**Claude Mylon**'s father, Benoist Mylon, was a counsellor to Louis XIII and Controller-General of Finance. Claude was his parent's third son and he was brought up in a well-off family. He made the law his profession and Costabel writes [1] that he:-

... was admitted to the bar as an advocate before Parlement in1641, even though he lacked two years of being twenty-five, the legal age of majority.

Mylon is important in the history of mathematics, not for his own achievements, but for his role in the *Académie Parisienne*, the group of scholars which was a continuation of the group formed in Paris by Mersenne, which was to form the foundation on which the Paris Academy of Sciences was formed. Mylon joined Mersenne's mathematical circle in around 1645 when he began to take careful notes of mathematical discussions in the group. At this time Mersenne was still in control of the group but on Mersenne's death in 1648 Le Pailleur took over the role of director of the Académie Parisienne. Mylon took on the role of secretary of the academy.

After the death of Le Pailleur in 1654, Mylon had access to all the correspondence between members of the Académie Parisienne and the numerous scientist with whom they had corresponded. At this stage Mylon carried on the important task of making the discoveries of mathematicians available to other mathematicians. He sent information on Fermat's and Frenicle de Bessy's number theory problems to Holland. Fermat had asked for a cube *n* such that the sum of the divisors of *n* is a square, and a square *n* such that the sum of the divisors of *n* is a cube. Frenicle de Bessy had asked for an integer *n* such that the sum of the divisors of *n* is 5*n* and the sum of the divisors of 5*n* is 25*n*. Similarly he asked for an integer *n* such that the sum of the divisors of *n* is 7*n* and the sum of the divisors of 7*n* is 49*n*.

Mylon also corresponded with van Schooten about the problems on games of chance, in particular the dice and points problems, that Fermat and Pascal were considering. The dice problem asks how many times one must throw a pair of dice before one expects a double six, while the problem of points asks how to divide the stakes if a game of dice is incomplete. Mylon maintained contact with Pascal after he gave up his mathematical studies and corresponded with Roberval.

Mylon's attempts to contribute to mathematics were much less successful than he was as a communicator of the results of others. He attempted to find the area enclosed by the curve known as the Pearls of Sluze. He also attempted to prove the result found by Wren concerning the length of the arc of the cycloid. As Costabel writes [1]:-

These efforts stand as a monument to his inadequacies as a mathematician ...

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