Clever of you to catch that tune, however you are mistaken as to whom is humming. Watch it over and pay close attention, you will realize that it is actualy Zolt J. Kimbly humming while he is wearing the mask. It's easy to tell when he sighs then asks if he can take the mask off.
And no, just because it is humed does not mean that Bethoven ever did exist in Artimis.
It is possiable, however, that his Artimis equivilant composed it. If you have seen the movie then you shoud remember that the other side of the gate is our world, folowing the same time line, but not the same scientific trail. If you take into consideration that we know the " Ode to Joy " as a product of Ludwig Van Bethovan, who existed in OUR world, then it is safe to assume Bethovan had an equivliant in Artimis who was able to compose the same music.
Death is, as they say, the high cost of living.