You don’t necessarily need to be able to measure the height precisely to be able to measure the change in height precisely. If the error in your measurement technique is dominated by systematic but unknown errors, then subtracting two measurements will cancel out the error.
When Radhanath Sikdar, a mathematician and surveyor from Bengal, first identified Everest as the world’s highest peak in 1852, he measured it to be exactly 29,000ft (8,839m) high, but it was [eventually] publicly declared to be 29,002ft. The arbitrary addition of 2ft was to avoid the impression that an exact height of 29,000ft was nothing more than a rounded estimate.
Since the convention is to measure height above sea level, Everest was taller during the last ice age than it is now (even accounting for the fact that it has continued to rise since then.)
I believe K2 was the tallest mountain for a short time as little as 10 years ago. (due to human measurements).
Defining the “tallest mountain” is itself problematic, as at least four realistic definitions could be employed, with different results.
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The point on the surface furthest from the center of the earth. Because the earth is ellipsoid, a mountain 20 miles high in central Antarctica would be closer to the center of the earth than a beach in Singapore, on the equator. Sitting here on the Texas gulf coast, I am further from the center of the earth than the highest Antarctic mountain peak.
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The highest point above sea level. But because Mount Everest is not visible from the sea, that has no relevance. It’s like saying the tallest basketball player plays for the Denver Nuggets, where he is the highest above sea level.
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The point highest above surrounding terrain (the basketball court above), where the peak is the furthest above any relevant observers interested in how high it is.
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As in 3, but the case of a mountain on an island could be argued to have a given height above the floor of the ocean, irrespective of the historically variable level of the water that covers the lower parts of the mountain. It’s all still mountain, all the way down past the beach.
Which of the above do you wish to use as a definition of “tallest mountain”?
Another thing is that when one sees Everest in person, it doesn’t really look that tall because there are several mountains in the immediate area that are almost as tall. It definitely has to be pointed out to you. Also one of the best viewing places is a “hill” named Kala Pattar. Its height is about 18,000 feet so Everest is “only” 11,000 feet taller.
The Urals are another mountain range that were among the tallest in the world when they were young. And like other such ranges, they formed from a tectonic collision.
One of the problems with talking about old mountain ranges is that even though it’s fairly straightforward for structural geologists to determine roughly how much crustal thickening occurred, it’s much harder to determine how directly that would have been reflected in elevation. For example, the Rockies were thought to be a not-especially-tall broad highland during the subduction event that formed them, but the high topography today owes its existence to the interaction between the earlier thickened crust and more recent extension and uplift in western North America. If geologists were looking at the Rockies a billion years from now, the crustal thickening when they were formed would be obvious, but there might not be a lot of evidence to suggest what the current mountain range was like.
What further complicates things is that the mechanisms for continental-continental plate collisions aren’t particularly well understood. During the early days of plate tectonic theory, the Himalayas were a little baffling. The main driver of plate movement is the force of subducting plates “sinking” in the mantle (slab pull) but continental crust doesn’t subduct. That makes a plate boundary like the Himalayas, where you’ve got two relatively large pieces of continental crust that appear to have been pushing together for a very long time, very hard to explain. It seems that the Indian Plate must still be attached to the sinking ancient oceanic crust, but the exact mechanism for that, and what happened to a large portion of “missing” continental crust on the Indian Plate, is still not fully understood.
So, with that in mind, it’s not entirely clear how common Himalayan-style plate collisions have been throughout Earth history or if them being manifested by extremely tall mountain ranges is the usual situation. It could be that the situation in the Himalayas today is rare and that Mt. Everest really is one of the tallest mountains ever.