All the mathematical prerequisites were there already. Let's say some Newtonesque mathematician invents it in the Roman Empire. Well what would happen? A timeline would be nice.
All the mathematical prerequisites were there already
With Roman Numerals? You'd need a major change to base 10 (or somesuch) first.
The Greeks thought this race would continue forever
This was not really the question.
Let's say someone invents the concepts of zero and infinity in 0 A.D. Then in 50 A.D. some smart guy invents Calculus. Well how does this affect the Roman Empire?
And even if, the only way without changing basically all of Greek thought is to POD with Archimedes. Let's say maybe Archimedes instead of dying at the Roman soldier's hands is taken back to Rome and is persuaded to establish a school there. And some of his pupils continue his work. (This is a major problem with the possibility of Calculus in the period. Archimedes did do a lot of the the background work and did himself have a good understanding of infinitesimals, but his work was practically ignored until the Byzantine period.) Now out of that you could get a limited Integral Calculus. But that departure is a bit earlier than what was requested.
There was no 0 AD. There wasn't even an AD 0.
Did Roman numerals have a way to represent nonintegers?
The greatest Roman contribution was the killing of Archimedes.
He, if anyone in the ancient world was to, would have developed calculus. His later works are the same as early questions in a calculus course. The most likely date for an ancient discovery of calculus would be from Archimedes.
Yes.. yes.. and no the everyday people thought it was wrong but they couldn't prove it, because when they also looked at the problem and split it into infinite steps like Zeno did they couldn't parse out that the race would have a limit and thus Zeno's mathematical proof that it would go on forever looked unassailable and stood for centuries. They did think it would go on forever when examined in Zeno's manner, and that's the problem when it comes to discovering calculus.