He is perhaps best known today among mathematicians for Mersenne prime numbers, those written in the form Mn = 2n − 1 for some integer n. He also developed Mersenne's laws, which describe the harmonics of a vibrating string (such as may be found on guitars and pianos), and his seminal work on music theory, Harmonie universelle, for which he is referred to as the "father of acoustics".

He corresponded with Giovanni Doni, Jacques Alexandre Le Tenneur, Constantijn Huygens, Galileo Galilei, and other scholars in Italy, England and the Dutch Republic.

"[7] In 1635 Mersenne met with Tommaso Campanella but concluded that he could "teach nothing in the sciences ... but still he has a good memory and a fertile imagination."

However Robert Lenoble has shown[9] that the principle of unity in the work is a polemic against magical and divinatory arts, cabalism, and animistic and pantheistic philosophies.

Mersenne was concerned with the teachings of some Italian naturalists that all things happened naturally and determined astrologically; for example, the nomological determinism of Lucilio Vanini ("God acts on sublunary beings (humans) using the sky as a tool"), and Gerolamo Cardano's idea that martyrs and heretic were compelled to self-harm by the stars;[10] Historian of science William Ashworth[11] explains "Miracles, for example, were endangered by the naturalists, because in a world filled with sympathies and occult forces—with what Lenoble calls a "spontanéité indéfinie"—anything could happen naturally"[12]: 138 Mersenne mentions Martin Del Rio's Investigations into Magic and criticises Marsilio Ficino for claiming power for images and characters.

He also criticises Pico della Mirandola, Cornelius Agrippa, Francesco Giorgio and Robert Fludd, his main target.

His greatest service to philosophy was his enthusiastic defence of Descartes, whose agent he was in Paris and whom he visited in exile in the Netherlands.

He submitted to various eminent Parisian thinkers a manuscript copy of the Meditations on First Philosophy, and defended its orthodoxy against numerous clerical critics.

The perceived harmony (consonance) of two such notes would be explained if the ratio of the air oscillation frequencies is also 1 : 2, which in turn is consistent with the source-air-motion-frequency-equivalence hypothesis.

He also performed extensive experiments to determine the acceleration of falling objects by comparing them with the swing of pendulums, reported in his Cogitata Physico-Mathematica in 1644.

The books were allegories, but were obviously written by a small group who were reasonably knowledgeable about the sciences of the day,[citation needed] and their main theme was to promote educational reform (they were anti-Aristotelian).

These pamphlets also promoted an occult view of science[citation needed] containing elements of Paracelsian philosophy, neo-Platonism, Christian Cabala and Hermeticism.

[citation needed] Mersenne led the fight against acceptance of these ideas, particularly those of Rosicrucian promoter Robert Fludd, who had a lifelong battle of words with Johannes Kepler.

Mersenne had been a regular correspondent with Galileo and had extended the work on vibrating strings originally developed by his father, Vincenzo Galilei.