How Tall Can Mountains Be?

Olympus Mons, the tallest mountain in our Solar System, towers 21,000 meters above the surface of Mars,nearly two and a half times the height of Mount Everest.

On Earth, you would need a spacesuit to survive at that altitude but could
there even be a mountain that tall here on our home planet?
Based on the strength of Earth's gravity and the density and strength of rock, in principle you could make a single conical mountain that stretched
between New York and Chicago and soared over 45km!

That's twice the size of Olympus Mons and definitely dwarfs Everest.
However, there are a couple of reasons why we can't actually have that humongous of a mountain on Earth,For one, Earth's crust is made up of continental plates that essentially float in the semi-solid rock of the mantle below.

If you add more weight above the surface, they sink lower into the earth's hot interior,
and when they sink far enough, they soften and basically melt.
For our conical mountain, that gives a new height limit of just 15km.
As well, the powerful collision of two tectonic plates, which creates mountains in the first
place, also fractures and cracks the rock, weakening its structure and exposing it to erosion.

Over millions of years, freeze-thaw cycles pry at these cracks, while winds claw at the
slopes and streams and glaciers carve deep valleys into the mountainside, all weakening
the mountain's support.This can end badly.For example, 3,764m tall Aoraki/Mount Cook in
New Zealand had its top fall off one night in 1991, trimming it down to a 3,754m mountain.

Given all the factors that conspire to limit the height of mountains,
sinking into the earth's mantle, fractures, and erosion.I wouldn't
bet on our tallest mountains getting too much taller than they
already are.Then again, Mount Everest is still growing, 50 years
from now, it could be 30 cm taller than it is today... or it could
be a good deal shorter. We'll just have to wait around to find out.
And, who knows? Maybe we'll be on Mars by then, anyway.

REFERENCES:

Scheuer, P. A. G. 1981. How High Can A Mountain Be? J. Astrophys. Astr. 2: 165--169.
http://www-old.ias.ac.in/jarch/jaa/2/165-169.pdf