What is an ivory tower professor?

Answer 1

An "ivory tower professor" is one who, in the view of the person applying that phrase to someone, inhabits an intellectual world that has little or no connection with real life. Such a professor would do research and publish but lack knowledge of practical matters. Sort of a "head in the clouds" academic. For a background on this descriptive phrase follow the Wikipedia link below.

Answer 2

When a critic is accused of living in an 'ivory tower' the suggestion is that he has lost touch with reality - that he doesn't know what the real world is like.

The notion that there is only one sort of reality - and that this is known to the person leveling the charge, but not to the one receiving it - is one of the silliest ideas in all literature.