You two will take different tacks when it comes to discovery of the unknown: You'll rely more on your education, on the methods you've learned to seek things out intellectually, while your pal will rely more on gut instinct paired with a pure rebellious streak. Needless to say, those two methods are incompatible with each other! You won't be able to share in each other's original ideas, because you'll put up walls against the ways in which you'll reach those ideas.
You might dismiss your maverick friend's ideas as foolishness, simply because they haven't been substantiated in a way that's understandable to you. And they may not trust your reliance on books and the more formal avenues toward learning. If you can learn to respect each other's methods and listen to each other, you'll find that you both have your own brand of brilliance to bring to the table.