Claudius Ptolemy, a pioneering astronomer and mathematician, is the shining exception to the rule that theoretical pursuits like mathematics did not flourish under the Romans.

As I noted in a post I made earlier today, there are three basic reasons (I think) for this underperformance:

First, theoretical inquiry was never prevalent in the ancient world - the only place approximating a center of mathematical study in classical history would probably be the Library of Alexandria under the Ptolemies, a royal prestige project with no equivalents (besides the competing Library of Pergamum). Although the Library of Alexandria remained open through at least the first three centuries CE, the Romans never funded it in the way the Ptolemies had, since they had no political reason to do so.

Second, the Romans - though seldom actually hostile to scientific advances or inquiry - did not really encourage it. There is a(n apocryphal) story in Petronius' Satyricon that nicely illustrates this attitude:

"But there was once a workman who made a glass cup that was unbreakable. So he was given an audience of the Emperor with his invention; he made Caesar give it back to him and then threw it on the floor. Caesar was as frightened as could be. But the man picked up his cup from the ground: it was dinted like a bronze bowl; then he took a little hammer out of his pocket and made the cup quite sound again without any trouble. After doing this he thought he had himself seated on the throne of Jupiter, especially when Caesar said to him: 'Does anyone else know how to blow glass like this?' Just see what happened. He said not, and then Caesar had him beheaded. Why? Because if his invention were generally known we should treat gold like dirt." (51)

This never happened - but the story illuminates the Roman tendency not to meddle with the status quo. Lacking any conception of our idea of progress, the Romans never emphasized pursued theoretical inquiry (mathematical or scientific) with the aim of advancing technology.

Finally, and I think most importantly, Greco-Roman culture in the imperial era was characterized by great veneration for the past, and especially for literary classics. It was more socially prestigious to comment on, compile, and refine the works of respected authorities than to innovate.