[thearn4]

Another thing that I'll toss in there (as a math PhD) is that the more advanced a topic is, the harder it is to truly grok it on your own without at least SOME connection to a subject matter expert. A mentor can really help you to understand something from several different perspectives, which is really critical to gaining your own expertise (versus a cursory understanding).

Now not all professors are great at this, but I would say that a great many would love nothing more than to talk about the things that they know very well.