It's worth pointing out that Nate Silver is a rare individual. He's been wildly successful with data science despite not having a deep academic background, which is not the common case. His story is a useful data point though.

Do you need multiple degrees to master data science? Hell no. The practice of statistical inference requires only a few key skills. The important part is understanding how to think in terms of probability and algorithms, which doesn't require a rigorous understanding of proofs and formulae. An advanced academic degree is useful but not required. The world is looking for people who can consistently get the right answer, regardless of their background.

The other side to this is that a degree will be required to work for wall st, google, harvard, etc. Degrees still matter and social signalling and so on and so forth. We all can't be as well known and popular as Nate Silver and at some point institutions need a way of establishing that a particular candidate is truly qualified. So if you're not a messianic ml rock star, sweating the degree might be a good idea.

The beauty of a purely empirical craft is that results are the only arbiter of success. Anyone can get the right answer. It might be awhile before society catches up to and utilizes this powerful idea, but the hiring competitions on sites like kaggle are a great start [1]. Until then the best case is being the next Nate Silver.

[1] http://www.kaggle.com/c/facebook-recruiting-iii-keyword-extr...