The highest unclimbed mountain in a particular region or in the world is often a matter of controversy. In some parts of the world surveying and mapping are still not reliable and there are not comprehensive records of the routes of explorers, mountaineers and local inhabitants.
However, a major problem relates to the definition of a mountain. Any particular mountain, in addition to its highest point, will also have subsidiary “tops”. Generally, a subjective view is taken of what is a mountain and what is a top. The horizontal distance between main peak and top, the difference in height, the topographic prominence of the top, as well as the general topography, all come into consideration. Although objective criteria have been proposed for distinguishing “peaks” from “tops” (a prominence of 610m, 2,000 feet is one definition), there is no widely agreed standard.
The Peakware World Mountain Encyclopedia has a list of unclimbed 7000m Himalayan peaks which includes “tops” [1]. The list is somewhat out of date: for example Lhotse Middle, 8430m, was first climbed in spring 2001. The information came from the UIAA which also provides a list of first ascents on its web site [2].
The mountain most widely claimed to be the highest unclimbed mountain in the world seems to be Gangkhar Puensum, 7541m (24,741 feet). It is in Bhutan where climbing of high mountains has been prohibited since 1994.
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