Roman empire did not consist of Latin-speaking "Romans" only. It included Greece, North Africa and what we call now Middle East. Probably a majority of the inhabitants of the Roman empire were Greek-speaking. And there were mathematicians among them. Menelaus, Ptolemy and Diophantus were living in the Roman empire. Some of them could be Roman citizens, some not. We know practically nothing about their lives. Most likely all were Roman citizens after the citizenship was granted to all residents of the empire.
So the correct questions would be:
Why Roman mathematicians wrote in Greek?
Why most of them preferred Africa for their residence?
And the answer is that there was a tradition among the Greeks, in Greek language, especially in the Middle East, especially in Alexandria. Tradition means schools, libraries, scientific environment. This environment was created by the Greeks in the Hellenistic times, and partially survived almost to the end of the Roman empire.
By the way, many Roman works in applied sciences and engineering were also written in Greek.
See a related discussion here:
Greek was the language of science in the Roman empire. Like Latin was the language of Science in Europe in 16-18 centuries.
EDIT. We really know nothing about Diophantus, except the books signed with this Greek-sounding name. Where did he live? When did he live? His masterpiece looks completely isolated (nothing remotely similar before or after or around his time). Could he create all this out of nothing? Very improbable.
EDIT2. The question implicitly assumes that science and mathematics (in the modern sense) are necessary (or common, or desirable) activities of a civilization.
Far from it. There was no mathematicians in Rome. But there was also no mathematicians in Parthian empire, India or China at that time. Mathematics (in the modern narrow sense) was invented by the Greeks, flourished in the Hellenistic world, then declined and vanished, as an activity, and very little of it spread elsewhere. Why should one expect it in Rome, or in Londinium or in the Parthian empire? This was just some marginal activity of the Greek culture.
It is only recently (since 17th century) that mathematics became important and mathematical research spread widely.