### Marin Mersenne

Marin Mersenne was a French theologian who was also an accomplished amateur mathematician, scientist, and philosopher. He is best known for two things. First, his name has been attached to a class of prime numbers called Mersenne primes. Second, he was indirectly responsible for many scientific achievements due to his extensive correspondence and collaboration with prominent scientists, mathematicians, and philosophers.

In 1588, Mersenne was born into a family of laborers and attended grammar school at the College of Mans. He studied at the Jesuit College at La Fleche from 1604 to 1609. At La Fleche he befriended fellow student Rene Descartes. The two would remain close friends and colleagues for the rest of their lives.

Beginning in 1609, Mersenne studied theology at the Sorbonne. He did so for two years, and then he joined the Minims, a religious order whose members focused on prayer, study, and scholarship. In 1611 he began his novitiate for the Minims at Nigeon, near Paris. The novitiate is a training and testing period that one had to go through before becoming a full member of the order. In 1612, in Meaux, he completed his novitiate. He travelled to Paris and in October 1612 at the Place Royale he was made a priest.

The order sent him to be a professor of philosophy at the Minim convent in Nevers from 1614 until 1620, at which point he returned to Paris, where he would live for the rest of his life, other than a few trips. The church supported him for the most part, although in later years, Jacques Hallé helped Mersenne out with money and by granting access to his library.

Mersenne's early publications were theological in nature, consisting of studies against Atheism and Scepticism. Almost all of his later work was scientific in nature, however, and it is for this work that he is remembered.

In 1644, Mersenne published Cogitata Physico-Mathematica. In the preface of that document, Mersenne made a claim about a class of prime number that had been identified many years before. These primes were of the form

2^{n}-1 (where n is a positive integer)

For a time it had been thought that if n was prime, then the resulting number would be prime. A counterexample of that (n = 11) had been published in 1536. Mersenne's claim was that for any positive n less than 258, if n = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 or 257, then the resulting number would be prime. Otherwise, he claimed, the number would be composite (that is, not prime). Mersenne was not able to verify all of these via calculation, because his computer was in the shop, but he was up front about the fact that he obviously hadn't checked them. At the time, nobody else could easily check them either. He was later shown to be wrong in more than one way. Not only did some of his values of n actually produce non-prime numbers (n = 67, for example), but also he had missed some values of n that produced prime numbers (n = 61, for example). In any case, although his list turned out to be incorrect and incomplete, his name still somehow became attached to the numbers. This type of prime number became known as a Mersenne prime.

Mersenne made far more significant contributions by collaborating with others, or by guiding them. During one part of Descartes' life, he was becoming less focused on serious pursuits. Mersenne reigned him in and got him back to work on philosophy. Mersenne also defended both Descartes and Galileo from religious attacks, as well as translating some of Galileo's work into French. It was these translations that made Galileo's work known outside of Italy. In addition, Mersenne continued some of Galileo's research in acoustics, which in turn prompted Galileo to make further advances in the field. Mersenne did some experiments using a pendulum to keep time, and suggested this use to Christiaan Huygens, who went on to create the world's first pendulum clock. He also tried to reveal alchemy and astrology for the unscientific practices that they were.

He corresponded with many of the people who would later make up the French Academy, as well as a host of other people. Because there were no journals or regular meetings of Europe's scientists, mathematicians, or philosophers, Mersenne was playing a crucial role. He communicated with everyone, exchanged ideas, gave suggestions, and it is because of this that his indirect contributions are difficult to gauge. He discussed such diverse subjects as mathematics, philosophy, music theory, physics, acoustics, and whatever else his associates happened to be pursuing. Among those he associated and corresponded with are Fermat, Pascal, Gassendi, Roberval, Beaugrand, Descartes, Huygens, Pell, Galileo, Torricelli, Peiresc, Beeckman, van Helmont, Hobbes, and Battista. After his death in 1648, letters from over 78 different people were found in his chambers in Paris. With his passing he gave one final gift, having previously asked that an autopsy be performed on his body in the interest of science.

#### Publications

- Quaestiones celeberrimae in Genesim (1623)
- L'impiété des déistes et des plus subtils libertins découverte et réfutée par raisons de théologie et de philosophie (1624)
- La vérité des sciences contre les sceptiques et les pyrrhoniens (1625)
- Euclidis elementorum libri, Apollonii Pergae conica, Sereni de sectione coni, etc. (1626, translations of ancient mathematicians)
- Questions theólogiques, physiques, morales et mathématiques (1634)
- Questions inouïes, ou récréations des savants (1634)
- Les mécaniques de Galilée (1634, translation of Galileo from Italian)
- Harmonie universelle, contenant la théorie et la pratique de la musique (1636-7)
- Nouvelles découvertes de Galilée (1639, translation of Galileo from Italian)
- Nouvelles pensées de Galilée sur les mécaniques (1639, translation of Galileo from Italian)
- Cogitata physico-mathematica (1644)
- Universae geometriae mixtaeque mathematicae synopsis (1644, enhanced re-publishing of "Euclidis elementorum libri, Apollonii Pergae conica, Sereni de sectione coni, etc." from 1626)

Sources:

- http://galileo.imss.firenze.it/vuoto/imerse.html
- http://www.utm.edu/research/primes/mersenne/index.html
- http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Mersenne.html
- http://www.newadvent.org/cathen/10209b.htm
- http://es.rice.edu/ES/humsoc/Galileo/Catalog/Files/mersenne.html