In mathematics, there is a very important class of surfaces called K3 surfaces. The name is a bit mysterious because, because there are no K1 or K2 surfaces. Weil explains how they were named in his Oeuvres, Volume II, p546: il s'agit des variétés kählériennes dites K3, ainsi nommées en l'honneur de Kummer, Kähler, Kodaira, and the belle montagne K2 au Cachemire. [It is a question of the kählerian varieties called K3 in honour of Kummer, Kähler, Kodaira and the beautiful mountain K2 in Kashmir.]

The mountain K2 was first climbed on July 31, 1954, about the time Weil was studying the surfaces.

When the Karakoram mountains were first surveyed, the peaks were numbered K1, K2, K3, ..., K36, ... more-or-less at random except (so I've been told) that Masherbrum (7806m) was numbered K1 because it was believed to be the highest peak in the Karakorams until people reached the head of the Baltoro glacier and saw K2 (8611m) in its full glory.

So which mountain is K3? Unfortunately, the easily available maps of the Karakorams are all very poor: only a small proportion of the peaks are named or numbered, and K3 does not occur. However, when I was in the Karakorams in June 2000, I learned that the Hushe villagers knew of a mountain called K3 --- it lies at the head of the Charakusa glacier on the ridge joining K6 (Baltistan Peak 7282m) and K7 (6934m). In any other region of the world, it would be a magnificent peak, but here it is little more than a bump on a ridge. Its height is 6355m and it is unclimbed.

[Richard Taylor has pointed out to me that the old records show that K3 must be one of the Gasherbrum peaks, and not the peak the Hushe villagers claimed to be K3. So which peak of Gasherbrum is it? Not the highest, Gasherbrum I (8068m), which is K5, nor the second highest, Gasherbrum II (8035m), which is K4 (according to Sivalaya, Louis Balme, 1978). One day, I will solve this mystery.]

The Hushe "K3"

The Hushe "K3" is in the centre of the picture, and K6 is at right.

The only obvious route I see is up the rock below and slightly to right of the summit, up the snow, and onto the ridge leading to summit that splits the sunlight from the shadow. It looks an interesting challenge.