Regiomontanus | Biography

Regiomontanus was the pen name of Johann Müller, responsible for what some call the "rebirth of trigonometry" during the century following his death. Although he was a practicing astrologer , he also was one of the first Europeans to closely observe certain celestial objects and events previously tied to superstitions. Regiomontanus published his own and others' translations of classical and Arabic texts with his then novel printing press. He predicted that sailors would one day be able to navigate according to the position of the moon, a process that eventually did arise during the Age of Exploration. (Some speculate that Regiomontanus' early death prevented him from anticipating Copernicus.) Once dismissed as a comparatively undisciplined technician, Regiomontanus is now recognized as the West's answer to Nasir al-Din or Nasir Eddin, having brought plane and spherical trigonometry within the purview of pure mathematics and out of its apprenticeship to astronomy.

Regiomontanus was born in an area once known variously as Franconia or East Prussia, now part of Russia, on June 6, 1436. His father was a miller, but nothing else is known of the family. Regiomontanus studied dialectics for two or three years at the University of Leipzig before entering the University of Vienna at age 14 under the name Johannes Molitoris de Königsberg, but quickly came to be known by a Latin variant of his hometown. Königsberg meant King's Mountain, so the translation regio monte yielded Regiomontanus. He was awarded a bachelor's degree in one year. After two years at Vienna Regiomontanus elected to study the mathematics and protocol of astronomy, then still indistinguishable from astrology.

Müller's teacher, Georg von Peurbach, was a reformist who decried existing Latin translations of Greek texts from which he was forced to teach. Peurbach was particularly unsatisfied with a reference called The Alfonsine Tables. Regiomontanus became part of the faculty during 1457 and joined forces with his former teacher to improve these source materials. A visiting Church official, Cardinal Bessarion, came to their aid in 1460 by contracting Peurbach to produce a new Latin translation of Claudius Ptolemy's Amalgest from the Greek instead of from its intermediate Arabic translation.

By the spring of 1461 Peurbach died at the age of 38, before the work was completed, and his last wish was that his student carry on his work. Bessarion became Regiomontanus' benefactor, teaching him Greek and taking him to Rome in search of ancient manuscripts. The cardinal's deeper motive was to forge common ground for the Greek and Latin factions of the Catholic Church. At various intellectual centers of Italy, they consulted with leading astronomers, particularly members of the Averroists. Regiomontanus was appointed professor of astronomy to take Peurbach's place, and finished the Epitome as promised. He even added commentary and revised calculations in some places, restoring omitted mathematical passages in others. Ironically, it would not see publication for decades after Regiomontanus' own death.

Regiomontanus' 1464 effort, De triangulis omnimodis libri quinque, presented what was likely the first trigonometrical formula for the area of a triangle , spearheading the application of algebraic and algorithmic solutions to geometric problems . This publication sported the still innovative notations for sine and cosine. Simultaneously, Regiomontanus was drawing up charts for trigonometric functions, particularly sine tables for use in the days prior to the invention of logarithms. His longitudinal studies bore the Tabulae Directionum, or "tables of directions" for fixed celestial objects in relation to the apparent movement of the heavens . This work introduced the tangent function, with which Regiomontanus would later compute a table of tangents. After moving back to Nuremberg to assume the post of Royal Astronomer to King Matthias Corvinus of Hungary, he found yet another sponsor. Bernard Walther was an amateur astronomer who funded an observatory and workshop, and commissioned various scientific tools of Regiomontanus' design for their use. Upon securing a printing press, Regiomontanus gave his old teacher's work precedence, making Peurbach's Theoriae planetarum novae one of the earliest mass-produced science texts. In 1474 Regiomontanus printed his own Ephemerides, an almanac of daily planetary positions and eclipses for the years 1475 to 1506. This was the reference Christopher Columbus used as leverage against the Jamaican aborigines, who found his prediction of a lunar eclipse awe-inspiring. More notably, one of the objects Regiomontanus had recorded during his research was the comet of 1472, renamed Halley's Comet upon its third return 210 years later.

As recorded in the Nuremberg Chronicle, Regiomontanus was summoned to Rome with hopes of reforming the Julian calendar. This was an ongoing problem many scientists, including Regiomontanus, had already pondered. Pope Sixtus IV awarded him the bishopric of Ratisbon, but he fell victim to a plague in the wake of the Tiber river flood of 1476. Regiomontanus' papers were inherited by Walther, who unfortunately did not disseminate them. Upon his death they were acquired by the Nuremberg Senate, where they languished for nearly 30 more years. Regiomontanus' projects in mathematics and science were extended by intellectual successors like Germany's Johann Werner and Belgium's Philip van Lansberge.

Regiomontanus was also a university professor, lecturing on Virgil and Cicero . Major classical works translated by Regiomontanus included the Conics of Apollonius and some writings of Archimedes. He also salvaged the only known extant portion of an uncopied manuscript by Diophantus. Regiomontanus' mathematical writing is generally classified as rhetorical, even careless, because of his habit of referring to proofs without actually presenting them. Of one in De triangulis he signs off, "...I leave it to you for homework."

Regiomontanus rejected the possibility that the Earth rotated around the sun ; however, being an early Renaissance man, not all of his beliefs were so fixed. It is suggested that Novara, a teacher of Copernicus, came into possession of a letter from Regiomontanus that implied a primitive Copernicanism , but this has not been proven. Regardless, Copernicus was inspired by Regiomontanus' critical notes to Ptolemy's Amalgest to revise the millennium-old view of the planet Earth and the solar system it shares.