Translation:He applied his great knowledge to the problem.
For my part, I think people are WAY too focused on the English sentences in this course about Esperanto. I especially love (i.e. hate) when people say "most native speakers would say X" - and "X" actually means something slightly DIFFERENT than what the Esperanto sentence says.
Remember what you're here to learn.
That's true, but it makes it a lot harder to learn when the sentences we're translating don't make much sense in the first place. This particular sentence isn't too bad, but there are definitely sentences in the course that don't make a lot of sense to even a native English speaker.