the ground in those places. The simplest answer to that part of the question, I think, is firstly that intellectual writing in the Greek language had a big headstart (thanks to colonisation and Alexander); and secondly that the Hellenistic kings tried their damnedest to create a blooming intellectual life on the model of places like Miletos and Athens. The Attalids and the Ptolemies in particular poured vast quantities of money into libraries, scholarship, and investigative survey work, and their shared language enabled a very rich flowering of elite intellectual culture.
Edit. By the way, I have a sneaking suspicion that that thing about Roman architects treating pi as 4 may be a myth. I know it's untrue in at least some cases: here's one case where Roman architects used the approximation 22/7, for example.