"Learned fool" is provided in the Tanaka Corpus. "Clever fool" is another possibility; see related question: <a href="https://english.stackexchange.com/questions/17525/is-there-a-word-for-clever-fool">Is there a word for "clever fool"?</A> 

A tempting answer might be "sophomore," which has come to mean "wise idiot," but this <a href="http://www.straightdope.com/columns/read/1982/whats-the-origin-of-sophomore">etymology is questionable</a> and the word more often connotes a second-year student.