Together with his childhood friend Andreas Hinterstoisser, he made numerous first ascents of peaks in the Berchtesgaden Alps, including some of the most difficult climbs of that time.

[1] In July 1936, Kurz and Hinterstoisser left Berchtesgaden, where they were serving in the military, and travelled by bicycle to Kleine Scheidegg, Switzerland to attempt the then unclimbed north face of the Eiger.

[2] During the ascent, Angerer was injured by falling rocks loosened by the warmth of the rising sun as they crossed the first ice field.

As a result of Angerer's worsening condition and their slow progress across the second ice field, they abandoned the attempt on the Eiger and decided to descend.

A further challenge arose when Kurz and his fellow climbers failed to retrace their route across the area now known as the Hinterstoisser Traverse and had to climb downwards.

[3] Later that day, amid worsening weather, a rescue team attempted to reach Kurz from below, ascending by means of the railway tunnel that ran through the mountain, the Jungfraubahn.

[3] Facing the futility of his situation, he said only "Ich kann nicht mehr" ("I can't go [on] anymore") and died of hypothermia shortly after.