**C V Mourey**was a French mathematician who is known solely from his work

*La Vraie Théorie des quantités négatives et des quantités prétendues imaginaires*Ⓣ which he published in Paris in 1828. On the title page of this first edition the author's address is given as 'Paris ... Rue des Quatre-Vents, no. 8'. This address constitutes the only biographical information on Mourey currently available. In 1861 a reprint of the book was produced by the same publishers, Bachelier [2]. In this later edition no address is given for the author, which suggests that by 1861 Mourey was deceased. It seems that Bachelier published the reprint at their own expense in response to demand for the first edition.

Seeking algebraic reform, Mourey had set out to discover a brand new set of definitions and fundamental principles as a basis for algebra. To this end, he developed a theory of directed lines, which constituted a single science of algebra and geometry; and, as an application of the theory, he gave a proof of the Fundamental Theorem of Algebra. His work was one of the first to introduce a geometric approach to imaginary numbers and had an influence on later mathematicians like Hamilton, Tait and De Morgan.

As early as 1846, an appeal for biographical information on Mourey was published in *Nouvelles annales de mathématiques*. The editors write that copies of Mourey (1828) have become extremely rare and that to their knowledge, amongst mathematicians in Paris, only Lefébure de Fourcy had a copy. They asked that those with biographical information on Mourey make contact. Since there was no published response to the appeal -- notably, Mourey himself failed to make contact with the editors -- it seems likely that Mourey had left Paris, or died, a short time after the publication of his book.

It seems that Mourey was truly an unknown in Paris's academic circles. Certainly, there is no indication, in either edition of his work, of his affiliation with any academic or scientific institution. He is not remembered as a student at any of the well known educational establishments in the city and has never been referred to in connection with the great mathematicians who were known to have been in Paris during that period; thinking of the young talents of Abel and Galois, but also of Cauchy, Poisson, Legendre, Hachette, Dirichlet, Fourier and Lacroix. While the work is scholarly, it was not written for the purposes of instruction, which supports the theory that Mourey held no fixed teaching position in mathematics.

The text itself offers no information on its author; notably, it is without reference to Mourey's mathematical influences and in this respect it is similar to the work of the great Greek authors. The most probable reason for the absence of references is that Mourey simply had no instinct to cite other authors. Consequently, we have no information on which mathematics books Mourey had read. Likewise, we have no information on the nature of Mourey's mathematical training. Presumably, Mourey did receive some training in mathematics: the strong focus on trigonometry and mechanics in the book suggests that he did receive some training in the practical application of mathematics.

From the preface of his book, we learn that Mourey's 1828 publication was in fact an abridgement of a larger manuscript which Mourey had not been able to publish in full because of certain undisclosed circumstances. Mourey writes:

From this we may infer that Mourey had published at his own expense and that he had restricted funds. The theory of a self-funded publication is also supported by the lack of evidence to suggest that Mourey's work was subject to peer review prior to publication. But if finances were an issue for Mourey, why did he not submit his work to be published in a journal, such as: Gergonne's Annales,Until now I have only dealt, as you understand, with the fundamental principles, and still I have written quite a considerable manuscript. However, as circumstances do not allow me now to have such a voluminous work printed, I have decided to publish this booklet first, which is but a small abstract.

*Memoire de l'Institut de France*or Ferrusac's

*Bulletin*?

There are a number of possible reasons. From indications given by Mourey in his preface, it appears that the work published in 1828 -- his only publication -- was the culmination of many years of private study: his mathematical researches had remained a private project until such a time when he considered his ideas to be sufficiently developed to share with others or until he had acquired the means to publish. Consequently, the impact of his work would have been a key consideration for Mourey. Had he published his results in a journal, he would have had to divide his work into a number of small contributions, on account of the amount of material, which might have had a negative bearing on impact.

Mourey may have also faced difficulties in getting his work published, as an unknown in academic circles with no-one to recommend him for publication. Mourey probably considered self-funded publication to be the quickest and easiest route to getting his work noticed by the mathematical community. Mourey dedicated his work to the 'Amis de l'Evidence' (or 'the friends of evidence'), which was probably not an actual group but a motto of Mourey's: he dedicated his work to all those who, like him, search for truth.

In spite of the paucity of biographical evidence for Mourey, there is one possible candidate whose life seems to fit his profile. This is a **Claude-Victor Mourey** (1791-1830), who was a *mécanicien à Paris*, and who was born in the Valay department in the Haute-Sâone region in the east of France; to parents Claude Joseph Mourey and Anne Françoise Fontaine. In 1822, having moved to Paris, he took out five-year patents for two machines he had invented: a timber-profiling machine and a tree saw. See [3] and [4]. He may have been employed as a draughtsman by *MM. Hacks et compagnie*, whose workshops were on the Grand Rue du Faubourg, Saint-Antoine, no. 47. In 1828, aged thirty-seven, Mourey would have made sufficient money from his inventions to enable him to publish a book.

In Paris, on 21 October 1829, Claude-Victor Mourey married Marie Claire Klein, daughter of Henry Klein and Marie Françoise Grégorie. He died in Paris on 30 July 1830, aged thirty-nine; just two years after *La Vraie Théorie des quantités négatives et des quantités prétendues imaginaires* Ⓣ was published and after only nine months of marriage.

Making a positive identification of this Claude-Victor Mourey with our mathematician is difficult because almost all the civil records for Paris prior to 1860 were destroyed by a fire at the Hôtel de Ville (where the paper records were stored) in May 1871 during the Paris Commune uprising: between five and eight million records were destroyed.

**Article by:** Elizabeth Lewis, St Andrews University

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