Christopher Clavius (25 March 1538 – 6 February 1612ENCYCLOPEDIA.COM Clavius, Christoph
/ref>) was a
Jesuit , image = Ihs-logo.svg , caption = Christogram A Christogram (Latin ') is a monogram or combination of letters that forms an abbreviation for the name of Jesus Christ, traditionally used as a Christian symbolism ...
German mathematician This is a List of German mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical struct ...
, head of mathematicians at the
Collegio Romano The Roman College ( la, Collegium Romanum, it, Collegio Romano) was a school established by St. Ignatius of Loyola Ignatius of Loyola, Society of Jesus, S.J. (born Iñigo López de Oñaz y Loyola; eu, Ignazio Loiolakoa; es, Ignacio de Loyo ...

Collegio Romano
, and
astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, g ...

who was a member of the Vatican commission that accepted the proposed calendar invented by
Aloysius Lilius Aloysius Lilius (c. 1510 – 1576), also variously referred to as Luigi Lilio, Luigi Giglio, was an Italian Italian may refer to: * Anything of, from, or related to the country and nation of Italy ** Italians, an ethnic group or simply a citi ...
, that is known as
Gregorian calendar The Gregorian calendar is the calendar A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months and years. A calendar date, date is the designation of a single, speci ...
. 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 Europe is a continent A continent is any of several large landmass A landmass, or land mass, is a large region In geography Geography (from Greek: , ''geographia'', literally "earth description") is a field of scienc ...

and his textbooks were used for astronomical education for over fifty years in and even out of Europe.

Early life

Little is known about Clavius' early life other than the fact that he was born in
Bamberg Bamberg (, , ) is a town in Upper Franconia Upper Franconia (german: Oberfranken) is a ''Regierungsbezirk A ' () means "governmental district" and is a type of administrative division in Germany. Four of sixteen ' (states of Germany) are s ...

in either 1538 or 1537. 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 The University of Coimbra (UC; pt, Universidade de Coimbra, ) is a Portuguese public university in Coimbra, Portugal. First established in Lisbon in 1290, it went through a number of relocations until moving permanently to Coimbra in 1537. The ...

University of Coimbra
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, where it is possible that he had some kind of contact with the famous mathematician
Pedro Nunes Pedro Nunes (; Latin: ''Petrus Nonius''; 1502 – 11 August 1578) was a Portugal, Portuguese mathematics, mathematician, cosmographer, and professor, from a New Christian (of Jewish origin) family. Considered one of the greatest mathematici ...

Pedro Nunes
(''Petrus Nonius''). Following this he went to Italy and studied theology at the Jesuit
Collegio Romano The Roman College ( la, Collegium Romanum, it, Collegio Romano) was a school established by St. Ignatius of Loyola Ignatius of Loyola, Society of Jesus, S.J. (born Iñigo López de Oñaz y Loyola; eu, Ignazio Loiolakoa; es, Ignacio de Loyo ...

Collegio Romano
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. In 1579 he 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 Erasmus Reinhold (22 October 1511 – 19 February 1553) was a German German(s) may refer to: Common uses * of or related to Germany * Germans, Germanic ethnic group, citizens of Germany or people of German ancestry * For citizens of German ...
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. In logic, Consequentia mirabilis, Clavius' Law (inferring of the truth of a proposition from the inconsistency of its negation) is named after him. He used the decimal mark, 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.


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. In the 1585 edition of his aforementioned commentary he located (independently of Tycho Brahe) the SN 1572, nova from 1572 in the fixed stars sphere (in the constellation of Cassiopeia (constellation), 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. As an astronomer Clavius held strictly to the geocentric model of the solar system, in which all the heavens rotate about the Earth. Though he opposed the heliocentrism, heliocentric model of Nicolaus Copernicus, Copernicus, he recognized problems with the Ptolemy, Ptolemaic model. He was treated with great respect by Galileo Galilei, Galileo, who visited him in 1611 and discussed the new observations being made with the Refracting telescope#Galileo.27s telescope, telescope; Clavius had by that time accepted the new discoveries as genuine, though he retained doubts about the reality of the mountains on the Moon and said he could not see the four Galilean moons, Jupiter's satellites through the telescope. Later, a Clavius (crater), 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 Mathematician, 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. The Academy existed in an informal capacity for many years before Clavius arrived 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. 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, 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. 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, to expand the pedagogical corps to support the growing need for professors, as the number of colleges at the time was rapidly increasing, as well as the training of missionaries in order to support their efforts in remote places. 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. 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.

Selected works

* * ''Novi calendarii romani apologia''. Rome, 1588 * ''Romani calendarii a Gregorio XIII P.M. restituti explicatio''. Rome, 1603 (An explanation of the Gregorian calendar) **
Romani calendarii a Gregorio XIII P.M. restituti explicatio
'. (European Cultural Heritage Online) **
Romani calendarii a Gregorio XIII P.M. restituti explicatio
'. (University of Notre Dame) * Commentary on Euclid, 1574 *
Elementorum Libri XV
'. Cologne, 1627 (Published online by the Sächsischen Landesbibliothek - Staats- und Universitätsbibliothek Dresden) * Treatise of gnomonics, 1581 * * ''Refutatio cyclometriae Joseph Justus Scaliger, Iosephi Scaligeri''. Mainz, 1609 * (Critical edition of his correspondence) Clavius' complete mathematical works (5 volumes, Mainz, 1611–1612) ar
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 Aloysius Lilius (c. 1510 – 1576), also variously referred to as Luigi Lilio, Luigi Giglio, was an Italian Italian may refer to: * Anything of, from, or related to the country and nation of Italy ** Italians, an ethnic group or simply a citi ...
* Computus * List of Jesuit scientists * List of Roman Catholic scientist-clerics * Bracket (mathematics)


* Ralf Kern, ''Wissenschaftliche Instrumente in ihrer Zeit''. Cologne, 2010. pp. 254 – 255. * * * * 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

External links

Christopher Clavius (1537-1612)
The Galileo Project *

* [https://hos.ou.edu/galleries//01Ancient/HeroOfAlexandria/1575//15thCentury/Vespucci//16thCentury/Clavius/ Online Galleries, History of Science Collections, University of Oklahoma Libraries]—High resolution images of works by and/or portraits of Christopher Clavius in JPEG and TIFF formats
Cristoforo Clavio
in th
Historical Archives of the Pontifical Gregorian University
* Project Clavius On The Web
A Web platform for the works and literature of Christophorus Clavius
CNR-IIT, CNR-ILC, APUG {{DEFAULTSORT:Clavius, Christopher 1538 births 1612 deaths People from Bamberg 16th-century German astronomers 16th-century German Jesuits German scientific instrument makers University of Coimbra alumni Gregorian calendar 16th-century German mathematicians 17th-century German mathematicians Jesuit scientists 17th-century German astronomers