Auer was born in Vienna, the son of the director of the Imperial Printing Press. He was educated at the Vienna Polytechnic and at Heidelberg University, where he was a pupil of Robert Bunsen.

In 1885 he made a major contribution to knowledge of the lanthanoid (rare-earth) elements. In 1840, Carl Mosander had isolated a new ‘element’ called didymium. Auer showed (1885) that this contained, on fractionation, green and rose-red portions. He named them praseodymia (‘green twin’) and neodymia (‘new twin’).

Auer was also one of the first to find some use for the rare-earth elements. Gas had been in use as an illuminant since the beginning of the century and, although an improvement on the early oil lamps, it had many disadvantages of its own. It was expensive, hot, smoky, and smelly. Auer realized that it would be better to use the gas to heat a solid that would itself provide light, rather than use the luminosity of the flame. He used a mantle over the flame, impregnated with thorium oxide and a small amount of cerium. The Welsbach mantle, patented in 1885, delayed the end of gas lighting for a few years. Unfortunately for Auer, his invention was too late for, in 1879, Edison had managed to burn an electric bulb for 40 continuous hours.

Later, in 1898, Auer tried to improve the electric lamp by replacing its carbon filament by metallic osmium, which has a melting point of 2700°C. Once more he failed, for the future lay with tungsten, which has a higher melting point of 3410°C.

He was more successful with the so-called Auer metal – an alloy consisting mainly of cerium with other lanthanoid elements. It is also called Mischmetal (German: mixed metal) and is used for flints in cigarette lighters.