Pierre de Fermat and Ren´e Descartes were two brilliant 17th century mathematicians who have had lasting impacts on modern mathematics. Descartes laid the groundwork for the Cartesian coordinate system that is frequently employed in modern mathematics and Fermat’s last theorem vexed the mathematics community until Wiles’ proof was published in 1995. Amidst their many ground-breaking accomplishments these two men produced solutions for another mathematical problem - developing a general method to find the tangent line to a curve.
In spite of their apparent genius, neither man’s method had the lasting impact of their other works. Descartes’ and Fermat’s methods were quickly superseded by the development of calculus thirty years later. In many ways these methods contributed to the development of calculus, yet in others they drastically deviated from it. This deviation is the driving force behind this investigation: why were their methods so different? And what does this reveal about the development of mathematics?
Skinner, Lindsay, "The World Before Calculus: Historical Approaches to the Tangent Line Problem" (2015). WWU Honors Program Senior Projects. 13.