He was known for his contributions to topology and other fields of mathematics, his interest in mathematical history and for being a keen alpinist. Vietoris attended the University of Vienna, where he earned his Ph.D in 1920. With his wife Maria Josefa Vincentia, born von Riccabona zu Reichenfels (July 18, 1901 - March 24, 2002), dying at age 100, they became one of the eldest couples of the world, having the sixth highest aggregate age of a married couple (total combined age).
He lends his name to a few mathematical concepts:
Vietoris lived to be 110 years and 309 days old, and became the oldest known Austrian man ever. In doing so, he also is a rare example of a supercentenarian already known for some other achievement.