This seems like an easy question. It is at the top of Mount Everest, of course. But is it that simple? It depends on how you define highest. If you mean the height above sea level, then yes, that is the correct answer. But the Earth is not a perfect sphere. It bulges at the equator, making it what we call an oblate spheroid. So if we define tallest by the distance from the center of the Earth, then we have to also take into account the fact that sea level near the equator is ‘higher’ than at points away from the equator.
If that is taken into account, then the highest point becomes the top of Mount Chimborazo in Ecuador, even though it is just 20,500 feet above sea level, compared to the 29,035 feet above sea level of Everest, though there is disagreement about the exact values depending on how it is measured and the shifts due to plate tectonics.
The Himalayan mountain is actually beaten by Chimborazo, in Ecuador. But Everest still wins on the traditional metrics: it’s nearly 9,000m above sea level, thousands more than any of its closest rivals.
But it’s not actually the furthest up, or the closest to space. Ecuador’s mountain tops it on that measure, and it’s all because of the Earth’s funny shape.
Everest only wins when measured from sea level. But if instead you measure out from the centre of the Earth, Chimborazo wins easily – and Everest wouldn’t even get into the top 20 mountains.
This is a highly political issue because of the tourism benefits that come along with bragging rights. Also apparently Chimborazo is much easier to climb than Everest and thus does not have the same cachet, and so I do not expect Everest’s fame to be diminished.