I find the definition of the prominence of a mountain peak very interesting:
"The prominence of a peak is the minimum height of climb to the summit on any route from a higher peak, or from sea level if there is no higher peak. The lowest point on that route is the col."
It's the peak's height minus how much the sea level would have to rise to make this peak the highest on its island.
For intuition, see the examples at https://en.wikipedia.org/wiki/List_of_mountain_peaks_by_prominence
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*my interpretation assumes a continuously ascending path from the imaginary sea level to the mountain top. I believe it's almost always the case in practice.
A counterexample is a peak within a crater.
