L. Sprague de Camp wrote Lest Darkness Fall, in which a historian took over Rome a few centuries after this. Taking over wasn't his main priority, but rather ensuring that the dark ages got skipped. I'm not going to ROT13 the spoilers because similar ideas are going to be presented here.
Basic strategy was, 'invent' distilled liquor and base 10 arithmetic to gather capital. Use this to produce the printing press and the semaphore. By this point, he was influential, and used his foreknowledge of history to prevent a royal assassination and gain favor with that king. He never actually took over, but he was the man behind the throne for that king and the next.
And he didn't even need to be super-smart, though he did need to know the language, be reasonably lucky, and better at hand-to-hand combat than one would expect (if he had been super-smart he wouldn't have needed that).
A predecessor was A Connecticut Yankee in King Arthur's Court, whose influences (past and future) are currently detailed on Wikipedia. [Edit: typo, actualy mouso.]
A recent discussion post has compared the difficulty of an AI destroying modern human civilization to that of a modern human taking over the Roman Empire, with the implication that it is impossible.
The analogy has a few problems: first, modern humans don't have much greater raw intelligence than the Romans, only a bit more knowledge and tools; an AI would have a genuine intelligence advantage. Second, a high-tech civilization like ours offers many more ways for a genius to cause chaos than existed in classical Rome: it's more plausible that you can throw a few existing technologies together to create a superweapon than that Ptolemy could have done likewise, and there's no ancient Roman equivalent to hacking a nuclear launch system.
But taking over ancient Rome might serve as an interesting upper bound on the difficulty of an AI taking over modern civilization. And it's a theme of Harry Potter and the Methods of Rationality that rationalists should be able to come up with creative solutions to seemingly hard problems. So if Professor Quirrell offered it as an extra credit assignment, how would you take over Rome?
Here are the rules:
- You are thrown back in time to the year 1 AD. You can choose to arrive anywhere in the world, but your method of arrival cannot itself give an advantage (you can't appear in a flash of light in the middle of a religious ritual or anything).
- You do not start with Roman citizenship or any other legal record of your existence.
- You keep your original physical characteristics, including sex, height, and fitness. You will appear in period-appropriate dress of your choosing, and can't carry any artifacts with you. You may start with enough money to live a patrician lifestyle for a year.
- You are intellectually near-perfect. You know all human knowledge as of 2012. You speak fluent Latin (and all other languages of the day) and can orate as eloquently as Cicero or Demosthenes. You are a tactical genius of the order of Caesar and Napoleon. And you have infinite willpower and goal-directedness: aside from human necessities like sleep or food, you need never rest.
- You win if you either become Roman Emperor (and are acknowledged as such by most Romans), or if a state you control conquers the city of Rome. You lose if you die, of old age or otherwise, before completing either goal.