Could carbon nanotubes be used to create an elevator to the moon? Prove it with math.?

The Moon moves around ! Its distance is varying constantly! How is maths going to "prove" that ? Any more silly questions ?

Distance to the moon varies by over 30,000 miles in one month's orbit, and the positions of the apogee and perigee precess (move around).

The Earth rotates 29 times faster than the moon orbits, so cannot anchor the base of the elevator except at the South Pole.

Better would be to construct a mass accelerator a couple kilometers long up the west face of Mt Everest or even Kilimanjaro. That could push a vessel into Earth orbit. From there a tractor rocket to send it to lunar orbit.

No. The moon is not in a geosynchronous orbit. Its position in the sky changes. So the elevator could not be anchored to one spot on the earth.