Levchin is one of several Silicon Valley luminaries who have talked big about the tech industry's timidity. So starting yet another payments company seemed decidedly unambitious.

Yet plenty of companies out there are still taking a run at the next moonshot. Their technologies don't let you share photos or offer you a deal on your next manicure. Instead, these companies could change the world in deep ways by solving tough problems, rather than the kind of "problems" too many startups make up as justifcations for the "solutions" they're trying to sell. Not that photo-sharing isn't great (Levchin did that, too). Unlike what the companies that follow are trying to do, however, it's not exactly shooting for the moon.