Technology is one part of the victory. The other part is working with people, because you can't take over the world alone (unless you are able to build an invincible battle robot, but first you need to get there). You need strategic skills, business skills, psychology skills, and cult-leadership skills, because you essentially face two types of risks -- one is the risk that your technological and military strategy fails (just like when you would lose in a strategic computer game), other is the risk that generally everything will go successully, until in some unexpected moment someone you trusted (or just did not think too much about) stabs you in the back (either literally, or steals or sabotages your technology, incites revolt, etc.).
I guess it would be wise to surround yourself with a cult following, and spend extra energy on convincing those people about your supernatural powers (there need to be some extra secrets, beyond your technology and medicine skills that people see). Those people must be convinced that killing and replacing you would not be even in their short-term interest; otherwise someone will be tempted someday, and it only needs one assassin to kill you. You can always promise much more than you can really deliver... and so can your enemies. Even if you bring education, medicine, food and technology, someone can kill you in exchange for a hope of eternal happiness. Or they can be blackmailed.
I am not sure if it would be safer to stay hidden and surround yourself with brainwashed puppets (skilled enough to do their jobs) -- so when someone must go to the Roman court, or someone is assassinated, it's them, not you. Basicly, for each skill you will exhibit (military strategy, technology, education, medicine, agriculture), select one or two persons already skilled in this area (leader, scientist, philosopher, healer, farmer), teach them, brainwash them, and let them pretend to the public it's their skill. You can also appoint a false prophet for the public. You would delegate some tasks to some people anyway, with this strategy you just hide yourself from the attention of the outside world.
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.