The influence of a Renaissance mathematics teacher.

Recent posts here have been all over the #histSTM map so I thought it was time to return to the roots and write something about a Renaissance mathematicus. It was first during the fifteenth century that Medieval European universities began to create dedicated chairs for the study of the mathematical disciplines — arithmetic, geometry, astrology, astronomy, surveying, cartography, designing and constructing sundials and mathematical instruments. The first such chair to be established in Germany was at the University of Ingolstadt in about 1470. Like its predecessors in Northern Italy this was principally a chair for teaching astrology and the mathematics and astronomy necessary to cast horoscopes to medical students. Those teaching in Ingolstadt, however, extended their activities to cover the full range of Renaissance mathematical studies. As well as producing medical students Ingolstadt also created full blood mathematical scholars, who would carry the seeds of mathematical studies to other towns and regions. One of those Ingolstadt seeds was Johannes Stöffler.

Contemporary Author’s Portrait Stöfflers from his 1534 published Commentary on the Sphaera of the Pseudo-Proklos (actually Geminos) Source: Wikimedia Commons

Johannes Stöffler was born in Blaubeuren in the Swabian Jura 10 December 1452. He received his first education in Blaubeuren and matriculated at the University of Ingolstadt on 21 April 1472 graduating BA in September 1473 and MA in January 1476. As many of the other contemporary mathematical scholars Stöffler entered a career in the Church rising to parish priest in Justingen in 1481. Parallel to his clerical work he became a highly active astrologer, astronomer, clock, globe and instrument maker. He was a very successful mathematicus and enjoyed a widespread good reputation. He constructed a, still extant, celestial globe for Daniel Zehender auxiliary Bishop of Konstanz in 1593, a clock for the Minster in Konstanz in 1596 and later another celestial globe Johann von Dalberg, Bishop of Worms. For Johannes Reuchlin, Germany’s leading Hebraist and prominent humanist scholar, he constructed an equitorium to determine the orbits of the Sun and the Moon.

Celestial Globe, Johannes Stöffler, 1493; Landesmuseum Württemberg Source: Wikimedia Commons

In 1507, the already fifty-five year old, Stöffler was appointed by Duke Ulrich I of Württemberg to the newly created chair of mathematics at the University of Tübingen. He extended his reputation as an instrument and globe maker as an academic with a successful series of technical publications.

Portrait of Johannes Stöffler produced for the Tübingen Professors’ Gallery 1614 Source: Wikimedia Commons

When he set up the first scientific publishing house in Nürnberg, Regiomontanus’ most successful publication was his ephemerides, sets of tables enabling the user to determine the position of the planets at any given time. Produced principally for astrologers they were also useful for astronomers, navigators and cartographers. There had been earlier manuscript ephemerides but Regiomontanus’ were the first printed ones and were distinguished from earlier ones by their high level of accuracy, leading to many pirated editions. Ephemerides are only calculated for a given number of years and Stöffler, together with the Ulm parish priest Jakob Pflaum, extended Regiomontanus’ ephemerides to 1531 and in a later posthumously published edition to 1551. The Regiomontanus/Stöffler/Pflaum ephemerides dominated the market and established Stöffler and Pflaum as the leading astrologers of the age.

In 1512 Stöffler published a text on the construction and use of the astrolabe, Elucidatio fabricae ususque astrolabii, which went through 16 editions up to 1620 and was highly influential.

The leading astrolabe maker in the early sixteenth century was the Nürnberger Georg Hartmann, who was probably the first instrument maker to mass-produce astrolabes in series. It has been shown that Hartmann’s work was based on Stöfffler’s book.

Georg Hartmann

Astrolabe from Georg Hartmann, Yale Source: Wikimedia Commons

As university teacher Stöffler exercised a major influence on his student the most famous of which were Sebastian Münster and Philipp Melanchthon. From 1514 to 1518 Sebastian Münster, already a fan of the Renaissance mathematical sciences, studied under Stöffler.

Portrait of the Cosmographer Sebastien Münster Christoph Amberger (1505-1562)

Later Münster would publish his Cosmographia in the publishing house of his step-son Heinrich Petri in Basel. The Cosmographia, “a description of the whole world with everything it contain”, an atlas but so much more was the biggest selling book of the sixteenth century. In an age where the edition of a book was usually counted in hundred the Cosmographia is estimated to have sold in excess of 120,000 in its German and Latin editions over a period of about one hundred years.

Title page of the Cosmographia first edition Source: Wikimedia Commons

Stöffler’s biggest influence on the history of mathematics was, without doubt through Philipp Melanchthon. Melanchthon a nephew of Reuchlin was something of a child prodigy.

Portrait of Philipp Melanchthon from an oil painting on wood by Lucas Cranach d. Ä. 1543 Source: Wikimedia Commons

He entered the University of Heidelberg in 1509 and graduated BA in 1511 just thirteen years old. In 1512 he changed to the University of Tübingen, where he came under the influence of Stöffler. Under Stöffler he studied the mathematical disciplines and became a passionate supporter of the art of astrology. He graduated MA in 1514. In 1518 he, just twenty-one years old, was appointed professor of Greek, on Reuchlin’s recommendation, at the University of Wittenberg.

In Wittenberg Melanchthon became Luther’s friend and supporter and during the Reformation as Luther’s “Præceptor Germaniae” (Germany’s schoolmaster) he was charged with designing, organising and establishing the new Lutheran Protestant education system. Melanchthon now had the chance to promote his love of astrology won as a student of Stöffler. Melanchthon established chairs for mathematics on all of the new Protestant Gymnasia (high schools) and university, choosing the ablest mathematical scholars available to fill the new positions. Thus Johannes Schöner became professor for mathematics on the new gymnasium in Nürnberg and Georg Joachim Rheticus and Erasmus Reinhold the mathematics professors in Wittenberg. Melanchthon’s aim was to produce new generations of professionally educated astrologers. Through his actions the Protestant education system became an active supporter of the mathematical sciences at a time when they were largely neglected within the Catholic education system. Melanchthon’s system would go on to produce many leading sixteenth century mathematical practitioners.

Stöffler is a good example of a Renaissance mathematicus who tends not to feature in the mainstream history of mathematics but who from the second row behind the big names still had a major influence on the evolution of the discipline through various channels.