MYLON, CLAUDE

(b. Paris, France, ca. 1618; d. Paris, ca. 1660)

mathematics.

Mylon’s place in the history of science derives from the service he provided in facilitating communication among more learned men in the decade from 1650 to 1660. He was the third son of Benoist Mylon, counselor to Louis XIII and Controller-General of Finance; he himself was admitted to the bar as an advocate before Parlement in 1641, even though he lacked two years of being twenty-five, the legal age of majority.

As early as 1645 Mylon had become concerned with mathematics, making written notes of new Cartesian mathematical problems. He was also in contact with Mersenne, Debeaune, and Roberval, and when Schooten passed through Paris he was able to transmit a considerable amount of new information to him. Mylon also served as secretary to the “Académie Parisienne,”a continuation of the Mersenne group, under the direction of F. le Pailleur, which in 1654 received Pascal’s famous “Adresse.” Mylon achieved a certain importance when the death of Pailleur, in November 1654, left the papers of the society at his disposal; it was thus he who told Schooten (who told Huygens) of Fermat’s and Pascal’s problems and solutions concerning games of chance. He also forwarded to Holland Fermat’s and Frenicle’s problems in number theory. In 1655 Huygens, who was making his first trip to France, visited Mylon; the following year he suggested the “commerce scientifique”that provides the chief documentation of Mylon’s career.

Mylon maintained a number of rather delicate relationships with other mathematicians. He had access to Pascal in his retirement (although to a lesser degree than did Carcavi), and while his affection for Conrart threatened his friendship with Roberval, the latter continued to make use of him as an intermediary. He was less happy in his two attempts at personal achievement: in 1658 he hazarded his own solution to the quadrature of the cubic curves known as the “perles de M. Sluse”and in January 1659, in the wake of the debate provoked by Pascal, he proposed to prove Wren’s solution of the length of the cycloid. These efforts stand as a monument to his inadequacies as a mathematician, and it is with them that all mention of Mylon by Huygens stops. No publication by him is known.

BIBLIOGRAPHY

On Mylon and his work, see J.-B. du Hamel, Astronomia physica, … Accessere P. Petiti observationes…. (Paris, 1660), 12, which includes an account of Pierre Petit’s pamphlet on the observation made by Mylon and Roberval of the solar eclipse of 8 Apr. 1652.

See also C. Adam and P. Tannery, eds., Oeuvres de Descartes, IV (Paris, 1901), 232, 397, which deals with the problem of the “trois batons”and Roberval’s “Aristarchus."

See L. Brunschvicg, P. Boutroux, and F. Gazier, eds., Oeuvres de Blaise Pascal, IX (Paris, 1914), 151–156; the letter referred to here (Mylon to Pascal, 27 Dec. 1658) is at the Bibliothèque Nationale, Paris, Res. V 859, with a demonstration by Mylon of “the equality of the cycloid and its partner."

There are numerous references to Mylon in Huygens’correspondence, as well as letters from him, in Oeuvres complétes de Christiaan Huygens, 22 vols. (The Hague, 1888–1950); see esp. I, 517, for Roberval’s demonstration on the surface of spherical triangles; II, 8–25, for Frenicle’s results on compatible numbers; “Propositio Domini Wren Angli. Demonstrata a Claudio Mylon die 26 Januarii 1659,”II, 335; and “La quadrature des perles de M. Sluse par Claude Mylon. En juin 1658,”II, 337. Mylon’s role in the problem of games of chance is discussed in “Avertisse- ment,”XIV, 4–9. See also The Correspondence of H. Oldenburg, I (London, 1965), 225.

Pierre Costabel