Why fantasize about Da Vinci? Why not choose a subject much closer to our own time like, say, Francis Crick? I recall a story he told that as a child he wanted to become a scientists but was concerned that all the important discoveries had already been made.

Really...if you don't know Crick's story, go read up! In his lifetime, man went from not even being sure what category of chemical was responsible for inheritance to sequencing the full human genome, and Crick was there for a number of very important steps. Oh, and did I mention that he was originally trained as a physicist? and that in his final years he was deeply involved in neuroscience research concerned with the nature of consciousness?

For anyone who is really concerned with knowledge and its limits, I would also recommend the book "Impossibility: The Limits of Science and the Science of Limits". Don't waste your time with this sort of pop science drivel...