"Rigor and Proof in Mathematics: A Historical Perspective" by Israel Kleiner. Mathematics Magazine December 1991, 64:291-314.
This paper gives a very nice overview of how the understanding of rigor in mathematics has evolved from the early ages to the 20th century.
http://www.jstor.org/sici?sici=0025-570X%28199112%2964%3A5%3C291%3ARAPIMA%3E2.0.CO%3B2-Zhttps://www.jstor.org/stable/2690647