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— Theodore Roethke
I'm not sure how I would distinguish people who specialize in the impossible from people who simply don't accomplish much of anything at all.
You would have to notice when they acheive the impossible.
Or that they make visible progress towards the impossible.
Or that they acheive interesting side projects in their down time from working on the impossible.
That is a good one (that applies even under strict definitions of 'the impossible'). Closely related is if they make valuable tangential contributions to the non-impossible while working on the impossible.
I'd look for the explosions.
That's a tricky thing to specialize in. Got any ideas about how someone would go about it?
If you interpret "impossible" as meaning "things a lot of people call impossible", then the obvious method would be to make a list of such things, research them to see if there are any where you have a plausible chance of making a difference, and figure out which of them you'd prefer to specialize in.