A loser who was really a winner.

Christoph Clavius (1538-1612) Educational Reformer.

There is an unfortunate tendency amongst non-specialists when viewing the history of science to divide the scientists of the past into ‘winners’ and ‘losers’, famous examples being Copernicus and Ptolemaeus or Darwin and Lamarck.  Regarded from this perspective Christoph Clavius is definitely counted amongst the losers, a last deluded defender of the geocentricity of Ptolemaeus. In discussions on the evolution of the new astronomy in the early modern period he is usually ignored or if mentioned at all, only as a footnote in connection with the calendar reform. However as an educator and educational reformer Clavius actually played a very central and important role in the development of the new astronomy in the 17th century. The mathematical sciences were neglected almost to the point of extinction within the mediaeval educational system, the schools teaching almost no mathematics and the universities only paying lip service to a narrow curriculum of mathematical topics at the very lowest level. In order for the mathematisation of nature, that many historians regard as the core of the scientific revolution, to be consummated it became necessary in the 16th and 17th centuries to reform the prevailing education system and introduce a thorough grounding in the mathematical sciences in order to produce the mathematicians, astronomers and physicists capable of carrying out the task. The man who undertook this reform for the Catholic education system in Europe was Clavius.

Christoph Clavius. Engraving Francesco Villamena, 1606 Source: Wikimedia Commons

Clavius was born 25th March 1538 in the German town of Bamberg, the see of the prince-bishop of Franconia and that is all that is known about his background and youth before he was received into the Society of Jesus, by Ignatius Loyola himself, in February 1555. The Jesuits sent him to the University of Coimbra where he remained until about 1560. By 1561 he was enrolled in the Collegio Romano (now the Gregorian University) in Rome where he was to remain until his death 6th February 1612, with the exception of six months in 1574 that he spent assisting Francesco Maurolico (1494 – 1575) in Messina in Sicily. At the Collegio he studied theology taking his final vows as a Jesuit in September 1575. He began teaching mathematics in 1563 and was named professor in 1567. In about1572 he was appointed to the commission considering the calendar reform, a position he held until the reform was carried out in 1582. Following the reform and the controversy it caused Clavius was appointed by the Pope to explain and defend the reform against its many virulent critics; he published seven works on the subject between 1588 and 1612.

As already indicated above, his main life’s work was the reform of the education system through the introduction of a full mathematical curriculum. Founded in 1534 by Loyola the Jesuits had had education as one of their main aims from the very beginning. At first their curriculum based on strict Thomist Aristotelian philosophy had little room for mathematics but after he became professor in Rome Clavius fought against stiff internal opposition to have modern mathematics included in the Jesuit programme and although he did not achieve the very extensive programme he had originally conceived he did succeed in making mathematics a central part of a Jesuit education. He trained the first generation of teachers himself in Rome and then sent them out through Europe to train further teachers creating rapid expansion in a sort of pyramid system. Not only did he write the curriculum and train the teachers he also wrote the textbooks for the Jesuit colleges and seminaries, of which there were 444 and 56 respectively by 1626. He wrote up to date innovative textbooks for every single one of the then mathematical disciplines all of which became standard works for both Catholic and Protestant educational institutions throughout Europe for the whole of the 17th century. Leibniz and reputedly also Newton learnt their geometry from Clavius’ Euclid. Clavius and his fellow workers were also innovative, within the Collegio there existed a small institute for advanced mathematical studies, a unique facility within Europe at this time. This institute introduced the new symbolic algebra of Viète into Italy and was responsible for its diffusion there. Clavius himself was responsible for several important notational innovations within arithmetic and algebra. They also tested and confirmed the spectacular discoveries that Galileo claimed to have made in his Siderius Nuncius in 1610. Clavius stood in close contact, by letter, with Galileo, a good friend, as he did with almost every well-known mathematician in Europe. Galileo is known to have regularly received transcripts of the mathematics lectures at the Collegio.

An impression of the effect of the Clavian mathematics programme on the development of science in the 17th century can be obtained by looking at some of the scientists who were its graduates. Among the Jesuits we have Mateo Ricci (1552-1610) and Johann Adam Schall von Bell (1591-1666) who introduced western astronomy and mathematics into China and from there into many other Asian countries. Christoph Scheiner (1573-1650) whose Rosa Ursina sive Sol on solar astronomy remained unequalled until the 19th century. Grégoire de Saint-Vincent (1584-1667) who was himself a great maths teacher in the Southern Netherlands and major contributor to the development of the calculus. Giovanni Battista Riccioli (1598-1671) and Francesco Maria Grimaldi (1618-1663) astronomers whose nomenclature of lunar features is still in use today; Grimaldi also made important contribution in optics to the theory of diffraction, a term which he coined. Of course not only future Jesuits attended Jesuit schools and the most famous 17th century recipients of a Clavian education were the trio of great French philosopher scientists Marin Mersenne (1588-1648), Rene Descartes (1596-1650) and Pierre Gassendi (1592-1655) whose collective contributions to the sciences are too numerous to be named here. Last but by no means least the Italian Giovanni Domenico Cassini (1625-1712) probably the greatest observational astronomer of the 17th century was also a Clavian graduate. These prominent names stand for a much longer list of minor figures.

For science to develop and expand it is necessary for the education system to produce new generations of scientists a problem that is being discussed very much throughout Europe and America today; in the early modern period, with the explosion in scientific activity, this problem was particularly acute and the man who solved it for the Catholic countries was German mathematician and educator Christoph Clavius who very much deserves to be regarded as a winner and not a loser in the historical development of the mathematical sciences.

This is a potted version of a public lecture that I will be holding at the Remeis Observatory in Bamberg at 7:00 pm on 24th June. Anybody who’s in the area is welcome to come and hear me waffle and if you ask some interesting question at the end I might even buy you a good Franconian beer.

Literature: There is an excellent biography, in English, of Clavius as an astronomer from James M. Lattis, Between Copernicus and Galileo: Christopher Clavius and the Collapse of Ptolemaic Cosmology, University of Chicago Press, 1994. Clavius as an educational reformer is dealt with extensively in Peter Dear, Discipline and Experience, University of Chicago Press, 1995.