If you measure height from sea level, then Mt. Everest was *still* the highest mountain in the world, even though we didn't realize it.
If you measure height as total relief (measuring from the base of mountain to the peak), then Mauna Kea in Hawaii is the highest mountain in the world (whether we knew it or not). from seabed to peak, Mauna Kea is over 10km high,while Everest is "only" 8.85 km high by this measure.
If you measure "height" as distance from the center of the Earth, then Mt. Chimborazo in Ecuador is the "highest" mountain on Earth (no matter when we realized it). Because the Earth is not a perfect sphere, but rather, sort of an oblate spheroid (to first order, it has a bulge along the equator; to second-order, it's pear-shaped, with a bulge south of the equator), the peak of Mt. Chimborazo is actually further from the Earth's center than either Mauna Kea or Everest. Its peak is 2km further from the center of the Earth than Everest's.
If a tree falls in the forest, does it make a noise?
Does the moon exist when we are not looking at it?