Abraham Robinson publishes "Non-standard Analysis." Non-standard analysis is based not on the theory of limits developed by Cauchy, but instead on the theory of infinitesimals first proposed by Leibniz.

The theory of infinitesimals was abandoned because, even though an intuitive understanding of their behavior could be grasped, a rigorous foundation did not exist. Infinitesimals were derided as merely vanished quantities.

Modern theories of infinitesimals are based on set theory and add a set of hyperreals to the real number system.

Author: Paul Koenig

References:
O’Connor, John and Edmund Robertson. 1997. “Robinson”. 23 October 1998 <http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Robinson.html>.

Robinson, Abraham. 1996. Non-standard Analysis. Princeton: Princeton UP.