Florimond de Beaune was a French jurist and mathematician. He was an early follower of René Descartes.
Background
De Beaune was born on October 7, 1601, in Blois, France. His father, also called Florimond de Beaune, was the illegitimate son of Jean II de Beaune whose brother was the archbishop Renaud de Beaune. However Florimond senior was made legitimate and inherited the title which eventually went to his son.
Education
De Beaune was educated in Paris where he went on to study law although his status meant that he had no need to take a degree.
Career
De Beaune's renown was due entirely to Descartes. The Notes brèves that de Beaune wrote on the Géométrie were translated and added during his lifetime to the first Latin edition, published by Schooten in 1649. The second Latin edition (1659-1661) also contained two short papers on algebra, edited by Erasmus Bartholin, that are de Beaune’s only posthumous publication. The letters published by Clerselier between 1657 and 1667 revealed to a wider public the esteem in which Descartes held his disciple from Blois.
Undoubtedly this was the reason why, in 1682, a chronicler concerned with celebrities of his province wrote a paper on de Beaune, drawing his information from sources close to the family while this was still possible. At the end of the nineteenth century a scholar from Blois confirmed the information by locating various documents in archives, and the great critical edition of Descartes’s Oeuvres once again brought attention to de Beaune. Paul Tannery had the good fortune to discover a great many handwritten letters in Vienne, which enabled him to gain a great deal of scientific clarity.
On the basis of his interpretation of the signature of these letters, Tannery committed an error in insisting on the spelling “Debeaune,” by which he is most frequently cited. Like Descartes, Debeaune at first did military service, but following a mysterious accident he had to lead a less strenuous life. Taking advantage of his law studies, he bought the office of counselor to the court of justice in Blois. The many years that he divided between this famous city on the banks of the Loire and his nearby country estate, excelling in both jurisprudence and mathematical research, bring Fermat to mind. However, Fermat does not appear on the list of correspondents that the chronicler of 1682 saw among the family papers, a list of which only a small part has been preserved.
Debeaune left his provincial retreat only for business trips to Paris. However, he had many visitors. The first part of Monconis’ diary mentions observatory instruments made by him. An inventory made after Debeaune’s death confirmed statements in parts of letters that have been preserved: he had built for his own use a shop for grinding lenses. He also had a magnificent library, worthy of a humanist of the preceding century.
Afflicted with various and painful infirmities, particularly gout, Debeaune resigned as counselor around 1648 and withdrew to a town house, the upper floor of which faced due south. There he had - at least for a time - an observatory at his disposal. However, his failing eyesight deteriorated rapidly, and he died shortly after having a foot amputated.
When he was very ill, Debeaune was visited by Erasmus Bartholin, whom he entrusted with arranging for the publication of several of his manuscripts. Despite the intervention of Schooten and Huygens in 1656, Bartholin fulfilled his obligations only partially. Of the manuscripts with which he was entrusted, only “La doctrine de l’angle solide construit sous trois angles plans” was discovered, in 1963. The “Méchaniques” mentioned by Mersenne, and the “Dioptrique” that Schooten knew in 1646 are still missing and may be lost.
The example of Debeaune reminds us that mathematics is sustained more by the perception of profound logical structures than by the invention and use of languages that find acceptance in the structures only with time. As Debeaune wrote to Mersenne, "I do not think that one could acquire any solid knowledge of nature in physics without geometry, and the best of geometry consists of analysis, of such kind that without the latter it is quite imperfect."
As Paul Tannery has shown, Descartes’s method for tangents misled Debeaune, at least initially. This purely algebraic method, which consists of determining the subnormal by writing that the equation obtained as a result of an elimination is to have two equal roots, is not susceptible of supporting a process of inversion. But if Debeaune, victim of a misconception that nevertheless bears the stamp of his mathematical genius, could give his problem (the first integration problem of a first-order differential equation) only an incorrect solution, he was nevertheless the only one to comprehend the remarkable solution to which it had led Descartes, a solution that anticipated the use of series. This was a remarkable solution that Leibniz, fifty years later, failed to recognize when he replaced it with the aid of new algorithms and the logarithmic function.
Connections
De Beaune married Philiberte Anne Pelluis on December 21, 1621, but the marriage lasted less than a year since she died in August 1622. He married Marguerite du Lot on December 15, 1623; this second marriage brought considerable wealth to de Beaune. The marriage produced three sons and one daughter; one of the sons became a priest.