# Category Archives: Local Heroes

## How far the moon?

Anyone coming to the history of the search for a method to accurately determine longitude through Dava Sobel’s Longitude might be forgiven for thinking that the lunar distance method was just some sort of excuse dreamed up by Neville Maskelyne to prevent John Harrison receiving his just deserts. This is far from being the case. The lunar distance method first explicated by Johannes Werner in Nürnberg at the beginning of the 16th century was the method supported by nearly all astronomers since at least Newton as they were of the opinion that it would not be possible to construct a clock sturdy enough to survive a rough sea voyage and extreme changes of temperature and accurate enough to keep its time over several weeks in the foreseeable future. It should be remembered that it was the astronomers, responsible for keeping track of time since the dawn of civilisation, who had invented and developed the mechanical clock and it was the astronomical instrument makers who were the leading clock makers of the period so they really did know what they were talking about. For these highly knowledgeable men the lunar distance method genuinely seemed to offer more hope of a solution to the problem.

The lunar distance method is one of several ‘astronomical clock’ methods of determining longitude. The theory says that if one has a set of tables detailing the position of the moon respective to a given star or group of stars for accurately determined time intervals for a given fixed position then by observing the moon’s distance from said star or stars locally and noting the local time it should be possible to calculate the time difference of the two observations, real and tabular, and thus determine the longitude of the current position relative to the fixed position in the tables. Four minute of time difference equal one degree of longitude difference.

Two lunar observations taken at the same true local times

with the observers separated by 90 degrees of longitude

To make this system viable one needs two things, an instrument capable of accurately determining the lunar distance on a moving ship and accurate lunar distance tables. The first problem was solved by the English mathematician and instrument maker John Hadley who I’ve written about before and the second by the German cartographer and astronomer Tobias Mayer who died two hundred and fifty years ago today on 20th February 1762, aged just 39.

Tobias Mayer

Mayer was born on in 17th February 1723 in Marbach but his family moved to Esslingen less than two years later.

Mayer’s place of birth in Marbach

Now the Mayer Museum

He grew up in comparative poverty and when his father died in 1731 Tobias was placed in an orphanage. He received only very basic schooling and was a mathematical autodidact. However at the age of eighteen he had already published a book on geometry and a town plan of Esslingen. In 1743 he moved to Augsburg where he worked for the Pfeffel publishing house and where he published a Mathematical Atlas and a book on fortification. His publications led to him being appointed to a senior position at the Homanns Erben cartographical publishing house in Nürnberg, one of the leading cartography companies in Europe, in 1745.

Mayer’s workplace in Nürnberg home of the Homanns Erben publishing house

Today the museum of the history of the city of Nürnberg Fembo Haus

In his six years in Nürnberg Mayer published about thirty maps and numerous astronomical papers with a special emphasis on lunar research. It was during his time in Nürnberg that Mayer laid the foundations of his lunar tables for the lunar distance method.

By 1751 Mayer enjoyed a reputation as one of the leading European astronomers and he was offered the chair of mathematics at Göttingen and the directorship of the university observatory. During the next ten years Mayer would publish extensively on astronomy, mathematics, geodetics, mensuration and the design and construction of scientific instruments. He died on 20th February 1762 of typhoid.

Although the moon obeys Kepler’s laws of planetary motion, because it is fairly large and lays between the earth and the sun it gets pulled all over the place by the force of gravity and as a result its orbit is a very ragged and irregular affair. In both the systems of Ptolemaeus and of Copernicus the models for the moon’s orbit are less than successful. Kepler ignored the problem and did not supply a lunar model in his system. This omission was corrected by the young English astronomer Jeremiah Horrocks who proved that the moon also has, at least in theory, an elliptical Keplerian orbit and delivered the best lunar model up till that time. Even the great Newton had immense difficulties with the moon and although he based his efforts on Horrocks’ work he was unable to show that the moon really conforms to his gravitation theory. It would have to wait for Simon Laplace to tame the moons orbit at the end of the eighteenth century. Before Laplace none of the mathematical models of the moons orbit was accurate enough to deliver tables that could be used for the lunar distance method.

Mayer took a novel approach, he argued that what was needed was not a new model but more accurate observations and more accurate calculations based on those observations and set to work to deliver and deliver he did. Over several years Mayer made very exact observations of the moons positions and very accurate calculations for his tables and thus he succeeded where others had failed. In 1752 he published his first set of lunar tables and in 1755 he submitted them to the Board of Longitude in London. With his tables it was possible to determine the position of the moon within five seconds of arc making it possible to determine longitude to within half a degree.

I am the more unwilling my tables should lie any longer concealed; especially as the most celebrated astronomers of almost every age have ardently wished for a perfect theory of the Moon … on account of its singular use in navigation. I have constructed theses tables … with respect to the inequalities of motions, from that famous theory of the great Newton, which that eminent mathematician Eulerus first elegantly reduced to general analytic equations.

Mayer’s preface to the 1760 edition of his tables.

Combined with Hadley’s quadrant now modified to a sextant the problem of longitude was effectively solved, although only for days when the moon was visible. After trials and a new improved set of tables, published posthumously, the Board awarded Mayer’s widow a prize of £3000 a very large sum of money in the eighteenth century although only a fraction of the sum awarded to Harrison. The calculations necessary to determine longitude having measured the lunar distance proved to be too complex and too time consuming for seamen and so Neville Maskelyne produced the Nautical Almanac containing the results pre-calculated in the form of tables and published for the first time in 1766.

The Tables of the Moon had been brought by the late Professor Mayer of Göttingen to a sufficient exactness to determine the Longitude at Sea to within a Degree, as appeared by the Trials of several Persons who made use of them. The Difficulty and Length of the necessary Calculations seemed the only Obstacles to hinder them from becoming of general Use.

Maskelyne’s preface to the first edition of the Nautical Almanac

Contrary to the impression created by Sobel the two methods, lunar distance and marine chronometer, were not rivals but were employed together as a double safety system. Thanks to Sobel’s highly biased book John Harrison’s efforts have become well known and Harrison has become a household name. Mayer however whose services to navigation are just as important remains largely unknown, an anonymity that he does not deserve.

## The house where Emmy lived

Yesterday Paul Halpern at PACHS posted a nice short piece with a photo of the grave stone of the German mathematician Emmy Noether at Bryn Mawr College. As I wrote in an earlier post I (almost) live in Emmy’s home town and actually studied mathematics at the same university so having seen where her life ended I thought it would be nice to show some photos of where it started.

Emmy was born in this house on the Hauptstraße in Erlangen

The plaque next to the door reads

Birthplace of the Mathematician

EMMY

NOETHER

Born 23.3.1882 Emigrated 1933

Died 14.4.1935 Bryn Mawr

Because her father was Professor of Mathematics at the university she was allowed to study mathematics there unusual for a woman at that time.

The Friedrich-Alexander-University Erlangen-Nürnberg was founded in 1742 in Bayreuth and moved to Erlangen in 1743. From 1801 the administration moved into this building where it still resides.

Emmy would have attended her lectures in the then still relatively new Kollegen Haus, which was built in 1889

She would have also crossed the road to study in the then new (now old) university library

Which looks like this from the side

The concrete bunker across the road at the end of the street in the new library

(It was in the old library that John Wilkins, the Aussie Anthropoid, and I got to see the plant drawings of Conrad Gesner when he came to visit me)

All of these universty building are within a couple of hundred metres of Emmy’s birthplace so she didn’t have far to go to do her studies. Emmy is one of the greatest 20th century mathematicians and deserves to be much better known than she is.

Filed under History of Mathematics, Local Heroes

## Nürnberg: Pencil Capital of the World!

The title of this post is something I wrote in a comment on my previous post on Conrad Gesner. Nürnberg which is home-base to two of the world’s largest produces of drawing and writing instruments Faber-Castell and Staedtler Mars, both of whom started out as pencil manufacturers, could style itself in American fashion, “Pencil Capital of the World!” In fact it chooses to market itself as “Dürer City” figuring for some reason that a world famous Renaissance artist is sexier than the humble lead pencil. Now why Nürnberg is the major centre for the production of pencils and how this came about is something that has puzzled me since I settled here and being a historian I of course set about one day to find out why. I am now going to explain the answer to this question because it’s an interesting example of Renaissance knowledge and technology transfer.

We now turn our attention to the history of the pencil. Pencils originally consisted of a lead rod fitted with a silver tip, this enabled the user to make a faint grey line on his writing material. Sometime in the first half of the 16th century a large natural deposit of graphite was discovered on the surface near Borrowdale in Cumbria in Northern England, the only graphite deposit ever found on the surface. It was soon discovered that one could write better with the new ‘black lead’ than with silver point and the graphite pencil was born. The original deposit of graphite was cut into sticks that were then bound with cloth or string to fashion a writing implement. Over the next decades a healthy trade in the new English black lead pencils developed and the landowner in Cumbria started searching for new supplies of raw material. Because this meant mining he employed the best mining engineers available, the German miners from the metal mines in Middle Europe. These miners returning home at the beginning of the 17th century told their German employers, the merchant traders of Nürnberg, about graphite and the English pencils. Always on the look out to turn an honest Mark and having the best artisan craftsmen in Europe at their disposal they decided to try and get into the pencil market. Despite having the best mining experts in their employ the Nürnberger were unable to find massive graphite deposits in the English style but did discover deposits from which they could recover crushed graphite. They mixed the crushed graphite with other substances, originally various things and then finally clay, and encased their ‘leads’ in a wooden sheath consisting of two hollow halves glued together, a development in pencil making borrowed from the Italians who had replaced the original bindings with wood, and so the modern pencil was born.  Staedtler was established in the late 17th century and Farber-Castell in the early 18th century and both are still thriving today although they have long gone beyond the humble lead pencil.

Filed under Local Heroes, Renaissance Science

## One day later

In my last post I commented on the priority disputes that Galileo carried out with other users of the telescope in the early years of telescopic astronomy. Some of his most vitriolic comments were launched from the pages of his polemical pamphlet The Assayer against the Franconian astronomer Simon Marius, who was born on 10th January 1573, for daring to claim in his Mundus Jovialis published in 1614 that he and not Galileo had first discovered the moons of Jupiter. This was provocation beyond all measure as the discovery of the Jupiter moons was by far and away the greatest of Galileo’s scientific triumphs.

Born Simon Mayr (Mayer in its almost endless orthographic variations, ask PZ, is the most common family name in the German Language) in the then village of Gunzenhausen (it’s now a town) about 60 kilometres south of Nürnberg, Marius the son of a barrel maker received a school stipend from the local Margrave because of his beautiful singing voice. His mathematical talents were recognised early and  he published his first astronomical work, observations of a comet in 1596. The local Lord, Joachim-Ernst Margrave of Ansbach appointed him court astronomer/astrologer and paid for him to spend six months studying under Tycho Brahe in Prague in 1601, where he also made the acquaintance of David Fabricius. Following this his patron paid for him to go to the University of Padua, where Galileo was Professor of Mathematics, to study medicine. In the Renaissance there was a very close connection between medicine and astronomy through the astrological medicine that was then in fashion and which I will blog about some day. It is not recorded if Marius and Galileo met but they certainly knew of each other’s existence because of an ugly incident concerning Galileo’s military or proportional compass; this is a multi-purpose calculating instrument. Galileo did not invent this instrument but he did design and market a superior model for which he gave personal instruction to the purchasers including supplying them with an unpublished set of instruction, all for the necessary fees of course. One of Marius’ private pupils Baldessar Capra stole Galileo’s pamphlet and published it as his own work. Galileo brought charges of plagiarism against Capra and he was found guilty and punished and at that time, 1607, Galileo exonerated Marius, who had returned to Ansbach in 1605, of all blame in the affair.

In 1608 the Margraves chief political advisor Johann Philipp Fuchs von Bimbach, a distinguished German soldier and diplomat, visited the autumn Fair in Frankfurt were a Dutch peddler offered to sell him a telescope, it should be noted that this was two weeks before Lipperhey first presented his telescope in Den Hague. The instrument had a cracked lens and the price was exorbitant so Fuchs von Bimbach did not purchase but on his return to Ansbach he told Marius of the incident and sketched diagrams of the lenses. The two were unable to get suitable lenses ground in Nürnberg, then the leading centre for the manufacture of spectacle lenses in Europe, so instead they imported a telescope from Holland. Later the purchased superior lenses from Venice and built their own telescope. It was with this instrument that Marius discovered the moons of Jupiter.

Unlike Galileo who, realising the capital that he could make out of his discovery, rushed into print with his legendary Sidereus Nuncius, Marius first published his discovery four years later in 1614. Galileo’s friends and supporters immediately informed the Maestro of the pretentious German who was out to steal his glory and although enraged he did not react at once. First in The Assayer published in 1623, his attack on the Jesuit astronomer Orazio Grassi in their dispute on the true nature of comets did Galileo unleash his venom on the German upstart. Not only did Galileo thunder against him for daring to steal his discovery of the Jupiter moons but he now made him responsible for Capra’s earlier theft of the military compass, completely ignoring his own exoneration of Marius from 1607. Poor Marius didn’t have a chance. Galileo was at the height of his powers a feted courtier in the glory that was Renaissance Rome and the most famous scientist in Europe whereas Marius was a nobody from the German provinces, a court astrologer with a proven bad reputation. Public opinion condemned him immediately as a plagiarist and a thief and he went to his grave in 1624 as an intellectual criminal. Interestingly Galileo played the religious card condemning Marius as a protestant and even the Jesuit astronomer Christoph Scheiner who had had his own bitter dispute with Galileo over the discovery of the sunspots sided with Galileo against the Calvinist (sic) intellectual thief, who was in fact a Lutheran.

Marius’ reputation remained ruined until the end of the 19th century when historians for the first time objectively examined the facts. It turned out that Marius’ data was different to Galileo’s and in fact his determination of the orbits of the four moons was superior to that of his rival. The astronomical data showed that Marius was not a plagiarist but an independent observer who deserves an honourable place in the history of astronomy. At first glance it would appear that Marius made his first recorded observation of the Jupiter moons before Galileo but appearances deceive. Marius, a protestant, was still using the Julian calendar whereas Galileo, a Catholic, was using the Gregorian one; making the necessary conversion Marius discovered the moons exactly one day later than Galileo.

Filed under History of Astrology, History of Astronomy, Local Heroes

## Emmy and the Habilitation

This is my contribution to Ada Lovelace Day1

I live on the edge of the university town of Erlangen in Franconia. Because I work afternoons and evening I go most mornings into the town to do my shopping, visit various libraries and to drink a cup of coffee whilst reading the local newspaper. On my way to the café where I start my day I walk past the house where Amelie ‘Emmy’ Noether was born on 23rd March 1882. Emmy Noether, for those of my readers who are not mathematicians or physicists, was one of the greatest mathematicians of the 20th century. I would like to emphasise mathematicians and not female mathematicians; there are few male mathematicians who can be considered her equal.

Born the daughter of the local professor for mathematics, Max Noether, Emmy studied maths here in Erlangen and took her doctorate in 1907 under Paul Gordan. In 1909 she joined David Hilbert, at that time the greatest mathematician in the world at Göttingen. Here she became part of an act in the emancipation of women in Germany that can at best be described as a circus, her Habilitation. In Germany in order to qualify as a professor an academic has to complete a Habilitation, a sort of second doctorate; in fact in East Germany under the so-called socialist government it was called the second doctorate. To habilitate an academic must first write and submit a thesis based on original research and then take an exam that consists of a lecture held and defended before all of the habilitated members of the faculty. As in the history of emancipation there are first women to study, first women to get doctorates Emmy was the first woman in Germany to Habilitate but it was not easy.

It was forbidden by a law, from 1908, for women to habilitate in Prussia so, in 1915, after a lengthy and heated debate within the faculty a special petition was sent to the ministry for an exception in order to allow Emmy to habilitate. The petition was rejected despite the fact that it explicitly stated that this was not an attempt to lift the general ban on women habilitating. During this whole circus my favourite comment was the one professor in the faculty meeting who bitterly opposed Emmy’s habilitation because she would be then entitled to eat in the private dinning room for habilitated faculty members and that was definitely not on. In the end it required Germany to loose the First World War and for the Emperor to abdicate before Emmy could finally habilitate in 1919; although it was clear that Emmy would never become a full professor in Göttingen.

As Hermann Weyl was offered Felix Klein’s chair in Göttingen he rejected it with the argument that as long as Emmy Noether was in Göttingen he was not worthy to take the chair over her head. Emmy told him not to be stupid as she would never be offered a chair and if Weyl didn’t take it somebody else less worthy would.

In 1933 when the Nazis seized power in Germany Emmy was forced to flee Germany not principally because she was a half Jew as is usually claimed but because she belonged to a circle of intellectual socialist in Göttingen. With Weyl’s help she received a position as guest professor at Bryn Mawr in the States. However her period in America was not long as she died as the result of complications following an operation on 14th April 1935.

I have not described Emmy’s life and work as there are excellent articles at Wikipedia and Mac Tutor

1) Dr Skyskull has an excellent post to Ada Lovelace Day

Filed under History of Mathematics, Local Heroes

## What’s in a Name?

Today is also the 533 rd. anniversary of the death of the 15th century’s most important mathematician and astronomer, John Miller. Now anybody reading the previous sentence is probably thinking who the f##k is John Miller? Shall we try with his name in the original German, Johannes Müller, is that any better? Probably not, how about Regiomontanus? AH! Now, you’ve probably heard of him. Johannes Müller is the real name of Regiomontanus who came from the town of Königsberg (English; Kings-Mountain) in Lower Franconia, not to be confused with the much more famous Königsberg in East Prussia, now known as Kaliningrad and once home to Immanuel Kant. Old reference books quite often claim that Regiomontanus came from the Prussian Königsberg to the annoyance of all patriotic Franconians.

The name Regiomontanus is a toponym that is a name adopted by a scholar or author based on a place name, usually his place of birth but sometimes his place of residence. Toponyms were very common in the Middle Ages, famous examples being Aquinas and da Vinci. Now the toponym Regiomontanus is not without controversy, as can be seen from this somewhat outraged comment from a Wikipedia editor:

It is not true that Regiomontanus came to be called after the Latin name of his place of birth, Königsberg, Bavaria, posthumously. In his time, it was common for scholars to Latinize their names in their publication.

As I have already pointed out the editor’s second statement is correct although, as I said many authors Latinised the names of their birthplaces rather than their family names. The problem is the first statement, which is unfortunately false. As a student Herr Müller did indeed Latinise his family name and was matriculated under the mane Molitoris. In later letters, when he was on his peregrinations through Italy and Hungary, he is often referred to as Ioannes Germanicus i.e. John the German. When he started publishing he used the toponym Ioannes de Monte Regio. As far as can be ascertained he never used the name Regiomontanus. The earliest know incident of his being named Regiomontanus is in a text of Phillip Melanchthon’s from 1531, 55 years after his death.

Nowadays he is universally known as Regiomontanus and it would be foolish for any historian to try and change that, but any good historian should be aware of the falseness of this name.

Filed under History of Astronomy, Local Heroes, Renaissance Science

## RIP Mr Ohm

On this day 155 years ago Georg Simon Ohm, he of the resistance omega, departed this life. Almost every day I walk past the little house in Erlangen in which he and his brother Martin, an algebraic logician,  were born. Today its the  Café Con Leche, which does a good cup of coffee and a good line in tasty Spanish cuisine and the shop Gummibärchen Land (Little Gum Bear Country!). This shop is exclusively dedicated to the sale of a much loved German childrens sweet the Gummibärchen (little gum bear), which is a fruit or wine gum in the form of a small teddy bear. They even do Gummibächen birthday cakes. With time I shall blog both of the Ohm brothers as Local Heroes.

Filed under Local Heroes

## City Seductions

This weekend the Nürnberg Stadt(ver)führungen 2009 are taking place and I am involved. The name is a play on words in German, combining the words Stadt (city) Verführung (seduction) and Führung (guided tour). The principle is actually quite simple, over a period of three days literally thousands of themed guided tours of the city are offered for a minimal charge to the general public.

As this is the International Year of Astronomy (IYA) my friends and I are involved (not for the first time) in a small way. On Saturday morning we are presenting four half hour lectures together with the town library on individual aspects of the history of astronomy in Nürnberg. My friend Hans is holding two lectures, one on Albrecht Dürer’s star map and one on Doppelmayr’s Celestial Atlas from 1742, my friend Günther is lecturing on astrolabes (Nürnberg was the main European centre for their production in the 16th century) and I shall lecture on the globe maker Johannes Schöner, who will at a later date be one of my local heroes here on my blog, as will Dürer. In the Afternoon Hans and I are both offering guided tours of our astronomy trail, his in German, mine in English for the tourists.

Last time we took part in the Stadt(ver)führungen the response was very positive so I’m looking forward to Saturday. However as I still haven’t formulated my lecture I wont have much time for my blog and so activity will probably be fairly low this week. Don’t worry I haven’t given up yet and will be back next week.

Filed under Local Heroes

## Local Historian

I am a member of that oft ridiculed specious the local historian. A figure much loved by the makers of Hollywood B-movies and TV crime series. The local historian an eccentric, pipe smoking, intellectual figure, and if English, usually with a beard and dressed in a tweed jacket he provides the necessary background information to Sir Toby Hetherington-Smyth the 18th century builder of the mysterious Hetherington Hall. In real life the local historian is usually an amateur who specialises in historical research of his home town, village or district mostly publishing the results of his often meticulous labours in the parish magazine or similar local publications.

Now I am English and do boast a beard, although in recent years it’s is mostly of the three or five day variety, but I am a non-smoker and don’t run to tweed jackets also my local history is of a somewhat different sort to the normal fare. I live about 20 km away from the City of Nürnberg (that’s Nuremberg for the English speakers) a city that is notorious nay infamous for its recent history, however in earlier times Nürnberg enjoyed a somewhat more positive fame. In the Renaissance, Nürnberg was one of the biggest, richest and most influential cities in Northern Europe; it also enjoyed an excellent reputation for art and culture. Between about 1450 and 1550 Nürnberg was also one of the leading European centres for the development of the mathematical sciences, this is one of the reasons that I became interested in this field of research, and many minor but significant figures in the history of science made their homes there. I am part of a group called the ‘Nürnberger Arbeitskreis für Astronomiegeschichte’ (Nürnberg history of astronomy study group); amongst other things we have initiated both an astronomy and a sundial trail in Nürnberg

You may have noticed that one of the categories for my Clavius article is ‘Local Heroes’ this is the first of  a series of such postings in which, in my capacity as local historian, I will feature Franconians who played a role in the history of science mostly in the early modern period. Thus using my blog as a sort of history of science parish magazine.

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Filed under Local Heroes

## 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.

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.