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Amber studied at ETH Zurich where he graduated in 1894, obtaining a diploma as mathematics teacher. The following years he was preparing his doctoral thesis, while he was assistant professor of Adolf Hurwitz and Carl Friedrich Geiser. During the academic course 1896-1897, he was professor of Albert Einstein.
From 1903 till his retirement in 1938, he was professor at secondary level in the high schools of Frauenfeld and Zurich. He worked also s expert actuary for insurance companies and continued to write expert opinions even after his retirement.
He was also a mountaineer, and a member of the Swiss Alpine Club for more than sixty years. He, alongside with Anton Zübling, were the first to climb Piz Gannaretsch (3040 m.) and Piz Vatgira (2982 m.).
