In Sketches from Memory: The Notch of the White Mountains (1835), Nathaniel Hawthorne wrote:
"Let us forget the other names of American statesmen, that have been stamped upon these hills, but still call the loftiest - WASHINGTON. Mountains are Earth's undecaying monuments. They must stand while she endures, and never should be consecrated to the mere great men of their own age and country, but to the mighty ones alone, whose glory is universal, and whom all time will render illustrious."
While a noble sentiment, it's also false. Mountains are not eternal, but rather ephemeral features on the Earth's landscape over the eons of geologic time.
So, how long does it take to erode away a mountain?
Since Mount Everest is 8,848 meters in elevation and there are 1,000 millimeters in a meter:
8,848 m * 1,000 mm/m = 8,848,000 mm
If Everest were to erode at 0.1 mm/yr:
8,848,000 mm / 0.1 mm/yr = 88,480,000 yr
But, the basic idea is sound. Mountains don't last forever. While 88.5 million years sounds like a long time to those of us who only live for a few decades on this planet, the Earth has been here for 4.5 billion years.
4,500,000,000 yr / 88,500,000 yr =50.8
In other words, you could erode away Mount Everest 50 times since the origin of the planet.
It may be hard to believe, but several times in the geologic past, the view in what's now the Northeastern U.S. looked like this:
High Himalayan-scale mountains. Where are they today? Gone. Eroded away. We see their remnants in sedimentary rocks in places like the Catskills. We walk on their deep metamorphic roots now exposed at the surface. We drive by the folded layers of rock that buckled and twisted when these mountains rose.
The evidence is all there, staring us in the face if we just take the time to look at the rocks.