In reality, though, intelligence is not facts; it's what you do with the facts you have. What connections can you see? How are things related? What makes things similar? In what ways can you influence a system?
A book is full of information, but is by no means intelligent. Similarly, any person that can tell you the hundredth digit of pi, but doesn't know how to use pi to solve a problem is about as useful as a book.
Truly intelligent characters are those like Sherlock Holmes and MacGuyver. They are able to solve puzzles with a minimum of information. They can see things that others cannot.
When you are creating a smart character, make sure not to confuse knowing lots of facts for being intelligent.