Fermat’s Last Theorem (ca. 1630): Pierre de Fermat was a French mathematician who played an important role in the mathematical revolution of the 17th century. Fermat’s contributions to mathematics were many. His discoveries frequently closely paralleled the work of his countryman René Descartes. For example, Fermat and Descartes independently developed a coordinate system for the study of geometric figures. The discovery of coordinate geometry gave 17th-century mathematicians the ability to manipulate geometric shapes using algebraic equations. This was the beginning of the study of analytical geometry, or the defining of geometric shapes using algebraic principles, a branch of mathematics in which Fermat played a key role. He established algebraic formulas for many geometric shapes, including hyperbolas and parabolas. He also made significant contributions to the study of curves that included finding the minimum and maximum values of the curves and solving for the area under a curve (see ANALYTICAL GEOMETRY). In cooperation with the French mathematician Blaise Pascal, Fermat established early theories on the study of probability, although this work was directed initially at predicting games of chance and not scientific research (see PROBABILITY). Despite his many achievements in mathematics, Fermat is most often recognized for his work on number theories and for proposing a mathematical theorem that took over 300 years to prove.
In mathematics, the study of number theory involves defining the properties of whole integers. The study of the theory of numbers was not unique to the 17th century, as its history most likely dates back to the time of Pythagoras. The Greek mathematician Euclid presented one of the first comprehensive descriptions of ancient number theo-