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Christopher Clavius

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The Reverend
Christopher Clavius
SJ
Born 25 March 1538
Bamberg, Bavaria, Holy Roman Empire
Died 6 February 1612 (aged 73)
Rome, Papal States
Alma mater University of Coimbra
Collegio Romano
Known for Gregorian calendar
Clavius' Law
Scientific career
Fields Mathematics, astronomy
Workplaces Collegio Romano

Christopher Clavius, SJ (25 March 1538 – 6 February 1612[1]) was a Jesuit German mathematician and physicist, head of mathematicians at the Collegio Romano, and astronomer who was a member of the Vatican commission that accepted the proposed calendar invented by Aloysius Lilius, that is known as the Gregorian calendar. Clavius would later write defences and an explanation of the reformed calendar, including an emphatic acknowledgement of Lilius' work. In his last years, he was probably the most respected astronomer in Europe and his textbooks were used for astronomical education for over fifty years in and even out of Europe.[2]

Early life

Little is known about Christopher Clavius' early life, with the only certain fact being that he was born in Bamberg in either 1538 or 1537.[3] His given name is not known to any great degree of certainty—it is thought by scholars to have perhaps been Christoph Clau or Klau. There are also some who think that his taken name, Clavius, may be a Latinization of his original German name, suggesting that his name may have been Schlüssel (German for 'key', which is clavis in Latin).

Clavius joined the Jesuit order in 1555. He attended the University of Coimbra in Portugal, where it is possible that he had some kind of contact with the famous mathematician Pedro Nunes (Petrus Nonius). Following this he went to Italy and studied theology at the Jesuit Collegio Romano in Rome. He was ordained in 1564, and 15 years later was assigned to compute the basis for a reformed calendar that would stop the slow process in which the Church's holidays were drifting relative to the seasons of the year. Using the Prussian Tables of Erasmus Reinhold and building on the work of Aloysius Lilius, he proposed a calendar reform that was adopted in 1582 in Catholic countries by order of Pope Gregory XIII and is now the Gregorian calendar used worldwide.

Within the Jesuit order, Clavius was almost single-handedly responsible for the adoption of a rigorous mathematics curriculum in an age where mathematics was often ridiculed by philosophers as well as fellow Jesuits like Benito Pereira.[4] In logic, Clavius' Law (inferring of the truth of a proposition from the inconsistency of its negation) is named after him.

He used the decimal point in the goniometric tables of his astrolabium in 1593 and he was one of the first who used it in this way in the West.[5][6]

Astronomy

Clavius wrote a commentary on the most important astronomical textbook of the late Middle Ages, De Sphaera of Johannes de Sacrobosco. The commentary by Clavius was one of the most influential astronomy textbooks of its time and had at least 16 editions between 1570 and 1618, with Clavius himself revising the text seven times and in each case greatly expanding it.[7] In the 1585 edition of his aforementioned commentary he located (independently of Tycho Brahe) the nova from 1572 in the fixed stars sphere (in the constellation of Cassiopeia) and found that the position of the nova was exactly the same for all observers. That meant that it had to be beyond the Moon, and the doctrine that the heavens could not change was proven false.[8]

As an astronomer Clavius adhered strictly to the geocentric model of the Solar System, in which all the heavens rotate about the Earth. Though he opposed the heliocentric model of Copernicus, he recognized problems with the Ptolemaic model. He was treated with great respect by Galileo, who visited him in 1611 and discussed the new observations being made with the telescope; Clavius had by that time accepted the new discoveries as genuine,[9] though he retained doubts about the reality of the mountains on the Moon and said he could not see the four Jupiter's satellites through the telescope.[10] Later, a large crater on the Moon was named in his honor.

Collegio Romano

During his time at Collegio Romano Clavius served as the head of the mathematicians, a public professor of mathematics, and as the Director of Advanced Instruction and Research at the Academy of Mathematics until 1610 in an official capacity and for two more years until 1612 in an informal role.[11] The Academy existed in an informal capacity for many years before Clavius' arrival in Rome in 1561. However, in 1580 in his document titled Ordo servandus in addiscendis disciplinis mathematicis, Clavius described a detailed curriculum for mathematics to have the College officially recognize the Academy.[11]

The curriculum he proposed contained three different curricula aiming to educate new Jesuits in mathematics. The curriculum contained three different courses: one year, a two-year, and a three-year. The course material to be covered were optics, statics, astronomy, and acoustics,[11] emphasizing mathematics.

His request was eventually denied, but nonetheless he was given the title of Professor of Mathematics. Clavius made another attempt in 1586 to establish the Academy as an official course at the Collegio Romano, but there was opposition from the philosophers at the College. The Academy remained an unofficial curriculum until 1593 or 1594.

Upon its eventual founding, the Academy required nomination by the Professor of Mathematics for admission. Clavius taught the advanced course within the Academy, but little is known about his specific teachings and work as a professor during his time at the College. The exact number of students that Clavius taught is unclear, but in a letter from Christoph Grienberger to Clavius in 1595, it is stated that at that time, Clavius had around ten students.[11] The exact structure of the courses and how they were taught is unclear. There has been no evidence to show whether the students he taught shared classes or the specific material he chose to cover. The purpose for founding the Academy was to train technical specialists,[11] to expand the pedagogical corps to support the growing need for professors, as the number of colleges at the time was rapidly increasing,[11] as well as the training of missionaries in order to support their efforts in remote places.[11] With the purpose of the Academy clear, most of what Clavius and his students did in the Academy is unknown. This lack of detailed information has led to most of what Clavius did during his years at the College falling into obscurity.

Clavius and Galileo Galilei often shared correspondence during his time at the College, discussing proofs and theories. It is likely that while running the Academy, he was also writing to Galileo and sharing his notes from the College's logic course to help Galileo in his endeavors to be able to adequately explain and demonstrate his ideas to others, which is something Galileo had struggled with in the past, specifically when trying to convince Clavius of his methods.[12]

Following his death in 1612, informal courses in the Academy continued at the College. However, due to the lack of mention of mathematicians in the College's catalog after 1615, it appears the Academy's official recognition by the Collegio Romano ended soon after Christopher Clavius's death.[11]

Selected works

Clavius' complete mathematical works (5 volumes, Mainz, 1611–1612) are available online.

See also

  • Asteroid 20237 Clavius
  • Clavius (crater), a lunar crater named after Clavius
  • Clavius Base, located in Clavius crater, in both the novel and film versions of 2001: A Space Odyssey
  • Aloysius Lilius
  • Computus
  • List of Jesuit scientists
  • List of Roman Catholic scientist-clerics
  • Bracket (mathematics)

From the 1913 Catholic Encyclopedia

Christopher Clavius (Christoph Clau) mathematician and astronomer, whose most important achievement related to the reform of the calendar under Gregory XIII; born at Bamberg, Bavaria, 1538; died at Rome, 12 February, 1612. The German form of his name was latinized into "Clavius". He entered the Society of Jesus in 1555 and his especial talent for mathematical research showed itself even in his preliminary studies at Coimbra. Called to Rome by his superiors as teacher of this branch of science at the well-known Collegium Romanum, he was engaged uninterruptedly there until his death. the greatest scholars of his time, such men as Tycho Brahe, Johann Kepler, Galileo Galilei, and Giovanni Antonio Magini, esteemed him highly. He was called the "Euclid of the sixteenth century"; and even his scientific opponents, like Scaliger, said openly that they would rather be censured by a Clavius than praised by another man. There has, however, been no lack of persistent disparagement of Catholic scholars even down to our own times; and therefore much that is inexact, false, and mythical has been put into circulation about Clavius, as for example that he was originally named "Schlüssel" (clavis, "key"), that he was appointed a cardinal, that he met his death by the thrust of a mad bull, etc. His relations with Galilei, with whom he remained on friendly terms until his death, have also been often misrepresented. The best evidence of the actual achievements of the great man is presented by his numerous writings, which at the end of his life he reissued at Mainz in five huge folio volumes in a collective edition under the title, "Christophori Clavii e Scoietate Jesu opera mathematica, quinque tomis distributa". The first contains the Euclidian geometry and the "Spheric" of Theodosius (Sphaericorum Libri III); the second, the practical geometry and algebra; the third is composed of a complete commentary upon the "Sphaera" of Joannes de Sacro Bosco (John Holywood), and a dissertation upon the astrolabe; the fourth contains what was up to that time the most detailed and copious discussion of gnomonics, i.e. the art of constructing all possible sun-dials; finally, the fifth contains the best and most fundamental exposition of the reform of the calendar accomplished under Gregory XIII.

Many of these writings had already appeared in numerous previous editions, especially the "Commentarius in Sphaeram Joannis de Sacro Bosco" (Rome, 1570, 1575, 1581, 1585, 1606; Venice, 1596, 1601, 1602, 1603, 1607, Lyons, 1600, 1608, etc.); likewise the "Euclidis Elementorum Libri XV" (Rome 1574, 1589, 1591, 1603, 1605; Frankfort 1612). After his death also these were republished in 1617, 1627, 1654, 1663, 1717, at Cologne, Frankfort, and Amsterdam, and were even translated into Chinese. In his "Geometria Practica" (1604) Clavius states among other things a method of dividing a measuring scale into subdivisions of any desired smallness, which is far more complete than that given by Nonius and must be considered as the precursor of the measuring instrument named after Vernier, to which perhaps the name Clavius ought accordingly to be given. The chief merit of Clavius, however, lies in the profound exposition and masterly defence of the Gregorian calendar reform, the execution and final victory of which are due chiefly to him. Cf. "Romani calendarii a Gregorio XIII restituti explicatio" (Rome, 1603); "Novi calendarii Romani apologia (adversus M. Maestlinum in Tubingensi Academiâ mathematicum)" (Rome, 1588). Distinguished pupils of Clavius were Grienberger and Blancanus, both priests of the Society of Jesus.

References

  1. Back to citation ENCYCLOPEDIA.COM Clavius, Christoph
  2. Back to citation "The books of Clavius were translated into Chinese, by one of his students Matteo Ricci "Li Madou" (1552-1610), and his influence for the development of science in China was crucial." Costantino Sigismondi, Christopher Clavius astronomer and mathematician
  3. Back to citation The exact year is somewhat unknown and depends on when one assumes a new year begins.
  4. Back to citation Amir Alexander (2014). Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World. Scientific American / Farrar, Straus and Giroux. ISBN 978-0374176815., p. 69
  5. Back to citation Apparently Francesco Pellos used the decimal point in his Compendio del Abaco already around 1492 but was much less known than Clavius. Jekuthiel Ginsburg, "On the early history of the decimal point", American Mathematical Monthly 35 (1928) 347–349.
  6. Back to citation "Christopher Clavius", School of Mathematics and Statistics, University of St Andrews
  7. Back to citation James M. Lattis, article Clavius, in New Dictionary of Scientific Biography, Volume 2.
  8. Back to citation Clavius himself acknowledged this in his 1585 commentary: «If it is true [that the nova is a new star] then Aristotle's followers ought to consider how they can defend his opinion about the matter in the heavens. For perhaps it should be said that the heavens are not made of a fifth element but changeable bodies - albeit less corruptible that the matter here on earth… Whatever it finally turns out to be (and I do not insert my opinion into such matters) it is enough for me at present that the star we are talking about is located in the sphere of the fixed stars.» Lattis, James M. (1994). Between Copernicus and Galileo: Christoph Clavius and the Collapse of Ptolemaic Cosmology. Chicago: University of Chicago Press. p. 151. ISBN 0-226-46927-1.
  9. Back to citation Koestler, Arthur (1989) [1959 (by Hutchinson, London)]. The Sleepwalkers: A History of Man's Changing Vision of the Universe. Arkana, Penguin. p. 430 (Part V, Chapter 1: Triumph). ISBN 978-0-14-019246-9.
  10. Back to citation Koestler, Arthur (1989) [1959]. The Sleepwalkers: A History of Man's Changing Vision of the Universe. Penguin. p. 373 (Part IV, Chapter 8, The battle of the satelites).
  11. Back to citation occurrence 11.0 Back to citation occurrence 11.1 Back to citation occurrence 11.2 Back to citation occurrence 11.3 Back to citation occurrence 11.4 Back to citation occurrence 11.5 Back to citation occurrence 11.6 Back to citation occurrence 11.7 Feingold, Mordechai, ed. (2002). Jesuit Science and the Republic of Letters. MIT Press. pp. 47–54. ISBN 9780262062343.
  12. Back to citation Wallace, William (1984). The Heritage of the Collegio Romano. Princeton: Princeton University Press. pp. 281–291. ISBN 9780691612195.

Bibliography

  • Ralf Kern, Wissenschaftliche Instrumente in ihrer Zeit. Cologne, 2010. pp. 254 – 255.
  • Lattis, James M. (1994). Between Copernicus and Galileo: Christoph Clavius and the Collapse of Ptolemaic Cosmology. Chicago: University of Chicago Press. ISBN 0-226-46927-1.
  • Karl Christian Bruhns (1876). "Clavius, Christoph". Allgemeine Deutsche Biographie (in German). Vol. 4. Leipzig: Duncker & Humblot. pp. 298–299.
  • Edmondo Lamalle (1957). "Clavius, Christoph". Neue Deutsche Biographie (in German). Vol. 3. Berlin: Duncker & Humblot. p. 279.
  • Christoph Clavius, Corrispondenza, Edizione critica a cura di Ugo Baldini e Pier Daniele Napolitani, 7 volumes, Edizioni del Dipartimento di Matematica dell'Università di Pisa, Pisa, 1992
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