Professor? Pun?

I just began to re-read this book after fifteen years, and already I'm driven to distraction by two things that occur on page 9 (Pevear & Volokhonsky text) that I didn't notice fifteen years ago or that I just read past. The first is the prince's remark that Princess Myshkin is "the last in her line." Where's the pun?

Second, just a few lines later, is Rogozhin's question to the prince: "... did you do any studying at your professor's?" If I'd been sitting with the prince and Rogozhin I would've interrupted, "Wait a minute. 'Professor'? I thought you said you went to Switzerland for your falling sickness and that you stayed with your doctor. Did I miss something? When did you say your doctor was a professor?"

Please help.

I have read the Chinese translation (My mother tongue is Chinese). A note in the book says that "in her line" also means "in some sense/in a sense/to some extent"( "在某种意义上“) in Russian. I don't get it. When you read on a few lines, you will see the author says it's a bad pun.

You should get a Norton Critical Editon of this book. It's rich resource.

As for Professor: the beginning of the dialog is just hidden and given by author's brief description, you must notice.

About bun:
"последняя в своем роде" ("the last in her line").
Myshkin ment "the last in family (clan, generation)"
But it can be also understood as "the least (worst) of a kind"