THere weren't any scientists in Greece and Rome (the scientific method isn't developed until the early modern period), but high levels of education in philosophy (which included the study of the natural world) was absolutely required for success in Roman government.

All the top civilian elites in the Roman empire received similar training at various philosophical schools in different parts of the empire (Athens had some of the most famous schools, but most major cities had a philosophical school). These schools not only trained people in philosophy (which, in the Roman world, was a catch-all for math, astronomy, etc), they also allowed the wealthy students who could afford it to meet one another and form networks and friendships that they would maintain for the rest of their lives. They also trained their students in a particular way of walking, talking, and carrying themselves that marked them as the educated elite. This was crucial if you wanted a government career, because these manners were - up until the fifth century CE - the way you were expected to act when you approached the emperor and his top officials. If you didn't have the right education and training, and didn't have friendships with fellow classmates who could introduce you to the right people to get you in with the government, you were facing a very steep uphill battle if you wanted to score serious political clout.

What this means is two-fold. On the one hand, to be educated, you had to either already be part of the elite or have access to some serious financial resources, because attending a philosophical school was very expensive. So people with philosophical training did tend to live luxiourious lives - if they were poor, they never got in the door. But on the other hand, as a consequence of the necessity of a good education for success in government, the Roman empire was run by a bunch of people who had gone through the Roman equivalent of a graduate degree in the humanities. That is, the Roman empire was run by a bunch of over-educated nerds. Even when things broke down and the army started selecting the emperor during the third century crisis, this education remained really important - emperors who didn't know their literature, philosophy, and manners were much more likely to alienate the aristocratic senate and find themselves with a knife in their back.