Christopher Clavius, SJ (25 March 1538 – 6 February 1612ENCYCLOPEDIA.COM Clavius, Christoph
/ref>) was a Jesuit German

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, 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 in 1551, just 11 years after he founded the Society of Jesus (Jesuits). It quickly grew to include classes from elementary school t ...

, 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, moons, comets and galaxies – in either ...

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 or Luigi Giglio, was an Italian doctor, astronomer, philosopher and chronologist, and also the "primary author" who provided the proposal that (after modifications) be ...

, that is known as the

Gregorian calendar The Gregorian calendar is the calendar used in most parts of the world. It was introduced in October 1582 by Pope Gregory XIII as a modification of, and replacement for, the Julian calendar. The principal change was to space leap years dif ...

. 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 large peninsula conventionally considered a continent in its own right because of its great physical size and the weight of its history and traditions. Europe is also considered a subcontinent of Eurasia and it is located entirel ...

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 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 public research 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 u ...

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, 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

Rome , established_title = Founded , established_date = 753 BC , founder = King Romulus (legendary) , image_map = Map of comune of Rome (metropolitan city of Capital Rome, region Lazio, Italy).svg , map_caption ...

. 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 The ''Prutenic Tables'' ( la, Tabulae prutenicae from ''Prutenia'' meaning "Prussia", german: Prutenische oder Preußische Tafeln), were an ephemeris (astronomical tables) by the astronomer Erasmus Reinhold published in 1551 (reprinted in 1562, 1 ...

Erasmus Reinhold Erasmus Reinhold (22 October 1511 – 19 February 1553) was a German astronomer and mathematician, considered to be the most influential astronomical pedagogue of his generation. He was born and died in Saalfeld, Saxony. He was educated, und ...

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 Pope Gregory XIII ( la, Gregorius XIII; it, Gregorio XIII; 7 January 1502 – 10 April 1585), born Ugo Boncompagni, was head of the Catholic Church and ruler of the Papal States from 13 May 1572 to his death in April 1585. He is best known for ...

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 Benedict Pereira (also ''Pereyra'', ''Benet Perera'', ''Benet Pererius'') (March 4, 1536 – 6 March 1610) was a Spanish Jesuit philosopher, theologian, and exegete. Life Pereira was born at Ruzafa, near Valencia, in Spain. He entered the Socie ...

. In

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premise ...

, Clavius' Law (inferring of the truth of a proposition from the inconsistency of its negation) is named after him. He used the

decimal point A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form (e.g., "." in 12.45). Different countries officially designate different symbols for use as the separator. The choi ...

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.

Astronomy

Clavius wrote a commentary on the most important astronomical textbook of the late Middle Ages, ''De Sphaera'' of

Johannes de Sacrobosco Johannes de Sacrobosco, also written Ioannes de Sacro Bosco, later called John of Holywood or John of Holybush ( 1195 – 1256), was a scholar, monk, and astronomer who taught at the University of Paris. He wrote a short introduction to the Hi ...

. 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 Tycho Brahe ( ; born Tyge Ottesen Brahe; generally called Tycho (14 December 154624 October 1601) was a Danish astronomer, known for his comprehensive astronomical observations, generally considered to be the most accurate of his time. He was ...

) 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. As an astronomer Clavius held strictly to the geocentric model of the solar system, in which all the heavens rotate about the

Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...

. Though he opposed the

heliocentric model Heliocentrism (also known as the Heliocentric model) is the astronomical model in which the Earth and planets revolve around the Sun at the center of the universe. Historically, heliocentrism was opposed to geocentrism, which placed the Earth a ...

Copernicus Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formulated ...

, 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 A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally meaning only an optical instrument using lenses, curved mirrors, or a combination of both to observ ...

; Clavius had by that time accepted the new discoveries as genuine, though he retained doubts about the reality of the mountains on the

Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...

and said he could not see the four Jupiter's satellites through the telescope. 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 mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

, 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 Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultrav ...

, 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

* Commentary on Euclid, 1574
''Gnomonices libri octo''
1581 reatise_of_gnomonics.html" ;"title="gnomonics.html" ;"title="reatise of gnomonics">reatise of gnomonics">gnomonics.html" ;"title="reatise of gnomonics">reatise of gnomonics* * ''Novi calendarii romani apologia''. Rome, 1588
''Astrolabium''
Rome, 1593 * * ''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) * ''Refutatio cyclometriae Joseph Justus Scaliger, Iosephi Scaligeri''. Mainz, 1609 *
Elementorum Libri XV
'. Cologne, 1627 (Published online by the Sächsischen Landesbibliothek - Staats- und Universitätsbibliothek Dresden) * (Critical edition of his correspondence) Clavius' complete mathematical works (5 volumes, Mainz, 1611–1612) ar
available online
.

References

* 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 *

* ttps://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

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