Academic Fail

[kılıç_mehmet]

Gospels were written significantly after the death of Christ

Depends on what you consider to be a significant time. Ten years? Twenty? How many?
And while we're there, we can discuss the authenticity of Pauline epistles, and the book of revelation.
It doesn't really end anywhere.

if they were written by those who didn't have first hand encounters with Christ then one gets into all the problems regarding oral history, which are many.

Well, one doesn't need to be a professor to figure this out.
There always is a certain doubt in everything, when speaking of religion in general. If this did not exist, there would be no thing called "faith" anyways.