# Who was the first to prove the fundamental theorem?

## Main Question or Discussion Point

Just curious who wrote the first proof of the fundamental theorem of calculus. Thanks.

## Answers and Replies

mathman
Science Advisor
Try google. The theorem was first proven rigorously by Cauchy.

HallsofIvy
Science Advisor
Homework Helper
There were many people who found different ways of finding tangent lines, and, in particular, the slope of the tangent line (i.e. derivative) before Newton or Leibniz. And finding areas by dividing into smaller and smaller sections goes back to Archimedes. It is the discovery of the "fundamental theorem", that states that these two problems are, in an important sense, "inverse" that make Newton and Leibniz the "creators" of the Calculus. Cauchy may well have been the one to prove the theorem rigorously, using limits (Newton and Leibniz used nebulous appeals to "infinitesmals" rather than limits), but the theorem was "discovered" by Newton and Leibniz.

phyzguy
Science Advisor