And this, ladies and gentlemen, is the problem with the term "polymath" -- too many people seem far too keen to apply it to themselves.

I think the best strategy at this stage in history is the "know everything about something and something about everything" strategy. Aside from making life more interesting, the more you know about fields outside your own specialty the more likely you are to have great ideas in your own field, since most "new ideas" in a field are really just of the form "hey, why don't we try this approach which they use in another field on this field?"