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Mathematical Treasure: Fermat’s Varia opera mathematica

Frank J. Swetz (The Pennsylvania State University)

The French mathematician Pierre de Fermat (1601–1665) is best known for his “Last Theorem,” proved in 1995 by Andrew Wiles, but he also made contributions to other aspects of number theory, the foundations of the calculus, and analytic geometry. For various reasons, including long periods of civil unrest in his relatively isolated home of Toulouse, many of Fermat’s results were not published until after his death. In particular, this 1679 volume was the first effort to bring together his significant works as well as his mathematical correspondence.

Title page of Fermat's 1679 Varia Opera Mathematica.

A portrait of Fermat that appeared in Varia opera mathematica.

Portrait from Fermat's 1679 Varia Opera Mathematica.

Fermat’s work on analytic geometry that predated Descartes’ La géométrie first appeared in print in this treatise.

Treatise on analytic geometry from Fermat's 1679 Varia Opera Mathematica.

Page 2 from Fermat's Varia Opera Mathematica.

Much of the work recorded in Varia opera mathematics fits within the prehistory of the calculus.

Pages 90-91 from Fermat's 1679 Varia Opera Mathematica.

Some of Fermat’s correspondence is reprinted as well.

Beginning of letter from Descartes to Fermat from the Varia Opera Mathematica.

Images from the works of Fermat as they were edited by Paul Tannery in the 19th century can be viewed in this Mathematical Treasure.

A full digitization of the copy owned by the Dibner Library can be found in the Internet Archive as well as at the Smithsonian Institution Libraries website.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Fermat’s Varia opera mathematica," Convergence (March 2022)