In a classroom scene, a teacher mentions that Everest is not Earth's highest geographical point. She asks what the actual highest point is, and the bell rings. The answer is Mt. Chimborazo in Ecuador, which is the furthest point from the Earth's center, but closer to local sea level than Everest. (The Earth bulges at the equator.) However, as the movie is set in 1962, and the analysis that led to Mt. Chimborazo being described that way was performed recently, it is extraordinarily unlikely that's what the teacher is referring to. Also, by the measurement that lists Mt. Chimborazo is highest, Everest is not 2nd, but 10th. Almost certainly, the reference is to K2, which is a point of contention.