Johann Regiomontanus was born Johann Müller of Königsberg but he used the Latin version of his name (Königsberg = "King's mountain").
Regiomontanus was a pupil of Peurbach. In 1461 he was appointed professor of astronomy at the University of Vienna, filling the chair vacated by Peurbach. In 1468 Regiomontanus was appointed astronomer to King Matthias Corvinus of Hungary.
A translator and publisher, Regiomontanus made important contributions to trigonometry and astronomy. His book De triangulis omnimodis (1464) is a systematic account of methods for solving triangles.
Regiomontanus built an observatory in Nuremberg in 1471 with funds from his patron and fellow scientist Bernard Walther. He also built a workshop to construct instruments at Nuremberg. He wrote Scipta giving details of his instruments.
In January 1472 he made observations of a comet which were accurate enough to allow it to be identified with Halley's comet 210 years (and three returns of the 70 year period comet) later. He also observed several eclipses of the Moon, a total eclipse on 3 September 1457, a partial eclipse on 3 July 1460 and another total eclipse on 22 June 1461.
Regiomontanus's interest in the motion of the Moon led him to make the important observation that the method of lunar distances could be used to determine longitude at sea. It was many years, however, before the position of the Moon could be predicted with sufficient accuracy to make the method practical and instruments constructed to give the lunar position with the high degree of accuracy necessary for the method. Regiomontanus describes how the position of the Moon can be used to determine longitude in the ephemerides for the years 1474-1506 which he published.
In common with many others he wrote on calendar reform, for example he wrote Kalendarium and De Reformatione Kalendarii.
Pope Sixus IV summoned Regiomontanus to Rome in 1475 to advise on calendar reform and to become bishop of Regensburg. However he died before he could take office. Some accounts say he was poisoned by his enemies, other accounts say he died of the plague.