ABSTRACT
The challenge that faced Leibniz and his followers was to make their intuitions about infinitesimals sufficiently clear and rigorous to avoid errors and misunderstandings. The founders of calculus were not able to meet this challenge adequately and, at least in part for this reason, the method of infinitesimals was gradually abandoned by mathematicians. A fully rigorous treatment of infinitesimals suitable for the needs of calculus was given only in the mid-twentieth century by Abraham Robinson.
