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‘Mathematics Made No Contribution to the Public Weal’

Citation for published version:
Henry, J 2011, '‘Mathematics Made No Contribution to the Public Weal’: Why Jean Fernel (1497–1558)
Became a Physician', Centaurus, vol. 53, no. 3, pp. 193-220. https://doi.org/10.1111/j.1600-
0498.2011.00234.x

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10.1111/j.1600-0498.2011.00234.x

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Contribution to the Public Weal’: Why Jean Fernel (1497–1558) Became a Physician. Centaurus, 53(3), 193-
220, which has been published in final form at http://dx.doi.org/10.1111/j.1600-0498.2011.00234.x

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‘Mathematics made no contribution to the public weal’:  

Why Jean Fernel (1497-1558) became a Physician 

[Centaurus, 53 (2011), pp. 193-220.] 

 

Introduction 

The historiography of the Scientific Revolution has always recognised the importance 

of mathematics in re-shaping natural knowledge and the practices associated with it 

during the late Renaissance and early modern periods. The historians of science who 

first forged the notion of a Scientific Revolution tended to interpret the historical 

developments in terms of elite natural philosophers (or even just “scientists”) 

recognising the importance of mathematics and deliberately introducing it into their 

attempts to understand the natural world. More recently, however, historians have 

realised the importance of a fairly extensive array of different mathematical 

practitioners, and have tended to see the Scientific Revolution as resulting from their 

innovations in both theory and practice. Mathematicians, not natural philosophers, 

showed the way to using mathematics in the understanding of the world.
1
 

 This recent work marks an important historiographical development, which 

has undoubtedly added to our understanding of the development of early modern 

attempts to establish knowledge of the physical world, and the best methods of 

discovering that knowledge. As such, it is a vast improvement on the earlier 

historiography. It seems to me, however, that the new historiography is tainted with 

some of the flaws inherent in the earlier historical accounts. Pioneers such as 

Alexandre Koyré, A. Rupert Hall, R. S. Westfall, and others, tended to give a 

teleological account, coloured by their knowledge that mathematics is such a crucially 

important part of the physical sciences of our day. Since every modern scientist 



  Page 2 of 50 

knows that mathematics is important, the historiographical argument seemed to run, 

an innovatory scientist in the past would have recognised it too (and in so doing 

would have confirmed his genius, and the fact that he was “ahead of his time”). In this 

kind of historical scenario, Galileo and Kepler were portrayed as physicists who 

recognised for the first time that physics should be firmly based on mathematical 

analysis of the natural world. Clearly, we’ve come a long way since then, and there is 

no denying the richness and nuanced authenticity of the history revealed in the more 

recent historiography. Even so, there seems to be a tendency among early modern 

historians of the physical sciences to regard the rise of mathematics, once its 

relevance was recognised, as inevitable and inexorable. Historiographical teleology 

and presentism still linger. 

 Part of the aim of this paper is to counter this tendency by reminding ourselves 

of the difficulties that lay in the way of the ‘mathematization of the world picture’. 

Far from being inexorable, or inevitable, there were many obstacles in the way that 

might have undermined the enterprise of mathematical physics altogether, and 

certainly delayed what we might regard as its eventual triumph by a couple of 

centuries. The mathematization of the world picture was a long and slow process. But 

this is not to say that the Scientific Revolution also had to mark time, so to speak, 

until non-mathematicians were made to realise the importance, indeed the 

indispensability, of mathematics. I am not offering here an explanation of why the 

‘Revolution’ took such a long time to be accomplished (much less suggesting that the 

delay was entirely due to opposition to mathematics). Rather, my point is that there 

was much more to the Scientific Revolution than the mathematization of the world 

picture. And I do not mean by this simply to point out the obvious fact that there were 

also contemporary innovations outside the physical sciences. We need to bear in mind 



  Page 3 of 50 

that, before the mathematization of the world picture, there was a majority of natural 

philosophers who believed that mathematics was not relevant to, much less necessary 

for, an understanding of the physics of the world. For such thinkers, the process of 

reforming scholastic natural philosophy, even in those parts of it which we would 

characterize as the physical sciences, could proceed perfectly well without any help 

from mathematics. Indeed, they had very good reasons for supposing that, if the 

reform of natural philosophy was to succeed, it must do so without making any 

diversions into the realm of mathematics.  

This is precisely why historians of the Scientific Revolution have found 

themselves turning from natural philosophers to mathematicians in order to 

understand developments. Only mathematicians saw the importance of mathematics, 

but they did not have it all their own way. On the contrary, many natural philosophers 

either dismissed the relevance of mathematics, or simply failed to regard it. I have 

argued elsewhere that the claims in recent historiography that early modern 

mathematicians were chiefly responsible for introducing the experimental method into 

natural philosophy have been overstated (Henry, 2011). In this paper, I want to 

address the assumption, explicit or implicit in modern accounts, that mathematics was 

recognised in the early modern period, as it is today, as inherently useful. In fact, the 

usefulness of mathematics was by no means apparent, even to the learned, in early 

modern Europe. For a complete understanding of the mathematization of the world 

picture, we need to look not just at the mathematicians, but at those who had little 

regard for mathematics. 

 I want to illustrate this by considering a single case study, although I will try 

to use it to make some more general observations. The case study concerns the 

eventual career choice of a would-be mathematician, by the name of Jean Fernel. This 



  Page 4 of 50 

is, indeed, the same Jean Fernel now known to history as one of the most innovatory 

and influential medical thinkers of the sixteenth century. Biographical evidence 

suggests, however, that Fernel tried to make a name for himself, and a living, as a 

mathematical practitioner, before he completely abandoned mathematics for 

medicine. Fernel’s achievements as a mathematician were not inconsiderable, but they 

have attracted scant scholarly attention. Another aim of this paper, therefore, is to 

consider for the first time, Fernel the mathematician. 

 The major source of information about Fernel’s life and work (apart from 

Fernel’s own writings) is a short biography written by his secretary for the last ten 

years of his life, the physician and humanist scholar Guillaume Plancy (1514–ca. 

1568), who had previously been a student of the French humanist scholar Guillaume 

Budé, and had worked with him until his death in 1540.
2
 Although the best source, 

Plancy’s Vita is by no means impeccable, and shows some inconsistencies; it is 

important, therefore, before going any further, to be aware of its shortcomings. 

 Plancy wrote the biography after Fernel’s death, but we do not know how long 

after. Plancy was definitely dead by 1574, and was reported to have died in 1568. His 

life of Fernel was not published until 1607, and there is evidence that Plancy had not 

properly refined and finished it, and that the manuscript from which it was published 

was in poor physical condition (Sherrington, 1946, pp. 147-50). But, even if we 

assume Plancy wrote the biography in 1558, it is clear that he did not have first hand 

knowledge of Fernel’s life before he began to work for him, in about 1548. In what 

follows, we are chiefly concerned with the period from about 1524 to 1530. The 

account of this period (as we shall see) includes some notable personal details of 

Fernel’s working and family life, but we have no way to check these against any other 

source.
3
 It seems unlikely (being too impertinent and disrespectful) that Plancy would 



  Page 5 of 50 

have fabricated his own account of these matters, but it is important to bear in mind 

that what he wrote was based on Fernel’s recollections of a period many years before, 

and must inevitably have been coloured by Plancy’s own preoccupations.  

 For our purposes, however, the important aspect of Plancy’s account of this 

early part of Fernel’s career is the attitude to mathematics that it displays. It seems to 

me that, even if (as seems likely) this aspect has been embellished by Plancy’s own 

scant regard for mathematics, it was not gratuitously intruded into the biography by 

Plancy. In what follows, therefore, I shall assume that Plancy’s Vita gives a fairly 

honest account of these episodes in Fernel’s life. But even if this is not the case, and 

Plancy offers in these parts of the Vita what we would consider to be a largely 

fictionalised account to enable him to promote his own anti-mathematical stance, it 

does not undermine my point. Either way, the case study shows anti-mathematical 

attitudes; as held by Fernel’s family (and conceded by Fernel himself) in the 1520s, or 

as held by Plancy sometime in the period between 1558 and 1574 (to say nothing of 

the opinions held by the several publishers who included the Vita in successive 

editions of Fernel’s Universa medicina from 1607 to 1680) (Sherrington, 1946, pp. 

149-50).
4
 

 

Jean Fernel, mathematician 

Jean Fernel became one of the most historically significant medical thinkers of the 

sixteenth century. At a time when severe cracks were beginning to show in the 

edifices of both Galenism, and the Aristotelian natural philosophy with which it was 

so closely linked, Fernel was one of only three thinkers who tried to develop a revised 

system of medical theory.
5
 The other two would-be reformers were Paracelsus, 

leading promoter of iatrochemistry, and Girolamo Fracastoro, the author of De 



  Page 6 of 50 

contagione (1546), in which discussion of the causative “seeds” of disease has often 

been seen as a foreshadowing of germ theory.
6
 Historiographically speaking, 

therefore, Fernel is in distinguished company. 

 

This portrait of Jean Fernel, which first appeared in his Medicina (Paris, 1554), sig. 

*iiiv, is the only known contemporary likeness. 

 

The son of a successful furrier and innkeeper, Fernel was born at Montdidier 

in the diocese of Amiens, and although he moved with his family to Clermont, near 

Paris, when he was twelve years old, he always designated himself as ‘of Amiens’ 

(Ambianus). He took a Master’s degree from the Collège de Ste Barbe, of the 

University of Paris, in 1519 and subsequently taught philosophy there while studying 

for the doctorate in medicine, which he was awarded in 1530. He lectured on 

Hippocrates and Galen at the Collège de Cornouailles for six years until his medical 

practice became so successful that he was forced to give up teaching. It was at this 

time, however, that he wrote the work (completed by 1538) which he later published 



  Page 7 of 50 

as De abditis rerum causis (1548; Fernel, 2005). This offered a new theory of 

contagious and pestilential diseases, which had always been anomalous with regard to 

ancient theories of disease. Fernel’s new theory moved closer to what historians of 

medicine, following Owsei Temkin (1977), call an ontological concept, rather than a 

physiological concept of disease (in which diseases are regarded as having their own 

independent existence, as opposed to being merely the result of an imbalance of the 

four bodily humours). Fernel saw his new theory as additional to, not a replacement 

for, Galenic theory and accordingly decided to clarify the nature and extent of the 

standard theory, before publishing his own. The result was the fullest exposition of 

Renaissance Galenism ever written, the De naturali parte medicina of 1542. For 

subsequent editions Fernel appropriated the term physiologia (which then signified 

the study of nature in general) as the title of this work (Fernel, 2003), and so gave rise 

to the modern usage of ‘physiology’ as the study of living systems. Fernel’s 

reputation as a practitioner increased after he succeeded in curing the serious illness 

of Diane de Poitiers (1499–1566), beloved mistress of Prince Henri (1519–99). At this 

time, Fernel feigned an illness of his own in order to avoid taking the post of chief 

physician to Henri, and when Henri became king in 1547 he avoided this post again 

by saying the position was the hereditary right of Henri’s father’s chief physician. 

Fernel ran out of excuses in 1556 and finally accepted the post of royal physician. 

Fernel attended the king at Calais in January 1557, when Henri brought an end to the 

English occupation, but he died at Fontainebleau the following year. It should be clear 

from this brief biography that in his day Fernel was recognised as one of the most 

successful medical practitioners in Europe, and inspired a group of followers, “more 

numerous than soldiers from the Trojan horse” (Sherrington, 1946, p. 155; Fernel, 

1607, sig. *7v) who practised medicine all over Europe.
7
 Furthermore, as a would-be 



  Page 8 of 50 

reformer of medical theory it seems fair to say that his influence upon his 

contemporaries was at least as great as Fracastoro’s, and even rivalled that of 

Paracelsus (particularly among more conservative thinkers who found Paracelsianism 

hard to stomach). 

In view of all this, it might seem that Fernel’s interest in medicine was bred in 

the bone, and that his achievement must have been the result of an unwavering 

commitment to medicine from an early age. In fact, this was very definitely not the 

case. Although devoted in his youth to assiduous study—so much so  that he was only 

forced to break off his studies when overwork caused him to succumb to a ‘quartan 

fever’—Fernel initially had no thought of any particular career. It was only after the 

enforced convalescence following this fever, when Fernel was already 27, that he 

‘began to talk over with his friends the career he should take up’ (Sherrington, 1946, 

p. 151; Fernel, 1607, sig. *4v). Rejecting divinity and jurisprudence, Plancy says that 

he chose medicine. Even then, however, Fernel spent a couple of years devoted to 

‘studies introductory to medicine’, namely philosophy and mathematics. Study for the 

MD took four years, Plancy tells us, and we known Fernel completed his MD in 1530. 

It was only in 1526 therefore, at the age of 29, that Fernel took up medicine. Even 

then, however, Fernel was evidently not fully committed. After the ‘first two years of 

basic work for the doctorate’, when many of Fernel’s fellow students were awarded ‘a 

first class’, Fernel only achieved a second class award. Plancy suggests that this was 

merely because Fernel, unlike his first class fellows, did not resort to bribes: ‘A “first” 

would assuredly have been granted’, Plancy wrote, ‘had the furnishing of his purse 

been equal to that of his head’ (Sherrington, 1946, p. 153; Fernel, 1607, sig.sig. *5r). 

There was another significant factor, however, which might explain Fernel’s 

comparative underachievement in medicine. In precisely these first two years of his 



  Page 9 of 50 

medical studies, Fernel published three significant mathematical books. In spite of 

opting formally for a career in medicine, it seems that, at the outset of his working 

life, Fernel wanted nothing so much as to make a name for himself as a 

mathematician.  

 Now, in some respects Fernel’s simultaneous interest in both medicine and 

mathematics is not as surprising as it may seem to modern readers. Although these 

two areas of study now seem widely separated to us, this was certainly not the case in 

Fernel’s time. Although the mathematical quadrivium was regarded as propaedeutic 

to the studies in each of the higher faculties (theology, law and medicine), geometry 

and astronomy, in conjunction with astrology, continued to be taught at more 

advanced levels in the faculty of medicine. It was not unusual, therefore, to find the 

most advanced mathematicians working not in the Arts Faculties but in the Medical 

Schools.
8
 Furthermore, many leading physicians at this time also published works in 

mathematics. Consider, for example, Alessandro Achillini’s Quatuor libri de orbibus 

(Bologna, 1498), Girolamo Fracastoro’s Homocentrica sive de stellis (Venice, 1538), 

and Girolamo Cardano’s Ars magna: sive de regulis algebraicis (Nuremburg, 1545). 

And let us not forget that even Nicolaus Copernicus was training to be a physician as 

he began to formulate his reformed cosmology. As Charles Webster has pointed out, 

‘Leading astronomers and cosmologers of the renaissance were educated as 

physicians; the two avocations were compatible and partly interchangeable’ (Webster, 

1982, p. 4). 

 Furthermore, after the bout of quartan fever which led him to decide upon a 

career, Fernel could not have formally chosen a career in mathematics if he had 

wanted to, for the simple reason that there was no such thing as a career in 

mathematics. As Kirsti Anderson and Henk Bos have recently pointed out, 



  Page 10 of 50 

‘mathematicians did not come from a well-defined group that earned their living from 

mathematics’ (Anderson and Bos, 2006, p. 697). Moreover, as Michael Mahoney has 

insisted, ‘one is hard pressed to find even a single, unified discipline of mathematics’ 

(Mahoney, 1994, p. 2).
 
Mahoney himself discerns ‘six broad categories’ of 

mathematician: classical geometers, cossist algebraists, applied mathematicians, those 

artists or artisans concerned with geometrical perspective and other aspects of 

projective geometry, mathematical magicians, and a group he calls the analysts who 

emerged a bit later in the early modern period, and who combined geometry and 

algebraic techniques in problem solving, and shared with the applied mathematicians 

a concern for pragmatism (Mahoney, 1994, pp. 2-14). 

Although there were some opportunities for such practitioners as private 

tutors, or as professors of mathematics in the universities, neither option was very 

lucrative. Professors of mathematics were even lower down the academic hierarchies 

than professors of natural philosophy, who were generally paid much less than 

professors in the higher faculties. The low status of mathematics in the universities 

clearly reflected a generally low opinion of mathematics among men of letters; 

although it was possible to take a degree in the liberal arts, it was not possible to take 

a degree in mathematics. Furthermore, the teaching of mathematics at university was 

generally of such a low level that it was not even intellectually rewarding. 

Consequently, those who did teach mathematics in the university system, seldom 

made it a lifetime’s career; it was much more usually undertaken for a few years only 

by young men biding their time before making their next career move (either into 

natural philosophy, or medicine, or perhaps something completely different).
9
 This 

remained true in spite of some notable attempts to reform the university curricula in 

the sixteenth century. Jesuit colleges elevated mathematics to a much more important 



  Page 11 of 50 

position in their curricula, but generally mathematics remained a minor, propaedeutic 

study in the arts faculties (Mahoney, 1994, p. 12).
10

  

Those who did spend their lives working as mathematicians usually did so 

outside the university system, and either had private means, or were lucky enough to 

attract the commitment of a wealthy patron. In England, for example, Thomas Harriot 

and Thomas Digges were able to make life-long careers as mathematicians thanks to 

steady patronage. John Dee, by contrast, sought the patronage of his Queen, but never 

succeeded in winning reliable support and had to leave England for patronage abroad. 

Galileo, managed to escape a poorly paid position as a professor of mathematics at 

Pisa and subsequently Padua, when he attracted the patronage of Cosimo II de 

Medici, while René Descartes expressed his gratitude that he never had to earn a 

living, being sufficiently financially secure that he could always pursue his own 

ambitions.
11

  

 In view of all this, then, it might be supposed that Fernel was just another of 

those medical men who continued to indulge a passion for mathematics, at least in his 

youth, but that his interest in mathematics was as a mere sideline, and was 

unexceptionable among university-trained medical men. If we look more closely, 

however, at Plancy’s life of Fernel and at Fernel’s three mathematical publications, a 

rather different picture emerges. Compared to most of his fellow physicians, Fernel’s 

interest in, and commitment to, mathematics was altogether exceptional. So much so 

that it seems impossible to deny that for a while at least, he seriously entertained 

ambitions to make a living as a mathematician. 

 If this is true, however, we need to ask ourselves why Fernel might have opted 

for this unpromising career choice. After all, as Mahoney has pointed out, in 

mathematics ‘There were no positions to be gained or held. There was no ladder of 



  Page 12 of 50 

advancement leading into a hierarchical elite’ (Mahoney, 1994, p. 21). What inspired 

Fernel to think that he might, against the odds, make a living as a mathematical 

practitioner? 

 It so happened that mathematics had enjoyed something of a revival in Paris 

during the opening decades of the sixteenth century. In 1495, seeking to reform the 

Arts curriculum at the Collège du Cardinal Lemoine, of the University of Paris, the 

leading French humanist Jacques Lefèvre d’Étaples (c. 1455-1536), placed renewed 

emphasis upon the importance of the mathematical quadrivium. The study of 

mathematics was subsequently encouraged by his colleagues, Jossé Clichtove (1472-

1543), and Charles de Bovelles (1479-1553). Furthermore, these three scholars 

published between them a considerable number of mathematical works. These 

included new editions of the arithmetics of Boethius and Jordanus de Nemore, and of 

the Sphaera of Sacrobosco, as well as treatises on geometry, astronomy, music, 

squaring the circle, doubling the cube, and so forth (Victor, 1978, pp. 36-44). 

 Furthermore, these three attracted into their circle a student at the Collège de 

Navarre who subsequently went on to become the leading French mathematician of 

his generation, Oronce Fine (1494-1555) (Marr, 2009). If his three older mentors were 

more interested in the mystical side of mathematics (they were interested in the 

theological use of number symbolism), Fine was much more concerned with the 

pragmatic aspects of mathematics.
12

 Although he too edited earlier works, including 

Euclid’s Elements (1536) and Peurbach’s Theoricae novae planetarum (1525), he was 

also an inventor of mathematical instruments, a leading cosmographer, and an 

influential mathematical teacher (including Petrus Ramus among his students). 

Undoubtedly, as one recent commentator has suggested, Fine was ‘one of the 

progenitors of a French renaissance of mathematics’ (Marr, 2009, p. 5). Fine became 



  Page 13 of 50 

especially active in publishing mathematical works following his release from a short 

prison sentence (possibly for charges connected with his practice of judicial 

astrology) in 1525, and in 1531 he was appointed to the newly established chair of 

mathematics in the Collège Royal, recently founded by François I (Pantin, 2009). 

Indeed, the king agreed to create a Royal chair of mathematics, alongside the more 

obviously humanist chairs of Greek and Hebrew, at the urging of Fine himself, who in 

an Epistre exhortative (1530) extolled the practical usefulness of mathematics and 

claimed that a chair of mathematics would lead to France ‘surpassing in sciences’ 

(Marr, 2009, pp. 7-8; Pantin, 2009, p. 17). 

 In view of this background, it is easier to understand why a brilliant young 

man, whose friends felt he could make a successful career in any of the three 

traditional professions, divinity, law, or medicine, might have harboured ambitions 

instead of forging a career in mathematics. Indeed, Plancy even records that, after his 

episode of quartan fever, when Fernel ‘began to talk over with his friends the career 

he should take up’, some of his friends proposed mathematics (‘alii mathematicas 

disciplinas… proponebant’) (Sherrington, 1946, p. 151; Fernel, 1607, sig. *4v). If we 

can assume that this is an accurate report, and a career in mathematics really was 

suggested by some of Fernel’s friends, it surely counts as testimony to the respect for 

mathematics in contemporary Paris, following the reformist educational schemes of 

Lefèvre d’Étaples and his circle, and the urgent activities of Fernel’s almost exact 

contemporary, Oronce Fine. 

Be that as it may, Plancy, having no interest in, and presumably therefore no 

knowledge of, this burgeoning of early sixteenth-century French mathematics, simply 

tells us that Fernel became determined to master mathematics:  



  Page 14 of 50 

he was unskilled in mathematics, so that he would stumble over examples 

commonly given by authorities in their exposition (of the subject); he felt it a 

scandal to be ignorant in a field of learning, which he admired no less than any 

other. So it was that he set out to cultivate his mind systematically, 

apportioning distinct and separate periods to his several studies. He gave the 

morning to arithmetic and mathematics; after the midday meal he turned to 

natural philosophy, and after supper to the Latin classics, paying special 

attention to their style (Sherrington, 1946, p. 151; Fernel, 1607, sig.sig. *4v). 

The liberal arts consisted of seven subjects, grouped as a foursome and a triad. 

Fernel’s day, it seems, was divided into studying the mathematical subjects of the 

quadrivium (arithmetic, geometry, astronomy, and music—essentially the 

mathematics of proportions) in the morning, and the trivium of linguistic studies 

(grammar, logic and rhetoric) in the evening. The afternoon was devoted to the 

natural philosophy of Aristotle which had long since become the mainstay of the 

university Arts curriculum, additional to the seven liberal arts.  

 According to Plancy, at this time Fernel ‘thought every hour lost which was 

not spent in reading and studying’, but his father, having seen Fernel through his 

university education to the MA, felt that he could no longer justify (to the rest of the 

family) paying for Fernel’s private studies (Sherrington, 1946, p. 151; Fernel, 1607, 

sig. *4r, and p. 152; Fernel, 1607, sig*4v). It was at this time (coinciding with the 

quartan fever that allegedly prompted him to consider his future) that Fernel decided 

to train as a physician. But, now having to pay his own way, he took a post as a 

lecturer in natural philosophy at the College of Ste Barbe in Paris. Moreover, Fernel 

did not abandon his mathematical studies, in order to make way for his medical 

studies. Indeed, if anything Fernel became much more focussed upon mathematics 



  Page 15 of 50 

than on anything else. This is evident from the biography which describes an 

extraordinary commitment to mathematics in Fernel’s daily life at this time. 

 Fernel had recently married and, using money from his wife’s dowry, he 

began to build up a collection of ‘the writings of all the old mathematicians’. But he 

did not stop there. He also built up a collection of astrolabes and other bronze 

mathematical instruments, many of which he had devised himself, and all of which 

were, as Plancy wrote, ‘costly’. What would undoubtedly have added to the cost was 

the fact that Fernel employed craftsmen and engravers to make these instruments for 

him, and they lived in the Fernel household. To off-set these expenses he gave lessons 

in mathematics to a number of ‘distinguished pupils’, and tried to earn money as a 

writer of mathematical treatises, and presumably by selling at least one of the 

mathematical instruments he invented, the so-called ‘monalosphaerium’. Indeed, his 

first book was an instruction manual for this instrument (Sherrington, 1946, pp. 153-

54; Fernel, 1607, sig. *5v-*6r; Fernel, 1527). 

 He also used the opportunity in his publications to ingratiate himself with 

potential patrons. He started, in his first publication, with Jacobus Govea, whom 

Fernel describes as ‘highly numerate and a renowned doctor of theology’, addressed 

the next to Johannes III, King of Portugal, and dedicated his final mathematical 

treatise before he committed himself to a medical career, to a Frenchman who acted 

as a patron to learned men, Martin Dolet.
13

 It seems clear that Fernel thought his best 

chance of a paying career in mathematics was through the newly burgeoning field 

known as cosmography. Accordingly, he dedicated the first two of his mathematical 

books to likely representatives of the greatest sea-faring nation at the time, Portugal.  

 

Jean Fernel, cosmographer 



  Page 16 of 50 

The period from 1490 to 1510, the period of the first major voyages of discovery, has 

recently been seen as marking a ‘cosmographic revolution’ (Vogel, 2006, p. 476). 

When Ptolemy’s Geography was first translated into Latin in 1406, the translators, 

Manuel  Chrysolaras and Jacopo d’Angelo, chose to translate the title as 

Cosmography. Ptolemy’s work, as might be expected from the author of the 

Almagest, was a mathematical treatment of various aspects of the Earth, including 

techniques for making map projections, the imposition of lines of latitude and 

longitude, and so forth. In some cases Ptolemy’s account required an understanding of 

the vault of the sky and its projection onto the surface of the Earth, and as such the 

book dealt with the whole world, or universe, not just the earth, and so 

‘cosmography’, the translators argued, was a more fitting title than ‘geography’ 

(Mosley, 2009, p. 425). Ptolemy’s Cosmography was first printed in 1475, and 

subsequently appeared in at least six editions before 1490. 

 One of the important aspects of Ptolemy’s work was that it assumed that there 

was one single globe of earth and water—a terraqueous globe. This, together with the 

experiences reported by those who undertook the various voyages of discovery, led to 

the final dismissal of an influential alternative view. The alternative, promoted by 

scholastic natural philosophers and supposedly based on abstract philosophical 

considerations derived from Aristotle, held that the sphere of the Earth was floating in 

a larger sphere of water, with only part of its top hemisphere above the surface of the 

water. Although the Ptolemaic view was held by a number of thinkers before this 

period, the final dismissal of the scholastic view can indeed be held to be a 

cosmographic revolution (Randles, 1993; Vogel, 2006). Although cosmography 

subsequently developed in a number of different ways (Mosley, 2009), it certainly led 

to a new field of applied mathematics, and seemed to offer new opportunities to men 



  Page 17 of 50 

like Oronce Fine and Jean Fernel. It is hardly surprising, therefore, that Fernel should 

try to master this new cosmography. Certainly, Fernel’s first two mathematical books 

mark their author out as someone with great ambitions as a cosmographer. 

 Fernel’s first publication, Monalosphaerium, partibus constans quatuor, as the 

title made clear, was specifically concerned with describing his newly invented 

‘monalosphaerium’ and instructing the reader in its various uses. Fernel’s instrument 

was essentially an astrolabe which managed to project all the information provided in 

different inscribed sections of an astrolabe on to one circle. He admitted its similarity 

to an astrolabe but believed it was an improvement upon the traditional instrument 

because it was equally comprehensive, but more convenient in use (Fernel, 1527, sig. 

Avir). The altitudes of the Sun, Moon and stars could be read from the 

monalosphaerium, and the lunar cycle derived from it. Thanks to inscribed 

coordinates of latitude and longitude of major cities, the latitude and longitude of any 

place could be found, and distances from one place to another. It was also useful, at 

least on a starry night, for giving the time in ‘equal hours’, and could be used to 

proceed from equal hours to unequal, and vice versa (Fernel, 1527, ff. 5r, 18r). And, 

of course, it could be used as a perpetual calendar, particularly for calculating Easter 

and other moveable feasts (Fernel, 1527, f. 7v). Fernel also showed how it could be 

used for determining the critical days in various fevers, and for drawing up 

horoscopes. 

 For good measure, Fernel provides a fourth and final part to the book which 

bears little relation to the first three parts, but which shows the reader how to calculate 

various things, such as the height of a tower, the distance between two places, and the 

depth of a cistern. The work closes with some discussion of the measurement of areas, 

and how to relate the area of a triangle to that of a square, or even to the volume of a 



  Page 18 of 50 

cube. This section seems to provide Fernel with the opportunity of showing what he 

himself can do as a mathematician, after previously confining himself to describing 

the monalosphaerium, since he declares himself to be now off the leash (Fernel, 1527, 

f. 25r).  

In the dedication, Fernel says that he wrote the work in response to Jacques 

Govea’s request for a work that would enable the young to pluck attractive blooms, 

and other resources from the mathematical disciplines, and thus adorn the rest of the 

arts, as if with jewels: ‘For mathematics is of a nature to bring lustre to tired topics, 

and to keep a mind in one’s body that is imbued with incredible life-long pleasure’ 

(Fernel, 1527, sig. Avir). Although Govea, who later became Rector of the College of 

Ste Barbe, was only at the beginning of his career there when Fernel dedicated the 

book to him, he already had the ear of the King of Portugal and that would be enough 

for Fernel to want to cultivate his friendship. Fernel tells us in the dedicatory epistle 

that after charging him with this duty to the young, Govea left Paris to visit the King 

of Portugal. Perhaps Fernel hoped that important French readers might be spurred into 

making sure that Fernel should continue to work for French maritime interests, rather 

than be tempted away by the attentions of the Portuguese (Sherrington, 1946, p. 172). 

Be that as it may, Fernel aimed at the top of the Portuguese tree with his next, 

and surely most important, work, Cosmotheoria. He dedicated this to the King of 

Portugal himself, João III (Fernel, 1528a)). Not knowing the King personally, he 

resorted to praising the achievements of renowned Portuguese explorers, from Henry 

the Navigator (1394–1460), and Bartolomeu Dias (c. 1450–1500), the first European 

to round the Cape of Good Hope (1488), while searching for the legendary Christian 

kingdom of Prester John, to Paulo (d. 1499) and Vasco da Gama (c. 1469–1524), who 

extended these explorations to find a route to India (Fernel, 1528a, sig. Avir-v). 



  Page 19 of 50 

Clearly, Fernel was attempting to flatter the King by association. Fernel did not rely 

solely on flattery, however. He clearly hoped that the practical usefulness of the 

information provided in Cosmotheoria, would be immediately recognisable to the 

king and his advisers, and would therefore attract patronage.
14

 

The main theme of the Cosmotheoria is the size of the Earth and of the 

heavenly spheres. But right at the outset he rejects the scholastic view of the floating 

Earth partially protruding from a separate sphere of water, and affirms the Ptolemaic 

view that the earth and seas form a single globe. ‘One must thus agree’, he wrote, 

‘that the earth looks like a wooden globe in which there are many hollows in which 

water can gather’ (Fernel, 1528a, sig. Bv; Randles, 1993, pp. 67-9). It is perhaps this 

aspect of Fernel’s second book which has led a leading historian of cosmography to 

describe it as ‘one of the most original contributions to cosmography in the French 

Renaissance’ (Randles, 1993, p. 67). As a measure of the importance of this issue, it 

can be noted that Copernicus also discussed the same matters in Book 1, Chapter 3, of 

his De revolutionibus (1543), ‘How Earth forms a single sphere with water’. Indeed, it 

has been suggested that the confirmation of the Ptolemaic single globe of earth and 

sea by the Renaissance voyages of discovery were what made it possible for 

Copernicus to develop his theory of a planetary (wandering) Earth.
15

 

 Fernel’s Cosmotheoria is also famous for the attempt to establish the length of 

a degree of a great circle of the Earth. Taking with him a reliable clock, Fernel 

travelled due north (or nearly due north) of Paris until he found the place where the 

elevation of the Sun at noon corresponded to one degree north (presumably this took a 

few days to establish). He then returned to Paris by coach and counted the number of 

times one of the coach wheels made a full revolution. Knowing the circumference of 

the wheel, he was able to calculate the full distance. Given the fact that Fernel 



  Page 20 of 50 

counted 17,024 revolutions of the wheel, there was some room for error. It is a 

testimony to the care with which he undertook this measurement, however, that the 

surprising accuracy of his result continued to impress subsequent investigators and 

commentators (Fernel, 2005, p. 10). Fernel declares the length of a degree of a great 

circle of the Earth to be 700 stadia, or 87½ Italian milliaria. But he then tries to help 

the reader to be able to understand these lengths in their own local terms. He starts 

with a digitus, which he says is the length of four grains of barley. Four digiti are a 

palmus; four palmi make a pes; and a cubit is one and a half pedes, or six palms. He 

then arrives at a measure for a passus geometricus of five pedes. The Italian stadium 

is 125 passus, and an Italian milliarium is eight stadia, or one thousand passus. A 

German milliarium, however, has 4000 passus, and the Swedish variety has 5000 

(Fernel, 1528a, f. 2r). 

 Having dealt in the first chapter with the size of the Earth, Fernel went on to 

discuss the dimensions of the sphere of air, and the sphere of fire, before dealing with 

each of the heavenly spheres in turn, including the sphere of the fixed stars, and the 

primum mobile. Although primarily concerned with the physical dimensions of the 

spheres, Fernel also considers the sizes of the circles (deferents and epicycles) 

assumed by astronomers in accounting for the precise motions of the heavenly bodies. 

There is nothing particularly new in the general approach, since it is based on the 

standard assumption that the heavenly spheres are nested contiguous with one 

another, and is in keeping with Peurbach’s Theoricae novae planetarum (1454, 

published posthumously, by Regiomantanus, in 1472). Clearly, however, Fernel was 

convinced that he was offering a new and more accurate assessment of the heavenly 

dimensions.
16

 It seems reasonable to suppose that Fernel believed that an accurate 

idea of the relevant dimensions would facilitate much needed improvements in 



  Page 21 of 50 

astronomy. It should not be forgotten that Fernel was writing not long after 

Copernicus had written his Commentariolus (ca. 1512), the first unpublished account 

of his heliocentric astronomy (and known only to a few, which did not include Fernel) 

(Copernicus, 1985, pp. 81-90). This was a time, therefore, when astronomers were 

casting around for a way to improve the principles of their art. Evidently, Fernel did 

not have Copernicus’s creative flair (not in astronomy, anyway—it would be a 

different matter when he finally turned to medicine), but by emphasising the 

improved accuracy of his measurements and calculations he was in good company. 

Even half a century later, Tycho Brahe (1546–1601) was pinning his hopes for the 

future of astronomy on more accurate assessments of planetary movements, rather 

than on the more drastic Copernican reforms (Thoren, 1990).  

 Fernel’s third, and final, mathematical treatise is rather different from the 

other two. Instead of focussing upon astronomical or cosmographical matters, it takes 

a much broader approach, seeking to show the value of mathematics in a number of 

different areas. Also, it is not dedicated to a potential Portuguese patron, but is 

dedicated to the now highly obscure Martin Dolet. It is possible that Fernel saw Dolet 

as a likely patron himself, or perhaps Dolet acted as a patronage broker. Fernel 

describes him in the dedication as a ‘most devoted patron and protector of learned 

men’ (Fernel, 1528b, sig. Aiiiir). Perhaps Fernel sensed that he was not going to 

succeed in attracting Portuguese patronage, and felt that broader claims about the 

usefulness of mathematics, rather than a focus on cosmography, were required if he  



  Page 22 of 50 

 
 

 
 

Fernel’s depiction of the sphere of Mercury, and table showing the various 

dimensions of different aspects of the sphere, including the epicycle and the body of 

the planet. From Fernel, Cosmotheoria, f.12v and f. 13r. with acknowledgement to 

Edinburgh University Library, Special Collections Department, Df.1.18/3. 

 



  Page 23 of 50 

was to have any sway with French patrons. De proportionibus, accordingly, is 

concerned with the proposition that ‘everything in nature (how much more so, in 

people and in medications) is created in a fixed proportion of components’. It was for 

this reason, Fernel says, that the ‘ancient philosophers’ believed ‘harmony is the sole 

principle of all things’ (Fernel, 1528b, sig. Aiiiir).  

 Fernel describes the mathematics of proportions as ‘a weapon considerably 

concealed’, because of the difficulty of using it, but which can be used in many 

different spheres. Ethical philosophy, he claims, deals with things which are so 

inextricably linked that only the theory of proportions can sort them out. Here he is 

drawing upon the suggestion of mathematically inclined humanists that music, as the 

discipline of proportions and balance, offers a science of the good life. The theory of 

proportions was seen, therefore, as an important scientia activa, essential for 

understanding both moral and political science.
17

 Similarly, even the study of the 

pulse in medicine relies upon a theory of proportions, we are told, since Galen 

attributed the pulses to musical harmonies in the body.
18

 There is, in short, Fernel 

says, a diverse harvest to be reaped, from geometry and astronomy to natural 

philosophy, and beyond. 

 In view of all this, it could hardly be said that Fernel had merely a dilettante’s 

interest in mathematics, or that his interest in mathematics went no further than that of 

other physicians. On the contrary, it seems impossible to deny that he was aiming to 

establish himself as a member of what he perhaps saw, in the period immediately 

following the revival of mathematics by Lefèvre d’Étaples and his circle and 

reinforced subsequently by Oronce Fine, as a growing community of vocational 

mathematical practitioners. Furthermore, in view of the nature of his publications and 

his attempts to win patronage for the kind of work detailed in them, it seems likely 



  Page 24 of 50 

that he harboured genuine ambitions to establish himself as a leading cosmographer. 

The fact that he was producing his mathematical works while working towards his 

MD should not be seen as diminishing his separate commitment to mathematics.  

 

Jean Fernel, mathematician manqué, and physican 

Why, then, did Fernel abandon mathematics and turn his attention entirely to 

medicine? After publishing his De proportionibus in 1528, Fernel never again wrote a 

mathematical work. All his subsequent publications were medical and, unlike his 

mathematical writings, they immediately established Fernel’s reputation as a leader in 

the medical arts and sciences. Furthermore, by the time his first medical publication 

appeared, the De naturali parte medicinae, in 1542, Fernel had long since sold off his 

collection of mathematical books and his collection of instruments. He had dismissed 

the instrument makers and engravers he had employed and housed, and he had 

notified his private mathematical pupils that ‘they must look elsewhere for a master’ 

(Sherrington, 1946, p.154; Fernel, 1607, sig. *6v). What caused this dramatic change 

of direction?  

 The answer is very clear in Plancy’s account of Fernel’s life. It was apparent 

to Fernel’s family, and in particular to his wife and his father-in-law, who lived in 

Paris and ‘often saw his son-in-law’, that Fernel was not making a suitable living out 

of his pursuit of mathematics. On the contrary, Fernel was ‘dipping into his wife’s 

marriage portion’ to fund his expensive indulgence in mathematics. Plancy hints at a 

domestic scene in which Fernel’s wife became increasingly distressed by the financial 

hardship into which Fernel seemed to be leading her and their two daughters. 

Whenever Fernel’s father-in-law came to visit,  



  Page 25 of 50 

he would take occasion to complain to his son-in-law that medicine, which 

had been his whole devotion formerly, now concerned him too little. He so 

clung to mathematics that neither love of his wife, nor the endearments of his 

children, nor the care of his house, could take him off them (Sherrington, 

1946, pp. 153-4; Fernel, 1607, sig. *5v-*6r). 

Eventually matters came to a head and Plancy tells us that the father-in-law, ‘moved 

by his daughter’s tears, lost his temper and scolded his son-in-law.’ It was as a result 

of these ‘entreaties and reproaches’ that ‘Fernel gave way at last’ and ‘renounced his 

mathematics and began to devote himself to medicine with a greater zeal than ever 

before’ (Sherrington, 1946, p. 154; Fernel, 1607, sig. *6v).
19

  

 It is perhaps worth remarking that the family’s concern about the comparative 

earning power of mathematics and medicine was surely vindicated. Long before the 

end of his life, Fernel’s earnings as a physician turned him into a wealthy man. As 

Plancy tells us, and this time he has first-hand knowledge: 

Throughout the time I lived with him (and I lived with him for ten years) his 

annual income often exceeded twelve thousand French pounds and rarely fell 

below ten (Sherrington, 1946, p. 170; Fernel, 1607, sig. ***2v). 

Just three years before this, Oronce Fine had died after enduring years of financial 

hardship. Dependent on courtly patronage, Fine all too often found himself, in spite of 

his undeniable achievements, ‘waiting and begging for payment for his efforts and 

being mocked and put off with courtly pittances’ (Marr, 2009, p. 9, quoting Fine’s 

son, writing in 1560). 

It is evident that Fernel’s own efforts to attract patronage repeatedly failed, 

and his pursuit of mathematics, in spite of his private tutoring, cost him more than it 

brought in. Sir Charles Sherrington, noting the sumptuousness of Fernel’s 



  Page 26 of 50 

mathematical treatises, assumed that he must have ‘had a generous patron at his 

back’. Each of the books was evidently published with a separate book of plates (no 

copies of which are known to survive), so they were clearly expensive to produce.
20

 

Sherrington’s assumption may well be correct but it only makes it more likely, rather 

than less, that Fernel was hoping to attract further patronage following upon his 

publications. Alternatively, Sherrington’s surmise may be wrong. Given that Fernel 

does not thank an already generous benefactor in his dedicatory epistles, but merely 

solicits for future patronage, it seems likely that Fernel actually paid for the printing 

of these books himself. Fernel is known to have employed his own engravers, and the 

excellent engraved illustrations in these three books (to say nothing of the lost extra 

booklets of plates), show every sign of having been closely supervised by the author. 

Perhaps this is why, as Plancy tells us, Fernel had to dip ‘into his wife’s marriage-

portion’ (Sherrington, 1946, p. 153; Fernel, 1607, sig. *5v). If so, then he would 

certainly be hoping that the expenditure on the books would eventually pay dividends 

by attracting sufficient interest that he might win patronage from them. When all this 

failed, it must have seemed obvious to everyone around him, and eventually even to 

Fernel himself, that mathematics was not a good choice of career, particularly if the 

option of a medical career was open to him. 

 

Fernel and the usefulness (or not) of mathematics 

It is possible, however, to discern another important factor in Fernel’s decision to 

abandon mathematics. It is usual in the historiography of mathematics, particularly in 

accounts of its gradual recognition during the Scientific Revolution as a crucially 

important way of understanding the world, to emphasise its practical utility. In 

contrast to the contemplative natural philosophy of the pre-modern world, 



  Page 27 of 50 

mathematics was always seen to provide practical information which could be put to 

use for the benefit of all. Or so the story goes. Plancy’s Life, however, presents a 

rather different attitude to mathematics. It seems that the pragmatic usefulness of 

mathematics was by no means obvious to everyone.  

 Plancy presents this alternative view of mathematics in a re-imagined 

quotation from Fernel’s father-in-law: 

‘Now, knowledge of mathematics is in itself as culture well enough, and 

exercises the wits, if one uses moderation in the time given to it. But it 

becomes a scandal when an honest man with duties to the public and his 

family reposes, so to say, to sleep on the quick-sands of the sirens, letting the 

years go by. Mathematics made no contribution to the public weal. Apart from 

a modicum of arithmetic and geometry it touched society little or not at all. On 

the other hand when we turn our gaze and thought to medicine we find it a 

science occupied either with sublime enquiry into Nature or with deeds of 

beneficence and utility. It is of right the worthiest of all the arts. Mathematics 

offers no comparison with it’ (Sherrington, 1946, p. 154; Fernel, 1607, sig. 

*6r). 

It is impossible to tell whether this quotation was reconstructed by Fernel in 

reminiscence, and told to Plancy while he was gathering information for the Life, or 

whether Plancy himself imagined it as typical of the kind of things any ‘man of 

experience’, as Plancy described Fernel’s father-in-law, would have said about 

mathematics. It seems certain, however, that Plancy himself did concur with these 

views. Immediately after attributing these words to the father-in-law, Plancy says, ‘he 

urged on Fernel these and other good reasons.’ Furthermore, at this point in his 

narrative he depicts Fernel’s father-in-law not only as a man of experience but also as 



  Page 28 of 50 

‘prudent and accomplished’ (Sherrington, 1946, pp. 153-54; Fernel, 1607, sig. *6r-v). 

This dismissal of the value of mathematics does not emanate from a critic of no 

standing, therefore, but from a man of supposed worldly wisdom. 

 There are also echoes of these criticisms of mathematics in Plancy’s own 

comments in the Life. Even before recounting Fernel’s abandonment of mathematics, 

Plancy had felt it necessary to apologise to the reader for Fernel’s infatuation with the 

subject: ‘Contemplation of the stars and heavenly bodies excites such wonder and 

charm in the human mind that, once fascinated by it, we are caught in the toils of an 

enduring and delighted slavery, which holds us in bondage and serfdom’ 

(Sherrington, 1946, p. 153; Fernel, 1607, sig. *5v-*6r). This foreshadows the 

comment about sleeping on the quick-sands of the sirens. Similarly, the father-in-

law’s unfavourable comparison of mathematics with medicine is reflected later in the 

Life when Plancy says that Fernel ‘bitterly regretted that he had formerly given 

himself up’ to astrology, if not mathematics more generally.  

In what is an unusually long discussion of any one topic in the biography, 

Plancy first tells us that Fernel came to believe that judicial astrology was ‘erroneous 

and unfounded’, before going on to say that he himself was ‘entirely at one with the 

teaching of this great man’ on this topic. ‘My view’, he wrote, ‘is that these impostors 

with their judicial astrology, pressing with extravagant zeal this absurd and ridiculous 

view of the influence of the stars, outrage both heaven and medicine’ (Sherrington, 

1946, p. 159; Fernel, 1607, sig. **2r). 

 It is important to note here, however, that Plancy does not object to the idea 

that the stars can affect things on Earth. His objection is to the claim that knowledge 

of such things can be discovered through mathematics. Consider, for example, this 

comment on the cause of pestilence: 



  Page 29 of 50 

I recognise willingly that often the Divine Power, whose decrees and plans are 

inscrutable, permits, in punishment of man’s misdeeds, and in order to turn 

man back from his errors, pestilence and contagion, for him to bear. I will not 

deny even that the stars by their malignity corrupt the air to such a point that it 

becomes a source of mischief to man and beast, and sows the seeds of death. 

But I hold that none of these things can be foreseen by help of judicial 

astrology, and they are known only by their actual event.
21

 

The objection is not just to the divinatory aspects of astrology, but to the inadequacy 

of its causal claims: 

Against the laws of Nature, they view matter as taking exceptional and strange 

forms, and sublunar bodies undergoing certain changes. They attribute these 

happenings to the ‘aspects’ and the ‘conjunctions’ of the stars (Sherrington, 

1946, p. 159; Fernel, 1607, sig. **2r). 

Conjunctions occur when two heavenly bodies appear close together, or coincident, 

against the background of fixed stars, and the aspects are particular angular 

separations of heavenly bodies, such as 60 or 90 degrees, which are supposed to be 

particularly significant. For Plancy, however, it is clearly an absurdity to imagine that 

the geometrical configuration of the heavenly bodies can have any kind of physical 

effect.
22

 

 Another factor which prevented educated men from recognising any 

usefulness in mathematics derived from the strict separation of mathematics from 

natural philosophy. Deriving ultimately from Aristotle’s views, the prevailing view 

was that natural philosophy was concerned to provide explanations of natural 

phenomena in terms of physical causes, and that mathematics could say nothing about 

causes, but could only give a particular kind of technical description of what was 



  Page 30 of 50 

going on in a physical system. So, a specific set of deferent and epicycle, allocated a 

specific combination of movements, could show us how the observed movement of a 

particular planet could be accomplished, but this assumed set-up could say nothing 

about how or why (or even whether!) the planet moved in this way, or what kept it in 

these motions. Generally speaking, mathematics was regarded as incompetent with 

regard to natural philosophy (Dear, 1995; Mancosu, 1996). 

The most famous (or, as it is seen in the standard historiography of science, 

infamous) illustration of the gulf between mathematics and natural philosophy, of 

course, is the preface added to Copernicus’s De revolutionibus orbium coelestium by 

Andreas Osiander, the Lutheran minister who had been delegated to supervise it 

through the press. As Robert S. Westman has pointed out, Osiander’s wording  

reveals that he was not so much concerned that the nature of the physical world might 

be thrown into confusion by Copernicus’s heliocentric astronomy; rather he was 

concerned that ‘the liberal arts, established long ago on a correct basis, should not be 

thrown into confusion’ (Westman, 1980, pp. 108-9, quoting Osiander). Copernicus 

was in danger of throwing the liberal arts into confusion because his book might seem 

to imply that geometrical astronomy could reveal to us the true nature of the World 

system, whereas, as all educated men knew, only natural philosophy could establish 

physical truths.
23

  

If the recent historiography devoted to uncovering the history of cosmography 

has correctly recaptured events, it seems that Fernel should be counted as one of those 

who was convinced of the power of mathematics for deciding upon controversial 

philosophical matters (in particular the precise arrangement of the sub-lunar spheres 

(especially the spheres of earth and water), and therefore sought to promote the 

usefulness of cosmography, even before Copernicus’s more powerful version of 



  Page 31 of 50 

mathematical realism pointed the way to what has been seen as the ‘mathematization 

of the world picture.’ The definitive history of cosmography has yet to be written but 

its practitioners seem to have developed, even before Copernicus, a mathematical 

realist view of the world (as opposed to the more traditional instrumentalist view 

implicit, for example, in Osiander’s preface).
24

 Moreover, their confirmation of the 

earth as a single terraqueous globe was an important factor enabling Copernicus to 

proceed with his own realist astronomy.
25

 It is arguable, therefore, that the renewed 

philosophical debate on the relevance of mathematics to natural philosophy, which 

emerged at this time, may have had its beginnings in the ‘cosmographic revolution’, 

rather than the Copernican revolution. If Osiander was content merely to declaim that 

the liberal arts had been established ‘on a correct basis’, there were evidently others, 

who were willing to discuss the matter, pro and con.
 26

 

If these debates ultimately led to the recognition that mathematics, far from 

being excluded from natural philosophy, could, and indeed must, contribute to our 

understanding of the physical world, it was a long, slow, process.
27

 At the time that 

Fernel was writing his mathematical works, the majority of the inhabitants of the 

Republic of Letters were unaware of the claims being made on behalf of mathematics 

and continued to regard it as irrelevant to natural philosophy, and therefore of little or 

no use to their concerns. We should not be surprised, therefore, much less 

disappointed, that Fernel the mathematician , who showed in the late 1520s that he did 

believe in the relevance of mathematics to our understanding of the physical world 

(not only by his confirmation of the Ptolemaic terraqueous globe, but also by his 

clearly realist claims about the physical dimensions of the planetary spheres—

deferents, epicycles, and all), soon abandoned the idea; or did so to all intents and 

purposes by abandoning the study and promotion of mathematics itself.  



  Page 32 of 50 

 Another contemporary claim in favour of the usefulness of mathematics, 

which is at least implicit and sometimes explicit in Fernel’s three earliest publications, 

is its use in training the growing mind. It is clear from the lavish nature of his three 

mathematical books, no less than from their content, that Fernel should be included 

among the so-called ‘mathematical humanists’, who wished to elevate mathematics in 

the disciplinary hierarchy because of its perceived usefulness in pedagogy.
28

 We can 

see this, perhaps, in Fernel’s concern that his mathematical book should be accessible 

to those without much mathematical training. In De proportionibus, for example, he 

tells us that he ‘deviated slightly from ancient mathematical practice’ so that he could 

‘put the proofs of what he had to say in few words, to prevent inducing nausea and 

disgust in people with little mathematical training, who have particularly hated 

proportions’ (Fernel, 1528b, sig. Aiiiir). Fernel was among the first generation of 

mathematicians to begin to exploit the almost complete corpus of Ancient Greek 

mathematics which had been recovered by humanist manuscript collectors in the 

fifteenth century. For humanist mathematicians like Leon Battista Alberti (1404-

1472), and Luca Pacioli (1445-1517), mathematics was in itself as representative of 

ancient glories as ancient philosophy, and they showed no hint of needing to 

demonstrate the importance of mathematics to philosophy. In so far as there was any 

concern to link the two, it was only to defend a vision of human learning as all 

interdependent. Celio Calcagnini (1479-1541), for example, suggested that  

Knowledge is all one body, which the Greeks call paideia and we 

humanitas… Thus the disciplines or parts of humanitas are connected among 

themselves… No one may therefore pursue physics without logic, nor logic 

without mathematics, nor anything without the support of rhetoric (Calcagnini, 

1544, p. 23).
29

 



  Page 33 of 50 

It was, however, easy to recognise the beneficial characteristics of mathematics in its 

own right. In particular, it was praised for the certainty of its proofs. ‘The manifold 

proofs of arithmetic and geometry’, wrote Pier Paolo Vergerio (1370-1445), ‘make 

these sciences a delightful study, and one possessed of a special certainty…’ 

(Vergerio, 1918 [1472], p. 127, quoted from Rose, 1975, p. 13). The humanists 

recognised the pedagogical implications: 

Geometry ought to be studied at an early age for it sharpens the intellect and 

makes the mind quick at perceiving… It is fitting for the prince to be 

instructed in both geometry and arithmetic… Besides there is much eruditio in 

it and it produces much caution, since very often mathematics denies what is 

conceded by dialectic… Astronomy reveals the secrets of the heavens and its 

study must not be withheld from the prince.
30

 

 If Fernel shared these same humanist attitudes to mathematics, however, it is 

certain that he also knew the cautions against mathematics which could also be found 

in humanist writers. In particular, the humanists seemed to be well aware that, 

although a knowledge of mathematics could be highly useful, it was possible to go too 

far, and become lost in a world of utter abstraction. Indeed, this belief was expressed 

by two of the ancient sources for the humanists’ admiration of mathematics, 

Quintilian and Cicero. Quintilian’s Institutio oratoria (I, 10) and Cicero’s De officiis 

(I, 6) both cautioned that too much immersion in mathematics could be a distraction 

from the vita activa required of the good citizen. For Aeneas Sylvius Piccolomini, 

writing in 1450, 

though these [mathematical] sciences are all delightful and useful to 

comprehend, still I could not urge too much expenditure of time upon them, 



  Page 34 of 50 

because advantageous as they are for the transient student, they can be harmful 

for a visitor who stays too long (Piccolomini, 1940, p. 123).  

Similarly, Roger Ascham, in 1563 insisted that, 

Some wittes, moderate enough by nature, be many tymes marde by over much 

studie and use of some sciences, namelie, Musicke, Arithmetick, and 

Geometrie. Thies sciences, as they sharpen mens wittes over much, so they 

change mens maners over sore, if they be not moderatlie mingled, & wiselie 

applied to some good use of life. Marke all Mathematicall heades, which be 

onely and wholly bent to those sciences, how solitarie they be themselves, 

how unfit to live with others, & how unapte to serve in the world (Ascham, 

1904, p. 190). 

Ascham even goes so far as to say that such unfortunate cases are ‘knowen nowe by 

common experience’ (Ascham, 1904, p. 190). If this was so, then it is evident that by 

the late sixteenth century there were significant numbers of mathematicians who had 

failed to heed the warnings and had become such solitary figures, unfitted for society. 

 It seems, then, that Fernel could hardly have been surprised to hear his father-

in-law announcing that ‘mathematics is in itself as culture well enough, and exercises 

the wits, if one uses moderation in the time given to it. But it becomes a scandal when 

an honest man, with duties to the public, and his family reposes, so to say, to sleep on 

the quick-sands of the sirens’. His wife’s father was drawing from the same humanist 

literature to criticise mathematics that Fernel used to defend it, and he was adding 

nothing new to these age-old strictures. Similarly, Fernel would not have been 

surprised had he seen Plancy’s later description of him as ‘fascinated’ by 

mathematics, and ‘caught in the toils of an enduring and delighted slavery’ which held 

him ‘in bondage and serfdom’ (Sherrington, 1946, pp. 154, 153; Fernel, 1607, *6r). 



  Page 35 of 50 

Indeed, it was perhaps Fernel’s own admiration for the humanists and their values that 

enabled him to recognise that he was in danger of becoming the kind of solitary 

thinker they warned against.  

 It should not be supposed, either, that when Fernel’s father-in-law dismissed 

the utility of mathematics as of little consequence (‘Apart from a modicum of 

arithmetic and geometry it touched society little or not at all’), he spoke merely from 

ignorance. For one thing, we should not forget that the words attributed to the father-

in-law must have been reported to Plancy by Fernel himself, during the last ten years 

of his life, and some twenty years or so after the incident. In a sense, what we are 

reading is not so much a specific utterance by one man but a reconstruction (by Fernel 

when he reported it to his secretary in recollection, and subsequently by Plancy, when 

he came to write Fernel’s Vita) of the kind of arguments familiarly used by the 

learned against mathematics. To support the suggestion that late Renaissance thinkers 

did not always see the practical usefulness of mathematics, we need look no further 

than Francis Bacon. Here was a thinker whose historical reputation rests to a large 

extent on the fact that he saw, when others did not, that knowledge of the natural 

world should not be regarded as knowledge for its own sake, but should be put to use 

to improve the lot of mankind. As is well known, however, Bacon never considered 

that mathematical knowledge had a major role to play in his vision for the betterment 

of our lives.  

 Again, this cannot be put down to an unfortunate oversight on Bacon’s part; 

something that he overlooked but would have seized upon (we can suppose) had he 

seen it. Bacon did discuss mathematics in both the initial Advancement of Learning 

(1605) and its expanded version, De dignitate et augmentis scientiarum (1623), but 

the only use for it that he seems to have recognised, as the humanists had before him, 



  Page 36 of 50 

was in pedagogy, for sharpening the wits and aiding concentration (Gaukroger, 2001, 

pp. 20-27). It is worth remembering also that Bacon’s father, Sir Nicholas, was 

involved in the plans to reconstruct Dover harbour in the 1570s, and was involved in 

the appointment of some of the leading English mathematicians who worked on the 

project as surveyors, engineers, and architects. Furthermore, Sir Nicholas himself 

showed a strong personal fascination with mathematics.
31

 Francis could hardly have 

missed the practical importance to England of what was, after all, the largest civil 

engineering scheme in Elizabethan Britain, particularly in view of his father’s 

personal involvement, and yet when he came to develop his own ideas about how 

knowledge of nature could be put to use for the benefit of mankind, he gave no 

thought to a role for mathematics. It seems that the separation between mathematics 

and natural philosophy was still so effective, in the early decades of the seventeenth-

century, that it was easy for Bacon to disregard mathematics while he was seeking to 

reform natural philosophy. Bacon wanted to reform natural philosophy to make it not 

only more authentic than Aristotelian natural philosophy, but also more useful. It is 

clear from his writings that the model he had in mind for useful natural knowledge 

was not mathematics, however, but natural magic (Rossi, 1968; Henry, 2002). 

Knowledge of supposed magical influences and interactions between things was 

always seen as something to be exploited for pragmatic benefits, and after the 

Renaissance recovery of the Corpus Hermeticum and other supposedly magical 

ancient writings such magical knowledge came to be regarded as part of the true 

ancient wisdom or philosophy.
32

 It would have seemed natural to Bacon to look to the 

newly revived magical tradition, therefore, as a way of reforming natural philosophy. 

The same could hardly be said of mathematics. Because mathematics did not, and 



  Page 37 of 50 

could not, offer causal explanations of natural phenomena, Bacon could, and did, 

dismiss it as irrelevant to his purposes. 

 Given the background that we have been surveying, a background which 

coloured nearly everyone’s perception of mathematics from before Fernel’s time 

through to Francis Bacon’s and even beyond (many, after all, were still puzzled by the 

title of Newton’s great book when it appeared in 1687—they wondered how there 

could be ‘mathematical principles’ of natural philosophy), it is hardly surprising that 

Fernel’s family, and other members of his household, such as Guillaume Plancy, 

should regard mathematics as a largely futile and sterile occupation. Irrespective of 

the innovatory work of men like Regiomontanus, Copernicus, Lefèvre d’Étaples, 

Fine, and many others who are now recognised by historians as greater or lesser 

contributors to the ‘mathematization of the world picture’, for most learned men, as 

for Fernel’s father-in-law, ‘Mathematics made no contribution to the public weal’, 

and ‘Apart from a modicum of arithmetic and geometry it touched society little or not 

at all’ (Sherrington, 1946, p. 154; Fernel, 1607, sig. *6r). 

 

Conclusion 

If Fernel was finally aroused from his slumbers on the quick-sands of the sirens by the 

distress of his wife and the anger of his father-in-law, and began to realise that he 

must choose a more suitable profession than that of mathematical practitioner, he did 

not need to look far. Fernel was, as we have seen, undertaking his mathematical work 

at the same time that he was training to be a physician. He completed the four-year 

curriculum leading to his MD in about 1530, and so in 1527 and 1528, the years he 

published his mathematical works, he must have been trying to combine his medical 

studies with his own commitment to mathematics. It was an easy matter, therefore, for 



  Page 38 of 50 

Fernel to simply concentrate on medicine. Indeed, the impression Plancy’s Vita 

presents is that Fernel resisted a medical calling during the time when he tried to 

establish a career as a cosmographer. Having abandoned mathematics, however, 

Fernel soon rose to become the most admired physician in France and one of the most 

admired throughout Europe.  

Nobody was ever in any doubt of the usefulness of medicine to society, of 

course, but it also had the advantage over mathematics that it was always perceived to 

go hand-in-hand with natural philosophy. Even Aristotle was said to have declared 

medicine and natural philosophy to be sisters.
33

 Certainly, Fernel’s own medical 

works paid a great deal of attention to natural philosophical considerations. His first 

major work (although withheld from the press until after he had published subsequent 

works), De abditis rerum causis (Paris, 1548), was divided into two parts, the first 

explicitly dealing with natural philosophy and the second with medicine. His earliest 

published work, De naturali parte medicinae (Paris, 1542), later became known 

simply as the Physiologia. This later title appropriated a term that usually referred to 

the whole of natural philosophy, and turned it into a term having reference only to the 

natural workings of the human body. Again, this suggests Fernel’s own belief in the 

close interconnectedness of natural philosophy and medicine (Fernel, 2005, pp. 3-4). 

This traditional alliance between medicine and natural philosophy may not have been 

much of a consideration for practising mathematicians, but in the eyes of most 

educated men it is likely to have ensured that medicine was regarded as more 

intellectually and culturally significant than mathematics. We can see this even in the 

reported speech which Plancy attributes to Fernel’s father-in-law. ‘On the other hand’, 

he says to his son-in-law after insisting mathematics touches society hardly at all, 

‘when we turn our gaze to medicine we find it a science occupied either with sublime 



  Page 39 of 50 

enquiry into Nature or with deeds of beneficence and utility. It is of right the worthiest 

of all the arts.’ Medicine is not just pragmatically useful but leads to a real 

understanding of the natural world. It was to be a very long time indeed before 

mathematics would be seen by educated persons routinely to have the same relevance 

to our understanding of nature. In the meantime, medicine remained the indispensable 

companion of natural philosophy, and Fernel’s father-in-law spoke for a number of 

succeeding generations when he said that ‘Mathematics offers no comparison with it’ 

(Sherrington, 1946, p. 154; Fernel, 1607, sig. *6r). 

 

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John Henry 

University of Edinburgh 

Science Studies Unit 

Chisholm House 



  Page 45 of 50 

High School Yards 

Edinburgh EH1 1LZ 

john.henry@ed.ac.uk  

 

NOTES 

                                                 
1
 Westman 1980; Jardine, 1988; De Pace, 1993; Høyrup, 1994; Dear, 1995; Mancosu, 

1996. 

2
 Sherrington (1946); the editor’s introduction in Fernel (2003), pp. 1-12; Siraisi 

(2007), pp. 122-25. 

3
 There is another early source, published before Plancy’s Vita, but it is shorter than 

Plancy’s and generally assumed to be based on access to a manuscript copy of Plancy. 

It appears in Thevet, 1584. On this and other early biographies, see Sherrington, 1946, 

pp. 148-9. 

4
 Sherrington, 1946, provides a complete list of editions of Fernel’s works, pp. 187-

207. 

5
 There were, of course, other innovators in the medical sciences in this period, 

particularly in the field of anatomy (Vesalius, Fabricius, etc.), but only Paracelsus, 

Fracastoro, and Fernel deliberately tried to develop a new theory of health and 

disease, intended to go beyond the prevailing Galenic theory. 

6
 On Paracelsus, see Pagel, 1958; Weeks, 1997; Grell, 1998. On Fracastoro, see Di 

Leo, 1953; Peruzzi, 1995. On Fernel, see Figard, 1903; Sherrington, 1946; and the 

editors’ introductions in Fernel, 2003 and 2005. See also the special issue of the 

journal, Corpus, devoted to Fernel: Kany-Turpin, 2002.  

7
 The quotation is from Guillaume Plancy’s Vita of Fernel, written about 1567 and 

first published in 1607: Guillaume Plancy, ‘Ioannis Fernelii D. Medici Vita’, in 

Fernel, 1607. A full translation of this is included in Sherrington, 1946, pp. 150-70, 

mailto:john.henry@ed.ac.uk


  Page 46 of 50 

                                                                                                                                            

and I quote from this throughout. The 1607 Vita is unpaginated, but for those who 

wish to consult the Latin, I provide the printer’s signature marks in Fernel, 1607, 

following the references to Sherrington’s translation. On Fernel’s influence see 

Sherrington, 1946, pp. 98-146; Brockliss, 1993; Brockliss and Jones, 1997, pp. 128-

38.  

8
 On the associations between medicine and mathematics see, for example, Maclean, 

2002, pp. 171-90. The distinguished scholar Lynn Thorndike wrote that Fernel 

‘continued the common medieval association of mathematics with medicine’; see 

Thorndike, 1941, p. 557.  

9
 See Westman (1980); Feingold (1984); and Schmitt (1984). 

10
 See Mahoney (1994), 12. 

11
 On patronage, Dawbarn and Pumfrey, 2004; Johnston, 2006. On Galileo, Biagioli, 

1993. On Descartes, for example, Gaukroger, 1995. See also, for a general survey of 

the different social backgrounds of mathematicians in this period, Biagioli, 1989.  

12
 Although it is necessary to distinguish between different kinds of practical 

mathematics. Fine was evidently interested in cosmography, cartography and related 

aspects of the mathematical sciences, but he disdained the use of mathematics in 

commerce. See Davies, 1960, pp. 30-31. 

13
 On Jacques Govea see Sherrington, 1946, p. 172. Jacques was uncle to the more 

famous humanist scholar Andreas Govea, who disputed with Petrus Ramus. I have 

been unable to discover anything about Martin Dolet (which perhaps explains why 

Sherrington makes no mention of him, in marked contrast to his treatment of Govea). 

Presumably he is the same Martin Dolet who published at Paris, in about 1508. It is 

possible that he acted as a patronage broker; this is discussed below.   



  Page 47 of 50 

                                                                                                                                            
14

 Practical utility seems to have been one of the two main concerns of potential 

patrons; the other being a concern for ostentatious or spectacular display, which 

would enhance the fame and prestige of the patron. For a full discussion of the nature 

of Renaissance patronage see Dawbarn and Pumfrey, 2004. See also, Moran, 1991. 

As far as I am aware there has been no previous discussion of Fernel’s attempts to 

attract patronage. 

15
 Copernicus, 1992, pp. 9-10; Vogel, 2006, pp. 479-80; Randles, 1993, pp. 69-70. 

There is no reason to suppose, however, that Copernicus knew of Fernel’s 

Cosmotheoria.  

16
 Albert van Helden says that ‘all educated persons after about 1250 were familiar 

with the principle of nesting spheres and the cosmic dimensions derived from it’ 

(Helden, 1985, p. 37). Unfortunately van Helden overlooks Fernel’s contribution to 

this aspect of cosmology. 

17
 For a fuller discussion of this aspect of the mathematics of proportions, see Høyrup, 

1994, pp. 163-4. On the science of the good life see Jones, 2006. 

18
 Fernel (1528b), sig. Aiiiir For a discussion of the use of proportions in medicine see 

McVaugh (1987). 

19
 Although Plancy makes Fernel’s father-in-law play the lead role here, Fernel’s wife 

came to the fore in later accounts. Lalande, 1771, Tome I, p.189, for example, said of 

Fernel that ‘il en auroit fait davantage si sa femme ne l’eût forcé, pour ainsi dire, à 

quitter l’étude stérile des Mathematiques’. It is significant for our purposes that 

Lalande attributes to Fernel’s wife a belief that mathematics is a sterile pursuit. 

20
 Sherrington, 1946, p. 4, where Sherrington tells us Fernel’s books cost 5 sols each, 

and the two books of plates were 10 and 12 sols each. See also Sherrington, 1946, pp. 



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15, 188 and 189. Sherrington cites as his source, Renouard, 1526-46, p. 428, but I 

have been unable to check this. 

21
 Sherrington, 1946, p. 160; Fernel, 1607, sig. **2v. Plancy is reflecting his master’s 

views here, since the stellar causation of pestilential disease is the main theme of 

Fernel’s De abditis rerum causis of 1548 (Fernel, 2005). Sherrington, 1946, fails to 

note this distinction between what is held to be valid in astrology and what is not, and 

tries to suggest (incorrectly) that Fernel, after writing the De abditis rerum causis, 

came to reject astrology tout court; Sherrington, 1946, pp. 33-4. For a fuller 

discussion of Sherrington’s attitude to Fernel’s astrology, see the editors’ introduction 

in Fernel, 2003, pp. 3-4. 

22
 For an excellent outline of the history of astrology, see Tester, 1987. See also 

Webster, 1982; Garin, 1983; Rutkin, 2006.  

23
 It is generally agreed that, in spite of Osiander’s intervention, Copernicus really did 

believe in the physical truth of his mathematically determined system. This seems 

evident from Copernicus’s own preface, his dedicatory epistle to Pope Paul III 

(Copernicus, 1992, pp. 3-6), and from the response of Copernicus’s friends, Georg 

Rheticus and Tiedeman Giese, when they heard what Osiander had done. Johannes 

Kepler claimed that Copernicus was the first thinker to reject the separation between 

mathematics and natural philosophy, but some modern scholars give this accolade to 

Kepler himself. See, for examples, Jardine, 1984, and Grant, 1994, pp. 38-9. It has 

also been suggested that Regiomontanus (1436-1476) was the first (Shank, 2002). 

24
 Attention was first brought to the split between realists and instrumentalists in 

astronomy by Pierre Duhem, 1908, 1969. The easy distinction between natural 

philosophers, seeking a realist cosmology, and mathematicians offering an 

instrumental astronomy, has proved highly fruitful for recent historiography and 



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undoubtedly reflects, to a large extent, the historical reality. Attempts to challenge this 

view by pointing to mathematicians who were realists, do not invalidate the 

distinction but, rather, add to our understanding of how mathematicians moved into 

the realm of natural philosophy (by becoming realists, in spite of being 

mathematicians). See Westman, 1980; Jardine, 1984; Jardine, 1988. Similarly, the 

recent attempt to claim that instrumentalism was not a genuine position but should be 

seen, rather, as ‘frustrated realism’ (frustrated by inability to come up with an 

astronomically satisfactory realist model of the cosmos) (Barker and Goldstein, 1998), 

has been countered by Michael H. Shank’s claim that instrumentalism (or 

fictionalism) was ‘an actor’s category in Osiander and sixteenth-century astronomy’ 

(Shank, 2002, p.179). 

25
  Westman, 1980, p. 136; Randles, 1993, pp. 69-70; Vogel, 2006, pp. 479-80. 

26
 Jardine, 1988, especially pp. 693-7, which is concerned with arguments about the 

certainty of mathematics; Mancosu, 1996; Høyrup, 1996. Jardine and Mancosu take 

their lead from a series of works by G. C. Giacobbe, which first drew attention to this 

debate on the Quaestio de certitudine mathematicarum. See, for example, Giacobbe, 

1972a; 1972b; 1973. See also De Pace, 1993. 

27
 As one leading historian of mathematics has argued, from the late fourteenth to the 

mid-sixteenth century ‘mathematics and formalized philosophy live largely separate 

lives’ (Høyrup, 1994, p. 125). For another account of the severe limitations on 

bringing mathematics and philosophy together see Molland, 1987. 

28
 Rose, 1975; Biagioli, 1989; Høyrup, 1994; Dear, 1995; Marr, 2009. 

29
 I am dependent here, and in the following discussion, on the account provided by 

Rose, 1975, pp. 5-18. On Alberti and Pacioli, and the lack of any concern that 



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mathematics needed to be justified in terms of its relationship to philosophy see 

Høyrup, 1994, pp. 148, 154. 

30
 Piccolomini, 1940, p. 210. This was originally written in 1450 as a letter of advice 

about the education of the young king, Ladislas V of Hungary (1440-1457). See Rose, 

1975, p. 14. Essentially the same assessment of the usefulness of mathematics in 

education can be seen, much later, in Francis Bacon’s Advancement of Learning of 

1603. 

31
 See Dawbarn and Pumfrey (2004); and Tittler (1976). 

32
 See Yates, 1964, and Walker, 1972. There is an alternative account of the reasons 

for Bacon’s inability to recognise the usefulness of mathematics, namely its 

association with magic. See, Yates, 1967 (reprinted in Yates, 1984). In my view the 

argument simply does not work, because Bacon adopted and adapted much of his 

philosophy from the magical tradition (see Rossi, 1968 and Henry, 2002), and so the 

association of mathematics with magic would not have been a reason to put him off. 

On the association of mathematics with magic see, for example, Zetterberg, 1980; 

Eamon (1983); Molland (1988); Henry (1990); and Henry (2008). 

33
 See, for example, Aristotle, Parva naturalia I, 436a 19-436b 1. For a discussion of 

the belief that medicine and natural philosophy were necessary complements to one 

another, see Temkin, 1977, and Temkin, 1991, pp. 8-17.