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The teaching of mathematics (as we understand the subject today) in France is said to result from Ramus. However, It was his predecessor Oronce Fine who convinced François 1 to include it at the College Royal, despite its not being thought much of as a subject (le peu d’eſtime qu’on faiſoit alors de cette ſcience. Jean-Pierre Niceron; Memoires pour servir a l'histoire des hommes illustres dans la republique des lettres…; Briasson; 1737). While the quadrivium of medieval learning – arithmetic, geometry, music (or harmony) and astronomy (or astrology) – did include arithmetic, what was it about math that didn’t fit medieval (religious?) thinking?

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    Wow. You must not know much about the practice of mathematics. Geometry is as close to the soul of math as you can get, proofs and all. – AlaskaRon Oct 28 '16 at 3:49
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    @AlaskaRon. Thanks, but glib comments about questioners' knowledge is not very helpful, especially when it doesn't address the question. It is precisely because I do not know that I'm asking. – Frogologue Oct 28 '16 at 14:46
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    @T.E.D. Good point, that wasn't very clear. I'm referring to the education provided in a school, university or similar academic institution where both the trivium and quadrivium were core elements during the middle-ages, more specifically from 11-12th C, and more particularly in Italy and France – Frogologue Oct 28 '16 at 14:46
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    Other than geometry, was there really all that much math to be studied in the medieval period? Even algebra wasn't, I think, commonly known in Europe until the 1400s. – jamesqf Oct 28 '16 at 17:52
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    @Mark C. Wallace Thanks for your interesting answer (and showing what you meant by sourcing the assertions ;o) This is a rather complex issue. As to your suggestion that "math was not taught is that it failed to help the mind appreciate God?", I don't know. – Frogologue Oct 28 '16 at 22:28
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Medieval scholarship was essentially a "great books" endeavor, where paragons of intellect were held to have the last word on many subjects (consider Aristotle for natural science or Galen for medicine). For mathematics, the Quadruvium included Arithmetic and Geometry (heck, that was two out of four), where Nicomachus and Euclid were the 'paragons' for mathematical sciences (Moslem works of mathematics entered into the west starting in the 12th century, such as Al-Khwarizmis's book on algebra, the 12th century was a period of increased work on mathematics. Certainly, before that, computation itself was highly impeded by the atrocious Roman number system. :)

Euclid's Elements include both sections on geometry and number theory and this is very close to the modern sense of mathematics, which consists of axiomitizing abstract objects and deriving their properties through rigorous proofs. Nicomachus is typical of medieval scholarship in that he considered arithmetic from an almost numerological viewpoint, instead of that of practical computation. Awesomely enough, he also wrote one of the early texts on music theory.

EDIT: I was perusing the book "The Universities of Europe in the Middle Ages" by H. Rashdall -pdf here - and he throws out the comment (pp 442-443) that mathematics were studied in Univ. Paris in the 1300s, however (italics added for emphasis):

Such books were Euclid (the first six books), the Almagestum of Ptolemy,
the de Sphaera of the Englishman Johannes de Sacrobosco,the Perspectiva Communis (i.e. Optics) of another Englishman, John of Pisa (written in 1280). Instruction in Algebra and Arithmetic is also mentioned in general terms. At the same time the mere fact that the Mathematical books are passed over with such scant courtesy by the reforming Cardinarls seems to show what there are other grounds for supposing, namely, the Mathematics were more seriously cultivated in Oxford and some of the German Universities than at Paris.

The faculty at U. Paris did not seem to be as interested in the Trivium and Quadrivium that at other places, either.

Another point of view is that mathematics might have been weaker (for idiosyncratic reasons?) at the Univ. level in France in late Medieval times, but there was also a parallel system of 'abacus' schools (for merchants) and quite a bit of elementary and grammar school education available, which may be where much of the (basic) mathematical learning took place. Some of this appears in David Sheffler's article Late Medieval Education: Continuity and Change, History Compass (2010, pp. 1067-1082).

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    I don't pretend to much knowledge on this era, but my gut agrees with the first sentence; they believed that all knowledge was prior, so there was no point to a branch of thought devoted to investigating/discovering. If math could teach us something, the ancients would have known it. – Mark C. Wallace Oct 29 '16 at 23:28
  • @AlaskaRon Yes, I tend to agree on your '"great books" endeavor' idea, but this still doesn't tell me why it would be disparaged in the 16th C. Thanks for contributing. I think I have come to a tentative solution to the question which I am posting now. – Frogologue Oct 30 '16 at 2:37
  • @Mark C. Wallace Ditto, but it was still being taught – Frogologue Oct 30 '16 at 2:45
  • @MarkC.Wallace Yes. In fact, oddly enough, some claim that one of the big steps in the creating of modern science was the rejection of Aristotle as unimpeachable truth, in the Condemnations of 1210, in France, no less. (I don't really follow this, because alchemy was very well established at this time, and it really was solidly a science). – AlaskaRon Oct 30 '16 at 6:25
  • @AlaskaRon Thanks, yes, excellent points, and this corroborates what I was suspecting: that "private" or commercial schools providing a more hands-on applied approach to numbers and calculation were becoming more favored, especially by the rising merchant class. Perhaps too France's (wannabe) self-identity as heirs to the Holy Roman Empire (via Charlemagne) would make the country more loyal to the ancients. I'll read up on Rashdall and Scheffler (if I can get a pdf ;o) – Frogologue Oct 30 '16 at 15:15
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I would not say that education in the Middle Age was "recalcitrant" to mathematics. (There was a general decline of education in Europe, but this was a decline in everything, nothing special about math). Arithmetic and astronomy were taught. The Church needed astronomy (not astrology!) for calendar purposes at least. This was called "Computus", computation of the date of Easter. Same happened in other cultures (Islamic, Chinese. One of the Seven Noble Arts of Confucius, an analog of European trivium and quadrium, was mathematics. Very non-trivial astronomical computations were practiced in India too.)

  • The Italian renaissance and its spread through Europe would hardly have occurred had there been a general decline. There may well have been periods of decline, but there was an overall improvement in mathematics in Italy from Fibonacci onwards. In the universities, arithmetic and astronomy were taught, but I'm not sure about their scope. And although the church may have needed a dumbed-down version of astronomy (ask Galileo), astrology was very much a next-door neighbor, as was the study of magic to mathematics... – Frogologue Oct 28 '16 at 22:48
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    @Frogologue: But Fibonacci did not come along until nearly the end of the Medieval period. Indeed, I think you could point to his introduction of Arabic numerals and the decimal system as one of the hallmarks of the shift from Medieval to Renaissance periods. – jamesqf Oct 29 '16 at 5:00
  • @Frogologue: There can be no doubt that there was a general decline, in EVERYTHING, which lasted at least 8 centuries. Then there was a slow recovery. Fibonacci belongs to the beginning of this recovery period. – Alex Oct 29 '16 at 17:10
  • @jamesqf. Yes, Fibonacci's Liber Abaci (1202) could be said to have invigorated mathematical learning and its practical applications, leading up through the various abacus schools of Italy to Luca Pacioli (1494) and his double-entry book-keeping. But what I'm after is why the statement "le peu d’eſtime qu’on faiſoit alors de cette ſcience [mathematics]" (the little esteem then given to this science) could be stated around 1530 in France... – Frogologue Oct 29 '16 at 23:42
  • @Alex There is "serious doubt that there was a general decline, in EVERYTHING", from the Carolingian Renaissance, through international trade to map-making and much more beside. The Middle-Ages = dark ages is a bit of a renaissance-cum-enlightenment caricature. But it's true that Fibonacci played an important role in the late medieval development of maths. – Frogologue Oct 29 '16 at 23:55
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"Late medieval" (as the OP defines it up to "…; Briasson; 1737") French education was not "recalcitrant" to math. France produced a noted mathematician, Rene Descartes in the seventeenth century, and later, Joseph Louis Lagrange in the eighteenth.

What may be true is that French mathematics education was "relativized" by other, more pressing concerns such as theology. For instance, of France's "Three Estates," the first estate is the clergy. The nobility is "only" second, and the people, third.

  • Descartes was born in 1596, and the medieval period is commonly considered to have ended in 1453. – Frogologue Oct 29 '16 at 23:49
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    @Frogologue: The OP said "late medieval" and included a citation, "…; Briasson; 1737." Even his earlier reference to Francois I is past 1453, so I used his definition, not the "standard" one. (I added a parenthetical to make this clear). – Tom Au Oct 30 '16 at 0:23
  • My bad. Actually the citation comes from a history book written in 1737 about this period and I have once again gotten my date dyslexified: 1543 instead of 1453... – Frogologue Oct 30 '16 at 2:44
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Not 100% certain, but I suspect a solution along these lines:
1. There seems to have been a "war" in France between the algorists and abacists, with counting-boards or -tables still being used perhaps all the way up to the French Revolution
2. France of François 1er (and yes, dammit, I'm a hundred years out of date, my apologies...) was also highly "competitive" with Italy, jealous of its Imperial Roman ancestry
3. Italy was most definitely leading the way in that most practical of mathematics, accounting.
So French math teachers may well have felt their methods were lagging behind and hence of little or lesser worth.
Comments welcome.

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