Coordinate geometry was introduced by Fermat and Descartes who did not address the foundational problems that prevented the Greeks from developing this approach. This development was important for science as it allowed geometry to be quantitative and use algebraic methods, making geometry more useful for science and engineering applications through a more systematic approach than the Greek axiomatic style. While lying in bed, the mathematician Rene Descartes saw a fly on his ceiling and wondered if he could precisely describe its location, realizing vague terms like "left" were not enough and hoping to develop a precise method using coordinates.