I would use the 10 trillion dollars to give every person on earth access to a system that would be (as close as modern technology allows) equivalent to A Young Lady's Illustrated Primer.

In today's terms, that might manifest itself as giving everyone free access to computers with high bandwidth internet connections, which they could use to access a YouTube-like website housing multimedia explanations of every topic imaginable, tailored to every target audience imaginable, combined with a sophisticated system that would create informational links (and/or allow users to create links) between every piece of media, such that another sophisticated system could propose a 'best route' to achieving deep understanding of any particular piece of knowledge.

After this had been done, all remaining money would be spent on a combination of incentivizing the world's best thinkers and educators to contribute (or continue contributing), research grants, and scholarships.