Category Archives: Small animals also make manure

Born under a bad sign.

Yesterday’s birthday boy has got to be a serious candidate for the most unfortunate astronomer of all times. Guillaume Joseph Hyacinthe Jean-Baptiste Le Gentil de la Galaisière (September 12, 1725 – October 22, 1792) was a French astronomer whose life as a scientist started auspiciously in that he was personally trained in his profession by the Cassini’s at the observatory in Paris. In order to understand when and why it all turned pear shaped we have to go back to the 16th and 17th centuries.

One of the consequences of the new cosmological models proffered by Copernicus in 1543 (heliocentrism) and Tycho in 1588 (geo-heliocentrism) was that the inner planets, Mercury and Venus, would or should cross, or as the astronomers say transit, the face of the sun. Now this does not occur by every orbit as the orbits of the planets are tilted slightly with respect to the apparent path of the sun around the earth and such transits are only visible from the earth when the planet, earth and sun are in the correct respective positions. For Venus this currently occurs in a pattern that repeats every 243 years, with pairs of transits eight years apart separated by long gaps of 121.5 years and 105.5 years.

Kepler the great astronomical calculator of the Early Modern period made the first accurate calculation for a transit of Venus for the year 1631 but unfortunately this was not observable from Europe as it took place at night. Even Kepler made mistakes and his calculations missed the next transit in 1639 but the brilliant young English astronomer Jeremiah Horrocks corrected Kepler’s tables and correctly predicted and observed this transit. Horrocks used one method of parallax based on the respective sizes of the sun and Venus to calculate the distance of the sun from the earth. His figures were wildly inaccurate but he did produce a figure for the distance that was many factors better than all previous estimates.

In 1663 in his Optica Promota James Gregory (1638 – 1675) sketched another method of parallax that could be used to calculate the earth sun distance that involved timing the beginning and end of a transit from widely spaced positions on the earth and then applying trigonometry to the figures obtained. This method was worked out in detail by Edmond Halley (1656 – 1742) who had first considered it whilst observing a transit of Mercury on St Helena in 1677; he published his mature reflection in 1716 suggesting an international effort to carry out the necessary observations. Even the long lived Halley did not live long enough for the next transit in 1761 but the French astronomer Joseph-Nicolas Delise (1688 – 1768) took up the idea and in 1760 expeditions of astronomers equipped with the best available instruments set off to all corners of the globe to observe the forthcoming transit. Among others the first sea trials of John Harrison’s timepiece to determine longitude was taken on the English expedition to Jamaica. Later James Cook would make another trial of a Harrison watch on his expedition to observe the 1769 transit in the South Seas. In 1761 Mason and Dixon, of the famous Line, were supposed to observe the transit from Sumatra but there ship was attacked by the French forcing them to return to England from whence the set out again only reaching South Africa from where they successfully observed the transit.

But what of Le Gentil? He had been chosen by the French Academy of Science to observe the transit from Pondicherry in India. He sailed from France in 1760 and made station on Mauritius, then known as Isle de France. As he was preparing to sail to Pondicherry he learned that it had been attacked and captured by the British so he changed his plans and shipped with a French frigate heading for Coromandel with only three months to go before the transit. However the captain of the ship hearing of the developments of the war with the British turned back to Mauritius forcing Le Gentil to observe the transit from a ship at sea making his observations scientifically worthless.

Back in Mauritius Le Gentil decided to stay in Asia for eight years and to observe the 1769 transit. He occupied his time by undertaking expedition around the Indian Ocean collection natural history data and specimens. In 1766 he decide to make his observations from Manila in the Philippines and set off by ship to his new destination. In the Philippines he changed his mind again and decided to return to Pondicherry. His decision was based on two factors a hostile attitude from the Spanish Governor of the Philippines and a request from the Academy of Science back in France to make his observations in India. After various adventures to sea he arrived in time for the transit in Pondicherry. He was treated with respect by the British authorities who even supplied him with a new high quality telescope and he set up his equipment for the great day. The days leading up to the transit and the days thereafter were perfect for observing however on the day of the transit the heavens were covered by clouds making all attempts at observing impossible. Le Gentil’s disappointment was only deepened as he discovered that the weather in Manila had been perfect for observing on the day.

Tired, ill and demoralised Le Gentil decided to return to France arriving in Mauritius in 1770 too ill to travel further. Finally late in the year he recovered sufficiently to set sail for France only to run into a hurricane at the Cape of Good Hope that drove his ship back to Mauritius where he landed again in 1771. Le Gentil had difficulties finding another ship prepared to take him back to Europe, finally a Spanish captain agreed to take him and after more sea adventures he finally arrived in Cadiz from where he proceeded overland back to France crossing the Pyrenees on October 8th 1771 however his trials and tribulations were long not over.

During his absence Le Gentil had been assumed dead and his heirs and creditors had already divided up his estate and the Academy of Science had awarded his position to somebody else. With the help of the King Le Gentil was able to get his position restored and in fact he married happily and had a daughter to comfort him in his old age. The last disappointment was the loss of his natural history specimens that had disappeared on the ship that had been driven back to Mauritius by the storm in his first attempt to return home. If ever an astronomer was born under a bad sign then it was Guillaume Joseph Hyacinthe Jean-Baptiste Le Gentil de la Galaisière.


Filed under History of Astronomy, Small animals also make manure

Pressure, friction and deafness.

Today’s post is for Jai at From the Hands Of Quacks for two reasons. Firstly she is writing a piece on history of science blogging for the History of Science Newsletter and in order to collect material she is conducting a survey at her blog for authors and readers of history of science blogs. So please pop over and devote two minutes of your time to filling out her questionnaire. While you’re there you could also take the time to read her excellent blog if you don’t already do so.

I was intending to write this post for Jai before I discovered her survey because today’s obscure scientist relates rather nicely to the main theme of Jai’s blog. From the Hands of Quacks is principally concerned with the history of aural surgery in the 19th century. Today’s birthday boy the French instrument maker, inventor and physicist Guillaume Amontons (August 31st 1663 – October 11th 1705) was deaf.

Amontons made a number of small but significant contributions to the history of science and is exactly the type of minor figure without whom scientific progress would not be possible but who in the popular presentation of the history of science are engulfed in the shadows cast by the so called giants.

As an inventor and instrument maker he produced improved versions of the barometer, the hygrometer and the thermometer. The last is particularly important as he invented an air thermometer that measured temperature using a gas instead of a fluid but did so by registering the change in pressure. This led to him making significant contributions to the development of the gas laws and in particular to directing research along the path towards the discovery of absolute zero.

Amontons other major contribution was the discovery and publication of the laws of friction; his three laws are:

1. The force of friction is directly proportional to the applied load. (Amontons 1st Law)

2. The force of friction is independent of the apparent area of contact. (Amontons 2nd Law)

3. Kinetic friction is independent of the sliding velocity. (Coulomb’s Law)

For a man who many people would, incorrectly, regard as handicapped Amontons managed to contribute much more to the evolution of science than many so-called able bodied scientists.


Filed under History of science, Small animals also make manure

A household name

My last post on John Flamsteed provoked a brief exchange in the comments between myself and Jim Harrison on the relationship between science and technology with footnotes on kitchen appliances, which forms a perfect introduction to my latest obscure scientist Flamsteed’s contemporary the Huguenot Denis Papin (1642 – 1712?) who was baptised on 22nd August. Now chances are that unless you are an avid historian of steam power you will never have heard of Monsieur Papin although the list of people with whom he worked reads like a who’s who of the scientific greats of the period. However Papin should really be a household name in the true sense of the term as he invented the pressure cooker. I find it interesting that we glorify scientists such as Newton or Einstein whose work whilst intellectual fascinating in truth has very little impact on the everyday lives of the common people whereas a man such as Papin whose invention can be found in the homes of many of those people disappears into obscurity.

Papin originally studied medicine but abandoned his medical practice in favour of mathematics and machinery. He became an assistant to Christian Huygens in Paris and was involved in Huygens’ attempts to create a vacuum under a piston using gunpowder. His own earlier studies of the vacuum had led to his speculation on using the vacuum as a motive force. During his time in Paris he also made the acquaintance and obtained the friendship of Leibniz. Sent by Huygens as a courier to the Royal Society in London Papin became an employee of Robert Boyle whom he assisted in his experiment with the air pump, the design of which he improved. As a result of these experiments Papin realised that the boiling point of water could be raised by increasing the pressure and this led him to the invention of the pressure cooker including the safety valve which would play an important role in the future harnessing of steam power. Papin realised that food could be cook with less energy and less loss of nutrients in his invention which he regarded as a boon for poor families.

After three years he left the employment of Boyle and became an assistant to Robert Hooke at the Royal Society. Leaving Britain he stayed briefly with Huygens in Paris before moving on to Venice where he was employed as director of experiments at the academy of Ambrose Sarotti. However this led nowhere and he returned to London and employment at the Royal Society. In 1687 Papin was appointed professor of mathematics at the University of Marburg, where he designed a simple one-cylinder atmospheric steam engine, which he published in 1695. In the atmospheric steam engine a piston is driven out of cylinder by expanding steam that is then forced to contract by cooling, causing a vacuum that sucks the piston back into the cylinder. Papin appears to have made no attempt to further develop or exploit this machine.

Papin on The Louvre in Paris with his piston

Courtesy of Arjen Dijksman

In 1707 Papin returned London and in 1712 he disappeared off the map and is assumed to have died. This year is significant, as it the year in which Thomas Newcomen invented his steam engine regarded as the first practical device to harness steam power but which is in fact only a modified version of Papin’s design. This raises the unanswered question as to whether Newcomen invented his machine in ignorance of Papin’s work or whether he copied it. In the history of technology this is not a trivial question as it was Newcomen’s engine that Watt improved and thereby laid the foundations of the industrial revolution.  To be fair to Newcomen Watt generally receives the laurels that are by rights his but the question remains whether they are by rights Papin’s. At least Papin gets the laurels for that most practical of household appliances the pressure cooker even if most people are not aware of it.


Filed under History of science, Small animals also make manure

The scientific potter.

For most people the name Wedgwood evokes visions of dinner services and ornate vases on mantelpieces. Biologists associate the name Josiah Wedgwood, born on 12th July 1730, with the maternal grandfather of Charles Darwin and the paternal grandfather of his wife Emma Darwin, née Wedgwood. However the good Josiah would have a place in the history of science if he had never produced any grandchildren. As I wrote in my brief post on Joseph Priestley, Wedgwood was along with Matthew Boulton, of steam engine fame, and Erasmus Darwin, Charles’ paternal grandfather, one of the founders of the Lunar Men, possibly the most interesting scientific society of the 18th century.


Josiah Wedgwood Source: Wikimedia Commons

Josiah himself was a potter who had served a traditional apprenticeship but who would go on to play a central role in the industrial revolution; he built up the family business into one the worlds leading ceramic companies. Wedgwood’s success was not only based on sound business sense but on systematic science based technique research. All of his life he conducted systematic scientific investigations into the composition of clays and glazes developing new forms of ceramic and finishes. His greatest scientific achievement was the invention of a pyrometer, a thermometer that determines temperatures visually, in order to be able to exactly control the temperature of his kilns; for this he was elected a member of the Royal Society. Outside of his work Josiah, along with his friends in the Lunar Society, was a passionate amateur scientist making active contributions to geology, mineralogy and botany.

Next time you stumble over the name Wedgwood remember that Josiah was not only the worlds most famous grandfather of a scientist but also an important scientist in his own right.


Filed under History of science, Small animals also make manure

John Wilkins Day

Regular readers of my meanderings on the history of science will have noticed that I fairly often refer to John Wilkins author of that excellent fount of biological wisdom Evolving Thoughts. The John Wilkins of my title however, is not the Internet’s beloved Aussie Anthropoid but his 17th century namesake the good Bishop of Chester who was born on the 1st of January (?) 14 February in 1614.

Greenhill, John, c.1649-1676; John Wilkins (1614-1672), Warden (1648-1659)

Greenhill, John; John Wilkins (1614-1672), Warden (1648-1659); Wadham College, University of Oxford;

Wilkins is one of those figures in the history of science who whilst making no real contributions to science itself succeeded in their work and writings in furthering the cause of science in a significant way. In his early writings Wilkins can be compared to a Martin Gardner or an Isaac Asimov. In fact the second comparison is more apposite as Wilkins wrote both science fiction and popular science books. One major difference is that whereas Asimov and Gardner are reacting to and reporting on the actual science of their age Wilkins is writing propaganda in an attempt to interest his readers in the new science of Copernicus, Kepler, Galileo and Mersenne which was still rejected by the majority of educated people in England at the time that he was writing.

Wilkins’ The Discovery of a World in the Moone was one of a series of stories published in the 17th century that use a fictitious journey to the moon as a means of presenting the Copernican world view. The first was Kepler’s Somnium published posthumously by his son-in-law in 1634. The second was Francis Godwin’s (another Anglican bishop) The Man in the Moone, or a Discourse of a Voyage thither, by Domingo Gonsales written earlier but first published in the same year as Wilkins volume, which it had strongly influenced, 1638. The last was Cyrano de Bergerac’s The Other World: The Comical History of the States and Empires of the Moon, which borrowed heavily from both Wilkins and Godwin and appeared in 1657. Wilkins followed this work with another piece of Copernican propaganda his A Discourse Concerning a New Planet in 1640. Of course all of these tales owe a debt to Lucian’s satire A True Story and Plutarch’s The Face on the Moon whilst at the same time anticipating Verne and Wells by more than two hundred years. Wilkins’ books were highly influential in spreading the heliocentric astronomy but he is also guilty of having started a scientific myth. In his work he claimed that Christoph Clavius, Europe’s most important astronomer in the first decade of the 17th century and a staunch defender of Ptolemaic geocentricity, had been converted to heliocentricity shortly before his death in 1612 by his institutes confirmation of Galileo’s telescopic discoveries. This claim is simply not true but in Wilkins’ defence it must be said that he was extrapolating from a deliberate false quote, published by Kepler, designed to imply the same.

In 1648 Wilkins published the 17th century’s equivalent of The Boy’s Own Book of Engineering Wonders his Mathematical Magick. The first half of this book was a description of the machines of antiquity as presented by Archimedes whilst the second half was more in the style of Leonardo and describes fantasy machines of the future. Leonardo and Wilkins were not alone in their fascination for machines both real and fantastic and this fascination was one of the driving forces behind the development of science in the Renaissance, but that is a subject for another post.

Wilkins was also the author of two related works on artificial languages. The first his Mercury or the Swift and Secret Messenger published anonymously in 1641 was the first book printed in English on cryptography. Interestingly one of Wilkins’ closest friends and fellow founding member of the Royal society, the mathematician John Wallis, gained his early reputation as a mathematician as a cryptographer for Cromwell in the English Revolution. His second book on languages An Essay towards a Real Character and a Philosophical Language, published in 1668 was an attempt at the establishment of an artificial universal language for the communication between natural philosophers i.e. scientists. This was part of a much larger interest in such projects throughout the 17th century, amongst others in the work of Bacon, Descartes and Leibniz, which is disgust briefly but informatively by the other John Wilkins in his book Species: A History of the Idea, (UCP, Berkeley, Los Angeles and London, 2009) pp. 57 – 65. As a foot note Wilkins’ Essay contains what appears to be the first ever proposal for a purely metric measuring system.

I have already briefly alluded to Wilkins main claim to fame the founding of the Royal Society. Wallis says that the Royal society had its origins in meetings of scientists organised by Wilkins in London beginning in 1645. After various diversions over Oxford and Cambridge this group came together formally in London in 1660, with Wilkins as their first Secretary, and gained their Royal Charter in 1662.

Wilkins is typical of a certain type of science fan who through their enthusiasm and active support do as much to further the cause of science as any scientist and in fact more than most. Such people need to be studied as much as the scientists if we are to truly understand the history of science.


Filed under History of science, Myths of Science, Small animals also make manure

Syphilis and Comets

The 6th August was the 456th anniversary of the death of the Renaissance medicus Girolamo Fracastoro. He is most famous for having given the disease syphilis its name in his poem Syphilis, sive morbi gallici i.e. Syphilis or the French disease. This tells the story of the shepherd Syphilis, who is struck down by the new disease because he has blasphemed. The name if the Latinised version of the Greek name Syphilos which can be translated as ‘lover of swine’, maybe Fracastoro is trying to say that syphilis is the result of bestiality.


Portrait of Girolamo Fracastoro by Titian, c.1528 Source: Wikimedia Commons

His other well known achievement as a doctor was his book from 1546 De contagionibus et contagiis morbis et eorum curatione, (Three Books on Contagions, the Contagious Diseases and their Treatment) which contains scientific descriptions of the plague, typhoid and foot and mouth disease. The book is also notable for Fracastoro’s contention that diseases are caused by seed-like entities a premise that foreshadows the germ theory of disease; although it should be pointed out that there are no links between Fracastoro and Koch.

Now some of you might wonder why I as a historian of mathematics should be interested in a mere medic? The answer is quite simple Fracastoro was, like many Renaissance medics, also an astronomer; the link being astrology, the main form of medicine in the Renaissance being astro-medicine or iatromathematics.*

In his capacity as astronomer/astrologer Fracastoro made two major contributions to the astronomical debate in the 16th century, firstly, he was one of several Paduan scholars who advocated a rejection of the Ptolemaic epicycle-deferent astronomy and a return to the Aristotelian homocentric astronomy. This was not new, the Islamic Aristotelian Averroes had suggested the same step in the 12th century criticising the Ptolemaic astronomy as infringing on the Aristotelian cosmological principle of homo-centricity i.e. that all heavenly bodies have a common centre of rotation, the earth. In the Ptolemaic system individual planets rotate around the centres of their epicycles that in turn rotate around the centres of their deferents, the earth. Averroes only criticised the Ptolemaic model as non-Aristotelian but al-Bitruji (fl. 1190) actually produced an improved mathematical homocentric model. Similarly in the early 16th century in Padua both Giovanni Battista Amico (1511? – 1536) and Fracastoro produced new homocentric models, Fracastoro publishing his Homocentricorum sive de stellis (Homocentric [Spheres] or Concerning the Stars) in 1538.

Now you may well ask what possible interest the publication of such a retrograde system, and the homocentric model is very inferior to the Ptolemaic system in explanatory power, could have for the evolution of astronomy? The answer is that it is part of the evidence that exposes a wide spread myth in the history of astronomy and cosmology. It is generally claimed in the popular presentations of the history of astronomy that Ptolemaeus’ geocentric view of the world reigned supreme, went unchallenged or was not questioned for 1400 years until Copernicus published his De revolutionibus. A different version of the same myth is that the scholastic synthesis of Aristotelian cosmology and Ptolemaic astronomy dominated the academic discourse without challenge until Copernicus etc. This is simply not true, both the Ptolemaic astronomy and the scholastic synthesis were criticised and questioned on many occasions and in the 16th century there were very lively debates amongst the astronomers and cosmologists of Europe on a large number of topics. The homocentricity of Fracastoro is just one example of these debates and Christoph Clavius the most influential arbitrator of all things astronomical and cosmological at the end of the 16th and beginning of the 17th centuries regarded the system of Fracastoro as at least as great a treat to his own preferred Ptolemaic system as the heliocentrism of Copernicus.

Another of the 16th century astronomical debates to which Fracastoro made a significant contribution concerned the nature of comets. In the 1530s Europe was visited by a series of spectacular comets and this produced several reactions under the leading astronomers. In Nürnberg, Johannes Schöner edited and published Regiomontanus’ book on comets and the measurement of cometary parallax that had been written in the 60s of the previous century but had remained unpublished due to his untimely death. In Ingolstadt Peter Apian published a series of pamphlets on his observations of these comets that included his observation, now know as Apian’s law, that the tails of comets always point away from the sun. This had already been known for a long time by the Chinese but was unknown in Europe. A lively debate developed between Gemma Frisius in Leuven, Jean Pena in Paris and Copernicus in Frauenburg concerning the nature of comets with Frisius concluding that comets were supra-lunar objects that focused the rays of the sun. This was of course in direct contradiction to the Aristotelian cosmology that stated that comets were sub-lunar. It was this debate that led the astronomers of Europe to try and measure the parallax of the 1577 comet with Tycho and Mästlin concluding that comets were supra-lunar and Tycho deducing from this that the crystalline spheres of Greek cosmology couldn’t exist. In Italy Fracastoro also observed the comets and independently arrived at Apian’s law, he also arrived at a very similar theory of comets to Frisius but reversing Tycho’s logic argued that comets must be sub-lunar because otherwise they would disturb the crystalline spheres; Fracastoro’s theories on the comets were taken up by Cardano.

There is a certain irony to the fact that Fracastoro published important texts on both syphilis and comets, as one of the prevailing medical theories of the period was that syphilis was a curse caused by comets. Fracastoro is a typical example of a relatively minor scholar who is today virtually unknown but in his own times made important contributions to the debate that propels the development of science.

*I shall post a detailed explanation of the connections between medicine and mathematics sometime in the future.


Filed under History of Astronomy, Renaissance Science, Small animals also make manure

Twinkle, twinkle little star how I wonder where you went?

On 3rd of August 1596 the Frisian amateur astronomer David Fabricius first observed the variable star Mira. There is some evidence that Mira might have been observed by earlier astronomers but it was Fabricius’ observation that eventual led to Mira being recognised as the first variable star.

Fabricius, whose real name would have probably been Schmidt, was a village pastor in East Frisian and serves as model for hundreds of similar clerics throughout Europe who in the 17th, 18th and 19th centuries contributed significantly to the development of, above all, natural history as devoted amateurs who invested their spare time in the study of nature. He made his first appearance on the European astronomy scene in 1592 when he wrote to Jost Bürgi, mathematicus and instrument maker at the court of Wilhelm IV of Hessen-Kassel, then the second most important centre for astronomy in Europe, requesting assistance in the construction of astronomical instruments. When he first observed Mira in 1596 he wrote a letter describing his discovery, he thought it was a nova, to Tycho Brahe in Hven the leading centre for astronomical research in Europe. Brahe was very impressed by the work of the Frisian cleric and an important scientific correspondence developed between the two men that lasted until Brahe’s death in 1601. On several occasions Brahe tried to convince Fabricius to come and work with him but the pastor preferred to remain in East Frisian. In 1601 Fabricius visited Tycho in Prague and during his stay he met Simon Marius with whom he also conducted an astronomical correspondence.

He did not however meet Brahe’s newest assistant Johannes Kepler who was in Austria dealing with family business during Fabricius’ visit, however a lively correspondence developed between the Frisian Pastor and the Imperial Mathematicus which lasted more than eight years with some of the letters running to 40 or 50 pages. This correspondence is very important for the history of astronomy because it is in these letters that Kepler outlines his path towards his first two planetary laws. Fabricius proved a worthy partner in this endeavour criticising and pointing out the weak points in Kepler’s argumentation. Criticism that Kepler was more than willing to accept from the man whom he regarded as the best observational astronomer in Europe after the death of Tycho. However Fabricius never accepted Kepler’s elliptical heliocentric orbits remaining a loyal Tychonicer, a fact that may have led to Kepler breaking off the correspondence somewhat abruptly in 1609.

In 1611 Fabricius’ son Johannes brought home a telescope from the University of Leiden where he was studying medicine. With this instrument the father and son, with the son this time in the leading role, discovered the sunspots. Although they were not the first European astronomers to make this discovery, this honour goes to Thomas Harriot, Johannes Fabricius was the first to publish it in his De Maculis in Sole in 1611. Unfortunately his publication went largely unnoticed and is not mentioned at all by Galileo and Christoph Scheiner in their monumental argument as to who first discovered the sunspots.

The end of David Fabricius’ life reads like something concocted by a Hollywood scriptwriter. Shortly before his death the worthy pastor held a sermon in which he claimed to know the identity of a chicken and goose thief but he did not reveal the name of the delinquent. On the 7 May 1617 he was beaten to death with a spade by the farmer, Frerik Hoyer, who thought that it was he who had been denounced from the pulpit.

The Fabricii, father and son, remain largely unknown to the world at large but a monument to them both was erected in the churchyard in Osteel, where David had been village pastor, in 1895.


David Fabricius is one of many scientific investigators who made significant contributions to the development of science but who remain largely unknown in our culture of big names and spectacular events.


Filed under History of Astronomy, Renaissance Science, Small animals also make manure

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.


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