Johannes Müller von Königsberg (6 June 1436 – 6 July 1476), known by his Latin pseudonym Regiomontanus, was an important German mathematician, astronomer, astrologer and translator.

He was born in the Franconian village of Unfinden near Königsberg, Bavaria — not in the more famous East-Prussian Königsberg. He is also called Johannes Müller, der Königsberger (Johannes Müller of Königsberg). His full Latin name was Joannes de Regio monte, which abbreviated to Regiomontanus (from the Latin for "Königsberg", "King's Mountain").

At eleven years of age, he became a student at the university in Leipzig, Saxony. Three years later he continued his studies at Alma Mater Rudolfina, the university in Vienna, Austria. There he became a pupil and friend of Georg von Peurbach. In 1457 he graduated with a degree of "magister artium" (Master of Arts) and held lectures in optics and ancient literature. He built astrolabes for Matthias Corvinus of Hungary and Cardinal Bessarion, and in 1465 a portable sundial for Pope Paul II. His work with Peurbach brought him to the writings of Nicholas of Cusa (Cusanus), who held a heliocentric view. Regiomontanus, however, remained a geocentrist after Ptolemy. Following Peurbach's death, he continued the translation of Ptolemy's Almagest which Peurbach had begun at the initiative of Basilios Bessarion. From 1461 to 1465 Regiomontanus lived and worked at Cardinal Bessarion's house in Rome. He wrote De Triangulis omnimodus (1464) and Epytoma in almagesti Ptolemei. De Triangulis (On Triangles) was one of the first textbooks presenting the current state of trigonometry and included lists of questions for review of individual chapters. In the Epytoma he critiqued the translation, pointing out inaccuracies. Later Nicolaus Copernicus would refer to this book as an influence on his own work. In 1467 Regiomontanus left Rome to work at the court of Matthias Corvinus of Hungary. There he calculated extensive astronomical tables and built astronomical instruments.

In 1471 he moved to the Free City of Nuremberg, in Franconia, then one of the Empire's important seats of learning, publication, commerce and art. He associated with the humanist and merchant Bernhard Walther who sponsored the observatory and the printing press. Regiomontanus remains famous for having built at Nuremberg the first astronomical observatory in Germany. In 1472 he published the first printed astronomical textbook, the "Theoricae novae Planetarum" of his teacher Georg von Peurbach. Peurbach worked at the Observatory of Großwardein (Oradea) in Transylvania, the first in Europe, and established in his "Tabula Varadiensis" this Transylvanian town's observatory as lying on the prime meridian of Earth.

In 1475 he went to Rome to work with Pope Sixtus IV on calendar reform. On the way he could publish his "Ephemeris" in Venice. Regiomontanus died mysteriously in Rome, July 6, 1476, a month after his fortieth birthday. Some say he died of plague, others by (more likely) assassination.

A prolific author, Regiomontanus was internationally famous in his lifetime. Despite having completed only a quarter of what he had intended to write, he left a substantial body of work. Nicolaus Copernicus' teacher, Domenico Maria Novara da Ferrara, referred to Regiomontanus as having been his own teacher.

In 1561, Daniel Santbech compiled a collected edition of the works of Regiomontanus, De triangulis planis et sphaericis libri quinque (first published in 1533) and Compositio tabularum sinum recto, as well as Santbech's own Problematum astronomicorum et geometricorum sectiones septem. It was published in Basel by Henrich Petri and Petrus Perna.

The crater Regiomontanus on the Moon is named after him.

One biographer has claimed to have detected a decline in Regiomontanus' interest in astrology over his life, and came close to asserting that Regiomontanus had rejected it altogether. But more recent commentators have suggested that the occasional expression of skepticism about astrological prognostication reflected a disquiet about the procedural rigour of the art, not about its underlying principles. It seems plausible that, like some other astronomers, Regiomontanus concentrated his efforts on mathematical astronomy because he felt that astrology could not be placed on a sound footing until the celestial motions had been modeled accurately. In his youth, Regiomontanus had cast horoscopes (natal charts) for famous patrons. His Tabulae directionum, completed in Hungary, were designed for astrological use and contained a discussion of different ways of determining astrological houses. The calendars for 1475-1531 which he printed at Nuremberg contained only limited astrological information — a method of finding times for bloodletting according to the position of the moon; subsequent editors added material. But perhaps the works most indicative of Regiomontanus' hopes for an empirically sound astrology were his almanacs or ephemerides, produced first in Vienna for his own benefit, and printed in Nuremberg for the years 1475-1506. Weather predictions and observations were juxtaposed by Regiomontanus in his manuscript almanacs, and the form of the printed text enabled scholars to enter their own weather observations in order to likewise check astrological predictions; extant copies reveal that several did so. Regiomontanus' Ephemeris would be used in 1504, by a Christopher Columbus stranded for a year on Jamaica, to intimidate the natives into continuing to provision him and his crew from their own scanty food stocks. Columbus accomplished this when he successfully predicted a lunar eclipse for 29 February 1504. Regiomontanus did not live to produce the special commentary to the ephemerides that he had promised would reveal the advantages the almanacs held for the multifarious activities of physicians, for human births and the telling of the future, for weather forecasting, for the inauguration of employment, and for a host of other activities, although this lack was again made good by subsequent editors. Nevertheless Regiomontanus' promise suggests that he either was as convinced of the validity and utility of astrology as his contemporaries, or was willing to set aside any misgivings for the sake of commercial success!

Much of the material on spherical trigonometry in Regiomontanus' On Triangles was taken directly and without credit from the twelfth-century work of Jabir ibn Aflah otherwise known as Geber, as noted in the sixteenth century by Gerolamo Cardano.