A public service announcement

For several months I have been writing a review essay of David Wootton’s fascinating and challenging book The Invention of Science, or better said not writing, as I have stalled, hit a roadblock, lost the thread or whatever. This being the case I have been doing what apparently writers are supposed to do in such situations writing other things. Now this is all very well but all that has happened is that I have found it increasingly more difficult to return to my review essay and complete it, so I have decided this has got to stop. Today I recommenced writing my review essay and have decided that I won’t write or post anything else until I do finish it, which might take some time. How long I can’t say at the moment. Until then nothing new will appear here at The Renaissance Mathematicus, I hope the break won’t be too long. When however blogging does resume here, normal service and frequency will be resumed, as I have several new posts already in the pipeline.



Filed under Autobiographical

Why there weren’t any scientists before the late nineteenth century.

It has become common practice for historians of science to admonish people who use the term scientist when applied to people who lived before the nineteenth century. They point out, correctly, that the word was first coined by Cambridge polymath William Whewell in 1833 at the British Association for the Advancement of Science meeting in Cambridge and first used in print by him a year later in his review of Mary Somerville’s On the Connection of the physical sciences. As Melinda Baldwin has shown in her guest post, The history of “scientist”, the term didn’t really become established until late in the nineteenth century or even early in the twentieth. On being thus admonished many people react negatively and ask pointedly whether historians of science mean that there was no science before 1833. On being told that this is not the case they argue that if people were doing science then it is perfectly acceptable to call them scientists. If they are doing science then they are scientists, end of story!

Unfortunately it is not as easy as that, because terms have connotations, which extend well beyond their simple denotations. For those readers who are not up on the jargon of linguistics or the philosophy of language I will try to explain the terms denotation and connotation with a simple example. Expert linguists and philosophers of language should look the other way for a minute or two. The name Sascha denotes the dog whose picture you can see in the top right hand corner of this blog. The name Sascha connotes, for me, all of the things that I experienced with him throughout the ten years that we shared our lives, a wild mixture of a thousand different emotions. Returning to the term scientists, it denotes quite simply someone who does science (whatever that may be, a can of worms I don’t intend to open today). To the distress of real life scientists, cartoonists, playwrights, film directors and others often present a sort of cardboard cut out generic figure as a scientist: white, male, bearded, wearing glasses and a white lab coat. Even the sexy female scientist presented in more up to date TV series is usually given the glasses and the white lab coat to establish their professional identity. This clichéd list of characteristics is the superficial connotation that is generated in their minds and often in that of their readers and viewers by the term scientist.

On a less superficial level the word scientists, as used since the beginning of the twentieth century, has a very strong set of characteristics, its connotation, that spring to the reader’s or listener’s mind when confronted with the term. This list of characteristic’s are usually centred round the scientist’s education, training and professional experience; the clue here lies in the word professional. The scientist is an expert who has undergone a lengthy and extensive specialist education and training to qualify them for their profession and who has enough experience in that profession to justify their being called a scientist. This set of characteristics for the scientist is something that only came into being, rather gradually, over the course of the nineteenth century. If we go back before that time the set of characteristics that we find associated with people doing what we would recognise as science is very different and in fact changed over the centuries, since science began to emerge in Europe in the High Middle Ages. In what follows I shall restrict my remarks to Europe and the period between about twelve hundred CE and eighteen hundred CE. The problems of using the term scientist for earlier periods and other cultures are even greater than those I will outline here.

In the high Middle Ages most of the sciences, as we now know them, simply didn’t exist. Alchemy/chemistry, including much that we would now call applied or industrial chemistry, was regarded as an art practiced by artisans. Where art here means technique or technology or even handcraft. Whilst its practitioners might regard themselves as seekers after or even possessors of knowledge their image was not even remotely like that of our image invoked by the word scientist. Mathematicus, astrologus, astronomus were all synonyms for the same profession, again the practitioner of an art, artisans. Mostly employed outside of the universities, often in the courts of rulers, these ‘mathematicians’ were usually principally employed as astrologers but their full job description included many other functions. Astronomer, horologist (that is designer and maker of sundials), hydraulic engineer in charge of designing water features in ornamental gardens and a whole host of other activities we would normally associate with a technician or engineer. Their social status was that of a craftsman, albeit an upper grade one, rather than that of an academic, also far from out image of the scientist.

Physics belonged in the universities, practiced by philosophers, but this was the physics of Aristotle, the study of nature and contained much that is foreign to our concept of physics. Also this was mostly a qualitative descriptive study and not a quantitative empirical one. Although some of its practitioners, such as for example Robert Grosseteste of Roger Bacon, espoused ideas similar to our concept of the scientific method in their writings their actually their actually practice bears little resemblance to that of modern scientists. Although bearing the same name, their institutions, the medieval universities, have very little in common with our modern institutes of higher educations.

There is very little change in this state of affairs up to the sixteenth century, as the demand for the use of mathematics in astronomy for cartography and navigation as well as astrology in medicine began to change the status of its practitioners. It is first in the seventeenth century when the work of people such as Kepler, a court mathematicus, and Galileo, a university teacher of astrology for medical students, began to intrude into the traditional domain of the philosophers and redefine the nature and subject matter of physics that quantitative empirical research began to make inroads into the universities. In this context it is highly relevant that when Galileo left the university for the Medici court in Florence he insisted on the title philosophicus as well as mathematicus because of the lowly status of the latter in comparison to the former, These practitioners became known not as scientists but as natural philosophers and their career profiles and public image were still substantially different to that of modern scientists. The seventeenth century also saw the gradual emergence of geology, zoology, biology and botany as separate disciplines with expert practitioners from the philosophers’ earlier domain of natural history. Chemistry didn’t make its way into the universities until the eighteenth century and then only as a handmaiden to medicine, only gaining recognition as a discipline in its own right in the nineteenth century.

Let us pause for a while and look at the career profiles of the most well known figures, who contributed to the evolution of the mathematical sciences in the sixteenth and seventeenth centuries. Copernicus was a canon of the cathedral chapter of Frombork and basically an administrator or civil servant of the prince-bishopric of Ermland (Warmia). Astronomy was so to speak his hobby. His life has nothing in common with our concept of a scientist. Tycho Brahe was a Danish aristocrat, who set up a research institute for astronomy and Paracelsian medicine on a Scandinavian island in something resembling a castle and which included a court jester and a pet elk, which got drunk and broke its neck falling down some stairs. Tycho’s life was about as far removed from the twenty first century idea of a scientist as you can get. As already mentioned Johannes Kepler was a schoolteacher and district mathematicus, meaning amongst other things astrologer, who went on to become a court mathematicus, meaning principally astrologer; once again almost nothing in common with a modern scientist. Galileo was actually a university professor for mathematics but his principle activity would have been teaching astrology to medical students. He later became a court philosopher, basically an intellectual court jester. Descartes was a mercenary or soldier of fortune, who then retired to the live of a gentleman of leisure, alternating with periods of being a court philosopher with the same function as Galileo. None of these people had any real formal education or training as a ‘scientist’. There were no white coats and with the exception of Tycho nothing even remotely resembling a laboratory. Neither Copernicus nor Kepler even had an observatory. Today, we would tend to regard Newton as a physicist but he was actually a professor of mathematics in Cambridge. However a professor, who had almost no students and whose lectures appear to have been very scantily attended. He abandoned academia to become Warden and then Master of the Mint a post with little to do with his scientific activities. None of these figures who are leading lights in the pantheon of scientific heroes even remotely fulfils our connotations of a scientist.

The term physics was first used in the way we use it at the beginning of the second decade of the eighteenth century and didn’t become common usage in this sense until the nineteenth century. The term physicist was first coined even later than the term scientist. It really was first in the nineteenth century that the people doing science first began to fulfil the connotations that we have when we hear or read the word scientist, so it really is for the best if we refrain from using the term for researchers who lived in earlier periods.






Filed under History of science

New lecturing attire

I have acquired a new T-shirt from the good folks at the History of Alchemy Podcasts, which will be worn with pride whilst lecturing on the history of alchemy (and other topics).

The elegant piece of attire can be witnessed below modelled by the lecturer in person on the market place in Erlangen this very Saturday.


Should you wish to also acquire such an elegant object of haut-couture and thereby support the excellent work of the History of Alchemy Podcasts then you can do so here. If you don’t already listen to the History of Alchemy Podcasts you should!

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A spirited defence

After I had, in my last blog post, mauled his Scientific American essay in my usual uncouth Rambo style, Michael Barany responded with great elegance and courtesy in a spirited defence of his historical claims to which I now intend to add some comments, thus extending this exchange by a fourth part.

On early practical mathematicians Michael Barany acknowledges that their work is for the public good but argues correctly that that doesn’t then a “public good”. I acknowledge that there is a difference and accept his point however I have a sneaky feeling that something is only referred to as a “public good” when somebody in power is trying to put one over on the great unwashed.

Barany thinks that the Liber Abbaci and per definition all the other abbacus books, only exist for a closed circle of insider and not for the general public. In fact abbacus books were used as textbooks in so-called abbacus schools, which were small private schools that taught the basics of arithmetic, algebra, geometry and bookkeeping open to all who could pay the fees demanded by the schoolteacher, who was very often the author of the abbacus book that he used for his teaching. It is true that the pupils were mostly the apprentices of tradesmen, builders and artists but they were at least in theory open to all and were not quite the closed shop that Michael Barany seems to be implying. In this context Michael Barany says that Recorde’s Pathway to Knowledge, a book on elementary Euclidean geometry, is eminently impractical. However elementary Euclidean geometry was part of the syllabus of all abbacus schools considered part of the necessary knowledge required by artist and builder/architect apprentices. In fact the first Italian vernacular translation of Euclid was made by Tartaglia, an abbacus schoolteacher.

Michael Barany makes some plausible but rather stretched argument to justify his couterpositioning of Recorde and Dee, which I don’t find totally convincing but slips into his argument the following gem. If you don’t like Dee as your English standard bearer for keeping mathematics close to one’s chest, try Thomas Harriot. Now I assume that this flippant comment was written tongue in cheek but just in case.

Michael Barany’s whole essay contrasts what he sees as two approaches to mathematics, those who see mathematics as a topic for everyone and those who view mathematics as a topic for an elitist clique. In the passage that I criticised in his original essay he presented Robert Recorde as an example of the former and John Dee as a representative of the latter. A contrast that he tries to defend in his reply, where this statement about Harriot turns up. Now his elitist argument is very much dependent on a clique or closed circle of trained experts or adepts who exchanged their arcane knowledge amongst themselves but not with outsiders. A good example of such behaviour in the history of science is alchemy and the alchemists. Harriot as an example of such behaviour is a complete flop. Thomas Harriot made significant discoveries in various fields of scientific endeavour, mathematics, dynamics, chemistry, optics, cartography and astronomy, however he never published any of his work and although he corresponded with other leading Renaissance scholars he also didn’t share his discoveries with these people. A good example of this is his correspondence with Kepler, where he discussed over several letters the problem of refraction but never once mentioned that he had already discovered what we now know as Snell’s Law. Harriot remained throughout his life a closed circle with exactly one member, not a very good example to illustrate Michael Barany’s thesis.

I claimed that there was no advance mathematics in Europe from late antiquity till the fifteenth century. Michael Barany counters this by saying: This cuts, for instance, the rich history of Islamic court mathematics out of the European history in which it emphatically belongs; it doesn’t cut it. Ignoring Islamic Andalusia, Islamic mathematics was developed outside of Europe and although it started to reappear in Europe during the twelfth and thirteen centuries during the translator period nobody within Europe was really capable of doing much with those advanced aspects of it before the fifteenth century, so I stand by my claim.

We now turn to Michael Barany’s defence of his original: In the seventeenth century’s Scientific Revolution, the new promoters of an experimental science that was (at least in principle) open to any observer were suspicious of mathematical arguments as inaccessible, tending to shut down diverse perspectives with a false sense of certainty. This he contrast with a, in his opinion, eighteenth century where mathematicians help sway over the scientific community. I basically implied that this claim was rubbish and I still stand by that to that, so what does Michael Barany produce in his defence.

In my original post I listed seven leading scholars of the seventeenth century who were mathematicians and whose very substantive contributions to the so-called scientific revolution was mathematical, on this Barany writes:

Thony pretends that naming some figures remembered today both for mathematics and for their contributions to the scientific revolution contradicts this well-established historical claim.

The, without any doubt, principle figures of the so-called scientific revolution are just some figures! Interesting? So what is Michael Barany’s well-established historical claim? We get offered the following:

Following Steven Shapin and many who have written since his classic 1988 article on Boyle’s relationship to mathematics, I chose to emphasize the conflicts between the experimental program associated with the scientific revolution and competing views on the role of mathematics in natural philosophy.

What we have here is an argument by authority, that of Steven Shapin, whose work and the conclusions that he draws are by no means undisputed, and one name Robert Boyle! Curiously a few days before I read this, science writer, John Gribbin, commentated on Facebook that Robert Hooke had to work out Boyle’s Law because Boyle was lousy at mathematics, might this explain his aversion to it? However Michael Barany does offer us a second argument:

But to take just his most famous example, Newton’s prestige in the Royal Society is generally seen today to have had at least as much to do with his Opticks and his other non-mathematical pursuits as with his calculus, which contemporaries almost uniformly found impenetrable.

Really? I seem to remember that twenty years before he published his Opticks, Old Isaac wrote another somewhat significant tome entitled Philosophiæ Naturalis Principia Mathematica [my emphasis], which was published by the Royal Society. It was this volume of mathematical physics that established Newton’s reputation, not only with the fellows of the Royal Society, but with the entire scientific community of Europe, even with those who rejected Newton’s central concept of gravity as action at a distance. This book led to Newton being elected President of the Royal Society, in 1704, the same year as the Opticks was published. The Opticks certainly enhanced Newton’s reputation but he was already considered almost universally by then to be the greatest living natural philosopher.

Is the Opticks truly non-mathematical? Well, actually no! When it was published it was the culmination of two thousand years of geometrical optics, a mathematical discipline that begins with Euclid, Hero and Ptolemaeus in antiquity and was developed by various Islamic scholars in the Middle Ages, most notably Ibn al-Haytham. One of the first mathematical sciences to re-enter Europe in the High Middle Ages it was propagated by Robert Grosseteste, Roger Bacon, John Peckham and Witelo. In the seventeenth-century it was one of the mainstream disciplines contributing to the so-called scientific revolution developed by Thomas Harriot, Johannes Kepler, Willebrord van Roijen Snell, Christoph Scheiner, René Descartes, Pierre Fermat, Christiaan Huygens, Robert Hooke, James Gregory and others. Newton built on and developed the work of all these people and published his results in his Opticks in 1706. Yes, some of his results are based on experiments but that does not make the results non-mathematical and if you bother to read the book you will find more than a smidgen of geometry there in.

In my opinion trying to recruit Newton as an example of non-mathematical experimental science is an act of desperation.

To be fair to Michael Barany the division between those who favoured non-mathematical experimental science and the mathematician really did exist in the seventeenth century, however it was largely confined to England and most prominently in the Royal Society. This is the conflict between the Baconians and the Newtonians that I have blogged about on several occasions in the past. Boyle, Hooke and Flamsteed, for example, were all Baconians who, following Francis Bacon, were not particularly fond of mathematical proofs. This conflict has an interesting history within the Royal Society, which led to disadvantages for the development of the mathematical sciences in England in the eighteenth century.

When the Royal Society was initially founded some mathematician did not become members because of the dominance of the Baconians and that despite the fact that the first President, William Brouncker, was a mathematician. Later under Newton’s presidency the mathematicians gained the ascendency, but first in 1712 after an eight-year guerrilla conflict between Newton and Hans Sloane, a Baconian and the society’s secretary. Following Newton’s death in 1727 (ns) the Baconians regained power and the result was that, whereas on the continent the mathematical sciences flourished and evolved throughout the eighteenth century, in England they withered and died, leading to a new power struggle in the nineteenth century featuring such figures as Charles Babbage and John Herschel.

To claim as Michael Barany does that this conflict within the English scientific community meant that mathematics played an inferior role in the seventeenth century is a bridge too far and contradicts the available historical facts. Yes, the mathematization of nature was not the only game in town and interestingly non-mathematical experimental science was not the only alternative. In fact the seventeenth century was a wonderful cuddle-muddle of conflicting meta-physical views on the sciences. However whatever Steven Shapin might or might not claim the seventeenth century was a very mathematical century and mathematics was the principle driving force behind the so-called scientific revolution. As a footnote I would point out that many of the leading experimental natural philosophers of the seventeenth century, such as Galileo, Pascal, Stevin and Newton, were mathematicians who interpreted and presented their results mathematically.


Filed under History of Mathematics, History of science, Newton

Some rather strange history of maths

Scientific American has a guest blog post with the title: Mathematicians Are Overselling the Idea That “Math Is Everywhere, which argues in its subtitle: The mathematics that is most important to society is the province of the exceptional few—and that’s always been true. Now I’m not really interested in the substantial argument of the article but the author, Michael J. Barany, opens his piece with some historical comments that I find to be substantially wrong; a situation made worse by the fact that the author is a historian of mathematics.

Barany’s third paragraph starts as follows:

In the first agricultural societies in the cradle of civilization, math connected the heavens and the earth. Priests used astronomical calculations to mark the seasons and interpret divine will, and their special command of mathematics gave them power and privilege in their societies.

We are taking about the area loosely known as Babylon, although the names and culture changed over the millennia, and it is largely a myth, not only for this culture, that astronomical calculations were used to mark the seasons. The Babylonian astrologers certainly interpreted the divine will but they were civil servants who whilst certainly belonging to the upper echelons of society did not have much in the way of power or privilege. They were trained experts who did a job for which they got paid. If they did it well they lived a peaceful life and if they did it badly they risked an awful lot, including their lives.

Barany continues as follows:

As early economies grew larger and more complex, merchants and craftsmen incorporated more and more basic mathematics into their work, but for them mathematics was a trick of the trade rather than a public good. For millennia, advanced math remained the concern of the well-off, as either a philosophical pastime or a means to assert special authority.

It is certainly true that merchants and craftsmen in advanced societies – Babylon, Greece, Rome – used basic mathematics in their work but as these people provide the bedrock of their societies ­– food, housing etc. – I think it is safe to say that their maths based activities were in general for the public good. As for advanced maths, and here I restrict myself to European history, it appeared no earlier than 1500 BCE in Babylon and had disappeared again by the fourth century CE with the collapse of the Roman Empire, so we are talking about two millennia at the most. Also for a large part of that time the Romans, who were the dominant power of the period, didn’t really have much interest in advance maths at all.

With the rebirth of European learned culture in the High Middle ages we have a society that founded the European universities but, like the Romans, didn’t really care for advanced maths, which only really began to reappear in the fifteenth century. Barany’s next paragraph contains an inherent contradiction:

The first relatively widespread suggestions that anything beyond simple practical math ought to have a wider reach date to what historians call the Early Modern period, beginning around five centuries ago, when many of our modern social structures and institutions started to take shape. Just as Martin Luther and other early Protestants began to insist that Scripture should be available to the masses in their own languages, scientific writers like Welsh polymath Robert Recorde used the relatively new technology of the printing press to promote math for the people. Recorde’s 1543 English arithmetic textbook began with an argument that “no man can do any thing alone, and much less talk or bargain with another, but he shall still have to do with number” and that numbers’ uses were “unnumerable” (pun intended).

Barany says, “that anything beyond simple practical math ought to have a wider reach…” and then goes on to suggest that this was typified by Robert Recorde with his The Grounde of Artes from 1543. Recorde’s book is very basic arithmetic; it is an abbacus or reckoning book for teaching basic arithmetic and book keeping to apprentices. In other words it is a book of simple practical maths. Historically what makes Recorde’s book interesting is that it is the first such book written in English, whereas on the continent such books had been being produced in the vernacular as manuscripts and then later as printed books since the thirteenth century when Leonardo of Pisa produced his Libre Abbaci, the book that gave the genre its name. Abbaci comes from the Italian verb to calculate or to reckon.

What however led me to write this post is the beginning of Barany’s next paragraph:

Far more influential and representative of this period, however, was Recorde’s contemporary John Dee, who used his mathematical reputation to gain a powerful position advising Queen Elizabeth I. Dee hewed so closely to the idea of math as a secret and privileged kind of knowledge that his detractors accused him of conjuring and other occult practices.

Barany is contrasting Recorde, man of the people bringing mathematic to the masses in his opinion with Dee an elitist defender of mathematics as secret and privileged knowledge. This would be quite funny if it wasn’t contained in an essay in Scientific American. Let us examine the two founders of the so-called English School of Mathematics a little more closely.

Robert Recorde who obtained a doctorate in medicine from Cambridge University was in fact personal physician to both Edward VI and Queen Mary. He served as comptroller of the Bristol Mint and supervisor of the Dublin Mint both important high level government appointments. Dee acquired a BA at St John’s College Cambridge and became a fellow of Trinity College. He then travelled extensively on the continent studying in Leuven under Gemma Frisius. Shortly after his return to England he was thrown into to prison on suspicion of sedition against Queen Mary; a charge of which he was eventually cleared. Although consulted oft by Queen Elizabeth he never, as opposed to Recorde, managed to obtain an official court appointment.

On the mathematical side Recorde did indeed write and publish, in English, a series of four introductory mathematics textbooks establishing the so-called English School of Mathematics. Following Recorde’s death it was Dee who edited and published further editions of Recorde’s mathematics books. Dee, having studied under Gemma Frisius and Gerard Mercator, introduced modern cartography and globe making into Britain. He also taught navigation and cartography to the captains of the Muscovy Trading Company. In his home in Mortlake, Dee assembled the largest mathematics library in Europe, which functioned as a sort of open university for all who wished to come and study with him. His most important pupil was his foster son Thomas Digges who went on to become the most important English mathematical practitioner of the next generation. Dee also wrote the preface to the first English translation of Euclid’s Elements by Henry Billingsley. The preface is a brilliant tour de force surveying, in English, all the existing branches of mathematics. Somehow this is not the picture of a man, who hewed so closely to the idea of math as a secret and privileged kind of knowledge. Dee was an evangelising populariser and propagator of mathematics for everyman.

It is however Barany’s next segment that should leave any historian of science or mathematics totally gobsmacked and gasping for words. He writes:

In the seventeenth century’s Scientific Revolution, the new promoters of an experimental science that was (at least in principle) open to any observer were suspicious of mathematical arguments as inaccessible, tending to shut down diverse perspectives with a false sense of certainty.

What can I say? I hardly know where to begin. Let us just list the major seventeenth-century contributors to the so-called Scientific Revolution, which itself has been characterised as the mathematization of nature (my emphasis). Simon Stevin, Johannes Kepler, Galileo Galilei, René Descartes, Blaise Pascal, Christiaan Huygens and last but by no means least Isaac Newton. Every single one of them a mathematician, whose very substantial contributions to the so-called Scientific Revolution were all mathematical. I could also add an even longer list of not quite so well known mathematicians who contributed. The seventeenth century has also been characterised, by more than one historian of mathematics as the golden age of mathematics, producing as it did modern algebra, analytical geometry and calculus along with a whole raft full of other mathematical developments.

The only thing I can say in Barany’s defence is that he in apparently a history of modern, i.e. twentieth-century, mathematics. I would politely suggest that should he again venture somewhat deeper into the past that he first does a little more research.


Filed under Uncategorized

Uccello and the Problem of Space

Nice post on Renaissance master of linear perspective Uccello

In the Dark

The other night I was watching an old episode of the detective series Lewis and it reminded me of something I wanted to blog about but never found the time. The episode in question, The Point of Vanishing, involves a discussion of a painting which can be found in the Ashmolean Museum in Oxford:


I won’t spoil the plot by explaining its role in the TV programme, but this work – called “The Hunt in the Forest” or “The Night Hunt” or some other variation on that title –  is by one of the leading figures of the Early Renaissance, Paolo Uccello, who was born in Florence and lived from about 1396 until 1475. He was most notable for his explorations of the use of perspective in painting, and specifically in “The Problem of Space”, i.e. how to convey the presence of three dimensions when the paint is…

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Not a theology student

On the 10 August 1591 (os) (according to Max Caspar, 11 August according to Owen Gingerich!) Johannes Kepler graduated MA at the University of Tübingen. This is a verified undisputed historical fact, however nearly all secondary sources go on to state that he then went on to study theology, his studies being interrupted, shortly before completion, when he was appointed school teacher and district mathematicus in Graz. A post he took up on 11 April 1594. The part about the theology studies is however not true. This myth was created by historians and it would be interesting to trace who first put it out in the world and it is also interesting that nobody bothered to check this claim against the sources until Charlotte Methuen published her Kepler’s Tübingen: Stimulus to a Theological Mathematics in 1998.

Johannes Kepler Source: Wikimedia Commons

Johannes Kepler
Source: Wikimedia Commons

One reason for the lack of control is because the version with the theology studies seems so plausible. At medieval universities all student started their studies with the seven liberal arts graduating BA, in Kepler’s case in 1588 having matriculated two years earlier. Those, who stayed on at the university now intensified those studies graduating MA, essentially a teaching qualification. Those, who now wished to continue in academia had, in the normal run of events, the choice between taken a doctorate in law, medicine or theology. We know that Kepler was initially very disappointed with his appointment as a school teacher for mathematics because he would have preferred to become a Protestant pastor, so it would seem logical that because he stayed on at the university after graduating MA he must have studied theology. However appearances can be, and in this case are, deceptive. The problem is that Tübingen, or at least the Tübinger Stift in which Kepler studied was not a conventional medieval university.

A major problem that the Lutheran Protestant Church faced following the Reformation was finding enough pastors to run their churches and enough schoolteachers for their schools. In areas that converted to Protestantism the churches naturally had Catholic priest many of whom were not prepared or willing to convert and the education system, including both schools and universities, was firmly in the hands of the Catholic Church. This meant that the Lutheran Church had to build its own education system from scratch. This was the task taken on by Phillip Melanchthon, whom Luther called his Preceptor Germania – Germany’s schoolteacher – a task that he mastered brilliantly.

The state of Baden-Württemberg, one of the largest and most important early Protestant states gasped here the initiative, setting up a state sponsored school and university system to educate future Protestant schoolteachers and pastors. The Tübinger Stift was established in 1536 for exactly this purpose. The Dukes of Württemberg also provided stipends for gifted children of less wealthy families to enable them to attend the Stift. Kepler was the recipient of such a stipend.

Tübinger Still (left and University (right) Source: Kepler-Gesellschaft e.V.

Tübinger Still (left) and University (right)
Source: Kepler-Gesellschaft e.V.

All the students did a general course of studies, which upon completion with an MA qualified them to become either a schoolteacher or a pastor depending on the positions required to be filled, when they graduated. Allocation was also to some extent conditioned by the abilities of the individual student. Upon completion of their MAs student remained at the university receiving instruction in the various practical aspects of their future careers, teaching practice, basic theology for sermons and so forth until a suitable vacancy became available. Only a very, very small percentage of these students formally matriculated for a doctorate in theology, an unnecessary qualification for a simple pastor. Most Catholic priest of the period also did not possess a doctorate in theology. Kepler was not one of those who chose to do a doctorate in theology but was simply a participant in the general career preparation course for schoolteachers and pastor; a course for which there were no formal final exams or qualifications.

Kepler had been in this career holding pattern, so to speak, for not quite three years when the Evangelical Church authorities in Graz asked the University in Tübingen to recommend a new mathematics teacher for their school. After due consideration the university chose Kepler, who had displayed a high aptitude for mathematics, for the position. After some hesitation Kepler accepted the posting. He could have refused but it would not have placed him as a stipendiary in a very good position with the authorities. He was also free to leave the system and return to civil life but this would have meant having to reimburse his stipend.

It was clear from the beginning of his studies that he could, or would, be appointed either a schoolteacher or a pastor but the young Johannes had set his heart on serving his God as a pastor and was thus initially deeply disappointed by his appointment. The turning point came in Graz when he realised, in a moment of revelation, that he could best serve his God, a geometrical creator, by revealing the mathematical wonders of that creation. And so he dedicated his life to being God’s geometer, a task that he fulfilled with some distinction.


Filed under History of Astronomy, History of science, Myths of Science