Advanced math problem (or is it?)!?

Question

A monk climbs a mountain at 7AM and reaches the summit at noon. Come morning he leaves the summit again at 7AM and descends to the bottom by the exact same route. PROVE that there is a time between 7AM and noon when the monk is in the exact same location as the day before. (Notice I did not mention anything about his velocity, which neither has to be constant nor positive).

First to have the poet's answer gets best answer.

Answer 1

I think this is a famous problem of Lewis Carroll.
You can think on two monks, the monk of your history and a clone of himself, the first climbing and the second descending the mountain. Both starting at 7AM and arriving at noon of THE SAME DAY. It is clear that they will cross in some point and time.
The day is irrelevant, for you are asking about the clock time.

I apologize for my bad english, but hope I made me understood.

Answer 2

this is a famous problem of Lewis Carroll.