Adrien Quentin Buée


Born: 6 October 1745 in Paris, France
Died: 11 October 1825 in Paris, France

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Adrien Quentin Buée was the son of Adrien Joseph Buée (1708-1778) and Marie-Angélique Gantellet (born 1714). He had brothers Pierre Louis Buée (1746-1827) and Auguste Buée. Let us note that there appears to be some confusion over the year of Buée's birth, with some sources giving 1748, for example [4], [5] and [6]. We have chosen to give 1745, following the most recent research on Buée contained in [3]. The confusion does not end there, however, since [3] quotes a source, the Avant Coureur of 11 April 1768, in which Buée is described as "aged 19 to 20" which fits the 1748 date. May we suggest that the probably incorrect 1748 date may well originate from this reference to his age in Avant Coureur.

There is no information about Buée's education. We know that he became a fine musician and a well-educated priest who had a surprisingly deep understanding of mathematics. This learning must have been gained at least in part during his education as a young man but no details have so far come to light. The first we know about Buée is that he arrived in Coutances Cathedral as master of music in February 1766. The Cathédrale Notre-Dame de Coutances was constructed in the 12th century in Coutances, a city in the department of Manche in Normandy, north west France. Buée's appointment was to replace the previous master of music at Coutances Cathedral, Pierre Simon Hollet de la Place, who had died on 5 January 1766 aged only twenty-four or twenty-five.

The Concert Spirituel was one of the first public concert series beginning in Paris in 1725 and continuing until 1790. Buée's brother Pierre Louis Buée was master of music of the cathedral of Dijon and had his motet Benedic, anima mea performed at the Concert Spirituel on 26 May 1765. In early April, Adrien Quentin Buée emulated his brother by having one of his motets performed at the Concert Spirituel in Paris. The Avant Coureur of 11 April 1768 reported:-
We announced that the two Motets on the Pseaume Super Flumina, which won the two prizes, were from the Abbé Giroust, Music Master of the Orléans Cathedral. There was a third Motet which deserved to compete, and which was also heard at the Concert with pleasure, it is by M Buée, Master of Music of the Cathedral of Coutances, aged 19 to 20. The Connoisseurs and the Amateurs have found that this composer possessed his art perfectly, that he knew how to design his composition with taste and that he lacked only the expression and the correct application of the music to the sense of the words, and it is the fruit of study and of reflection that he will not fail to acquire and that we can hope for his happy talents and his noble emulation.
On Thursday 2 June 1768 Buée had another of his motets performed at the Concert Spirituel, namely Noli amulari. The fame he had achieved at the Concert Spirituel was a factor in Buée being recommended for the position of music master in the collegiate church of Saint-Martin in Tours in September 1768. A collegiate church is manned by canons, and one of the early Abbots of Saint-Martin of Tours had been Alcuin of York. Buée was given until Christmas to arrange his departure from Coutances. He arrived in Tours to take up the position on 3 December, in plenty of time for Christmas. There was some unhappiness that Buée had left Coutances and a leading musician wrote to the canons of the cathedral of Coutances expressing regret that they had not increased his wages to try to keep such a talented young musician.

In August of 1771 Buée obtained a six week leave to go to Paris. In Paris he was able to get some of his music published, in particular, "masses for the use of the collegiate church of Saint-Martin." It appears that he made the most of this time to study with leading masters and to make friends with influential musicians. He was allowed to extend his stay in Paris for a few extra days and one of the canons from Tours asked him to buy copies of certain printed masses. He continued to lead this life, going to Paris for quite long visits; for example in 1775 he went from January to "the first Sunday in Lent." Although there is no evidence that Buée studied mathematics during his visits to Paris, from the expertise he later showed, it seems highly likely that he did discuss mathematics, a subject which seems to have been as interesting to him as music. In the summer of 1780 he went to Paris and in December of that year his Chapter supported him in his request to the Archbishop that he take holy orders.

In July 1782 he again obtained permission to go Paris where he intended looking for a new position. In December of that year the canons of Tours record his departure with sadness, praising his high qualities, and note that he will take up the position of master of music at the parish church Saint-Paul in Paris. This does not seem to be a very prestigious position but it appears that Buée was wanting to be in Paris to be in a position to look for something more important. Indeed in April 1786 he was appointed as successor to his brother as secretary and librarian of Notre-Dame cathedral chapter. It appears to be his great intellectual abilities rather than his musical skills which earn him this position but there were difficulties with the music master who was dismissed in the following year and Buée begins "teaching music and composition to altar boys."

In 1789 the storming of the Bastille saw the start of the French Revolution which brought massive changes to life in France. In February 1790 all religious orders were abolished, those clergy who were not dismissed became employees of the state. Buée remained as a priest in the diocese of Paris, and was an incumbent of the chapel Sainte-Anne and that of Saint-Eutrope but without income. Buée was strongly opposed to the Revolution and began publishing strongly worded anti-Revolution pamphlets. In 1790 he published De par la Mère Duchesne, Anathèmes très-énergiques contre les jureurs, ou, Dialogue sur le serment et la nouvelle constitution du clergé : entre M Bridoye, franc parisien, soldat patriote, M Recto, marchand de livres, ou tout simplement bouquiniste, M Tournemine, chantre de paroisse, et la mère Duchesne, négociante à Paris, autrement dit, marchande de vieux chapeaux  and in 1792 he published Nouveau dictionnaire, pour servir à l'intelligence des termes mis en vogue par la Révolution, dédié aux amis de la religion, du Roi et du sens commun .

In October 1790 priests were not allowed to teach and in November an oath requiring loyalty from the Clergy was drafted by the Revolutionary Assembly and was enforced by the end of the year. In March 1792 the Pope issued a papal bull excommunicating any priests who took the oath. Buée became a "prêtre réfractaire", that is a priest who had refused to take the oath imposed upon them, also called non-jurors. Being hunted down, prêtres réfractaires either went into hiding or fled the country. Buée choose to flee to England and settled in Bath.

Bath had a strong music tradition and one might have expected to find Buée's name among the Bath musicians. We have not be able to find any such, however, and all references to Buée that we have found for the time he spent in Bath refer to his work in mathematics and its applications. For example, in 1797 we find several of the problems in Dr Hutton's Mathematical Repository being answered by Buée.

In The Monthly Magazine 7 (1799) we read on page 319:-
Mr A Q Buée, a French clergyman of Bath, the intimate friend of the celebrated Mrs Hauy, is about to publish a work entitled, "Recherches Mathematiques sur la texture intime des Corps."
We are somewhat puzzled about the reference to "the celebrated Mrs Hauy". We do not know who this person is but suspect it is a misprint for "the celebrated M Haüy." Buée was certainly a friend of René-Just Haüy (1743-1822) who, like Buée, was a Roman Catholic priest who made important contributions to science, particularly to crystallography. We quote below comments made by Buée about "Abbé Haüy's Theories of Crystallography."

More details of Buée's "Recharches Mathematiques" are given by William Nicholson who writes in [1]:-
Proposals have been circulated by Mr A Q Buée, a French clergyman at Bath, for publishing, by subscription, a work entitled 'Recherches Mathematique sur la Texture intime des corps'; or, 'Mathematical enquiries concerning the intimate texture of bodies'; of which he is the author. It will be printed on fine paper, and illustrated with five copperplates. The manuscript is in the hands of the printer, and the work will be put to press as soon as one hundred and fifty subscribers shall be obtained at half a guinea each: the price will be greater to non-subscribers.
Nicholson continues giving a review of the outline which Buée gives of his proposed work. For details see THIS LINK.

In the Philosophical Magazine 9 (1801) we read on page 55:-
M Buée, an ingenious French clergymen, in a letter from Bath to the editor, dated 8th instant, wherein he mentions the 'Philosophical Magazine' with deserved commendation, shows that ..."
In fact Buée shows how to correct an error in Lazare Carnot's The Principles of the Differential and Integral Calculi.

In 1796 William Frend published The Principles of Algebra. In this work he opposes the use not only of imaginary numbers, but also of negative numbers. On 21 June 1801 Buée wrote a letter to William Frend which De Morgan reports on in Trigonometry and Double Algebra (1849):-
Perhaps [Frend's] work suggested M Buée's memoir. I have a letter in my possession from M Buée to Mr Frend, dated June 21, 1801, by which it appears that the former was desired by a gentlemen in whose house he was living (as tutor, perhaps) to write a private reply to Mr Frend's objections. This letter evidently contains the germs of the views which he afterwards published. ... According to Dr Peacock, M Buée is the first formal maintainer of the geometrical significance of √-1.
Buée's memoir, referred to by De Morgan in this quote, was the Mémoire sur les quantités imaginaires was read in 1805 at the Royal Society and was published in 1806. Gert Schubring writes [6]:-
Buée's paper is remarkable in its systematic evaluation of the earlier French discussion on the nature of negative and imaginary quantities. He achieves the establishment of a conceptual connection between the two basic concepts of length or absolute value and of direction which had been separated so systematically in France during the 18th century. Buée's achievements are likewise important for the conceptual development of the negative numbers and for the graphical representation of the complex numbers.
Buée writes in the paper:-
√-1 is therefore not the sign of an arithmetic operation, nor of an arithmetic-geometric operation, but of a purely geometric operation. It is a sign of perpendicularity.
In 1808 John Playfair criticised Buée's paper in an article he wrote for the Edinburgh Review. Playfair writes:-
... there have been more than one attempt to treat imaginary quantities as things really existing, or as certain geometrical magnitudes which it is possible to assign. The paper before us is one of these attempts; and the author, though an ingenious man, and, as we readily acknowledge, a skilful mathematician, has been betrayed into this inconsistency by a kind of metaphysical reasoning, which we confess ourselves not always able to understand.
In the 1850s, Hamilton and De Morgan discussed Buée's 1806 paper in their correspondence; see THIS LINK.

In 1804 Buée published Parallel of Romé de l'Isle's and the Abbé Haüy's Theories of Crystallography. The work is described as follows:-
[Buée's] short study on crystallography was translated by Robert Clifford  and privately printed. The work had been published in the Philosophical Magazine (nos. 74-75, 1804) under the title "A letter from Abbé Buée to Mr ****, on Mr Romé de l'Isle and the Abbé Haüy's theories of crystallography." Originally written in French, Buée had authored the letter in order to contrast the differences between the crystallographic systems of Romé de l'Isle and Haüy, which at the time were both considered similar in nature. It is an important critique of Romé de l'Isle's system, which Buée characterizes as primarily descriptive, as opposed to Haüy's mathematically based system.
In describing Abbé Haüy's Theories of Crystallography, Buée writes:-
I have now, sir, but one task left; to peak of the application our author has made of algebra and geometry to crystallography. Many persons complain of the difficulty necessarily resulting from it in the study of mineralogy; and dare not engage in it, uncertain whether they will find a compensation for their trouble. Our author has therefore adopted a double plan, and begins by exposing his theory by a series of reasonings and arguments which will suffice to make the reader understand it, or any discoveries made in consequence of it. He then exposes the theory in the most correct of all languages - mathematical analysis; by far the most interesting, and the only means of making discoveries oneself; and who can be callous to the pleasure of discovering an unknown truth?
In 1814 Buée left Bath and returned to France where he became an honorary canon at Notre-Dame Cathedral in Paris. He continued to publish works on science, mathematics and politics. For example he published Réflexions sur les deux éditions des oeuvres de Voltaire (1817), Notice sur M Laplace (1817), and Sur la révolution française et sur le gouvernement représentatif (1821). Buée continued his interest in the foundations of mathematics and wrote to a "mathematical gentlemen in London, who declines communicating his name to the public." His letter was published as "Solution to a Problem of Col Silas Titus" in the Annals of Philosophy in January 1815. Buée's letter begins:-
Having for many years considered the different algebraical methods for the solution of arithmetical problems by approximation to be deficient in their fundamental principles, I have been led to mistrust the whole science of algebra as generally taught, and am convinced that if we place implicit faith in it we shall be involved in the most revolting absurdities. Pell's problem, and all those which can be resolved by approximation, are examples of this kind.
The death of the Abbé Adrien-Quentin Buée, honorary canon of Notre-Dame Cathedral, is mentioned in number 46 of L'Ami de la Religion et du Roi (1826) where the two lines of text are especially careful to distinguish him from his brother Pierre-Louis Buée. We note that the two are indeed confused in many biographies.

Finally we note that Adrien-Quentin Buée is still remembered today by musicians who still perform his musical compositions and by mathematicians who understand that he was one of the originators of the geometrical interpretation of complex numbers.

Article by: J J O'Connor and E F Robertson


List of References (6 books/articles)

Mathematicians born in the same country

Additional Material in MacTutor

  1. William Nicholson on Buée's Recherches Mathematiques
  2. Hamilton and De Morgan discuss Buée's 1806 paper


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