Mathematical analysis—and, thus, the ideas of calculus—took centuries to develop. Probably the first to present some solid concepts in the field were the Greeks whose most important contribution was the method of exhaustion (expanding the measurements of an area to take in more and more of the required area).

For example, Zeno of Elea (c. 490-c. 425 B.C.E.) based many problems on the infinite; Leucippus of Miletus (fl. c. 435-c. 420 B.C.E.), Democritus of Abdera (460-370 B.C.E.; a student of Leucippus who also proposed an early theory about how the universe was formed), and Antiphon (c. 479-411 B.C.E.; who some historians believe tried to square the circle) would all contribute to the method of exhaustion. Eudoxus of Cnidus (c. 400-347 B.C.E.) would be the first to use the method on a scientific basis. Archimedes (c. 287-212 B.C.E.; Hellenic)—considered one of the greatest Greek mathematicians—took mathematical analysis one step further: He more fully developed the theory presented by Eudoxus that would eventually lead to integral calculus.