Somewhat based on this question, let's say a normal person from our world for some reason goes back into time - to the Hellenic Greece around 490 BC and somehow manages to become a philosopher. My question is, how will he compare to a scholar? Will he be able to achieve more, because of his knowledge?
The Character: The unlucky character is a person of above-average intellect (130), doing a PhD in Maths. He has not memorised vast amounts of information, but he enjoys research in maths, even if it is not related to his topic (which is why I haven't given the topic). Assume that the magic that brought him back into the past allows him to survive there, and communicate. The Ancient Greeks think he is a travelling scholar, but due to the magic, they don't question too closely.
Will he be able to revolutionise maths? He can't just say, "This is called integration" as he has to prove it.
Magic: To make things clear, I'll add this in. The magic allows him to communicate in Greek easily. He can understand it effortlessly, and it stops the Greeks from asking him very incriminating questions (like where are you from, etc). They simply think he is a travelling scholar and leave it at that. They also have given him food and a place to stay.