Müller held several positions in the Habsburg monarchy administration of mines and coinage in the Banat, Transylvania, and Tyrol.
Even articles by Mary Elvira Weeks on the discovery of tellurium, published in the Journal of Chemical Education in 1932,[5] and 1935[6] quote two different locations of his birth: one in Vienna, Archduchy of Austria and the other Hermannstadt, Principality of Transylvania (present-day Sibiu, Romania).
[8] After the dissolution of the Thesaurariat Müller became Oberinspector (chief surveyor) of all mining, smelting and salt production in Transylvania.
[3][4] Müller as the Austrian chief surveyor of mines in Transylvania was responsible for the analysis of ore samples.
This ore was known as "Faczebajer weißes blättriges Golderz" (white leafy gold ore from Faczebaja) or antimonalischer Goldkies (antimonic gold pyrite), and, according to Anton von Rupprecht, was Spießglaskönig (argent molybdique), containing native antimony.
[10] The following year, he reported that this was erroneous and that the ore contained mostly gold and an unknown metal very similar to antimony.
After a thorough investigation which lasted for three years and consisted of more than fifty tests, Müller determined the specific gravity of the mineral and noted the radish-like odor of the white smoke which passed off when the new metal was heated, the red color which the metal imparts to sulfuric acid, and the black precipitate which this solution gives when diluted with water.
Nevertheless, he was not able to identify this metal and gave it the names aurum paradoxium and metallum problematicum, as it did not show the properties predicted for the expected antimony.