"He is a bookworm."
Translation:הוא תולעת ספרים.
They are different things, aren't they? A bookworm is someone who likes to read, not necessarily to study.
I'm just a student of German and I don't really know, but I think "Gelehrte" is "learned"? If so, מלומד. And למדן is like, a learner, I can't really think of the right word in English, someone who likes to study or is good at it or studies a lot.