Uh,you certainly can,but I've never heard of anyone,no matter how talented and precocious, doing such a thing. I HAVE heard of individuals who never formally entered a Master's or PHD program, were self taught and produced on their own a work of original research that was so significant, they were immediately awarded a doctorate on the spot and a research position. Karl Weirstruass famously did this, of course-as have several others. I believe there's a prestigious professorship chair at Harvard that's awarded once in a generation for pulling off such a feat.
But I think you can count on your fingers the number of people who have successfully done this. The odds are definitely not with you.I know,I was once arrogant enough to think I could do it. Given my situation, part of me is still hoping I CAN-but I'm far more realistic about its probability of occurring, which converges very near to zero in the limit of the sequence of all my attempts prior to death.
By all means,though-I wish you luck.