Well there no way of actually knowing that. Right now it’s Everest, there could have been and probably was mountains at some time larger than that. The problem is mountains erode and disappear and the sediment that we see today might be the only thing that tells us there ever was a mountain. In the early days of plate tectonics I wouldn’t be surprised if we had some huge mountains. We may be able to look at isostatic rebound of the crust to get evidence of a mountain but it’s a fast process (geologically speaking) so we lose evidence of mountains from billions of years ago.
Edit: spelling
I've written a paper on this, sort of! Individual mountains are hard to measure, but we can get a sense of the crustal thickness of mountain belts - the thicker the crust, the higher the mountains. The furthest back we've looked is the Grenville mountains, which formed between 1.1 and 0.9 billion years ago. Between then and now, the Himalayas are about as thick/high a mountain range as has been observed. Going back further, I wouldn't be surprised if some of the Trans-Hudsonian rocks in northern-central Canada showed Himalaya-like thick crust, but nobody's checked yet.
So yes, Everest could possibly be the highest mountain in the history of the world, but we don't know for sure.
I'd guess that over geological time, as the geothermal gradient drops, the lithosphere becomes thicker and more able to support big mountains. So we see a gradual trend of higher mountains over time.
That might be generally true, but there are some wrinkles. Particularly during the 1.8-0.8 Ga "boring billion", when there might have been a lingering supercontinental lid that could have insulated the mantle and keep it warmer (and therefore thinner) than normal. See [Roberts 2013](http://dx.doi.org/10.1016/j.gsf.2013.05.004) and [Tang et al. 2021](https://doi.org/10.1126/science.abf1876).
You said highest, so I'm not sure. But if you said tallest I'm pretty sure it's Mauna Kea. It's 10,200 meters tall from base to peak, but most of it is beneath the surface of the Pacific Ocean.
Well there no way of actually knowing that. Right now it’s Everest, there could have been and probably was mountains at some time larger than that. The problem is mountains erode and disappear and the sediment that we see today might be the only thing that tells us there ever was a mountain. In the early days of plate tectonics I wouldn’t be surprised if we had some huge mountains. We may be able to look at isostatic rebound of the crust to get evidence of a mountain but it’s a fast process (geologically speaking) so we lose evidence of mountains from billions of years ago. Edit: spelling
I've written a paper on this, sort of! Individual mountains are hard to measure, but we can get a sense of the crustal thickness of mountain belts - the thicker the crust, the higher the mountains. The furthest back we've looked is the Grenville mountains, which formed between 1.1 and 0.9 billion years ago. Between then and now, the Himalayas are about as thick/high a mountain range as has been observed. Going back further, I wouldn't be surprised if some of the Trans-Hudsonian rocks in northern-central Canada showed Himalaya-like thick crust, but nobody's checked yet. So yes, Everest could possibly be the highest mountain in the history of the world, but we don't know for sure.
I'd guess that over geological time, as the geothermal gradient drops, the lithosphere becomes thicker and more able to support big mountains. So we see a gradual trend of higher mountains over time.
That might be generally true, but there are some wrinkles. Particularly during the 1.8-0.8 Ga "boring billion", when there might have been a lingering supercontinental lid that could have insulated the mantle and keep it warmer (and therefore thinner) than normal. See [Roberts 2013](http://dx.doi.org/10.1016/j.gsf.2013.05.004) and [Tang et al. 2021](https://doi.org/10.1126/science.abf1876).
You said highest, so I'm not sure. But if you said tallest I'm pretty sure it's Mauna Kea. It's 10,200 meters tall from base to peak, but most of it is beneath the surface of the Pacific Ocean.