1. This crisis finally perfected the definition of calculus and the theoretical system related to real numbers, and at the same time basically solved the continuity problem of infinite calculation in the first mathematical crisis, and pushed the application of calculus to all disciplines related to mathematics.
2. Crisis background:
Zeno Paradox: Zhi Nuo noticed the contradiction caused by the understanding of infinity, and put forward four paradoxes about the finiteness and infinity of time and space: "Dichotomy": an object moving to its destination must first pass through the midpoint of the journey, but to pass through this point, it must first pass through the 1/4 point of the journey, and so on to reach infinity. The conclusion is that infinity is an endless process and movement is impossible. "Achilles can't catch up with the tortoise": Achilles always has to reach the starting point of the tortoise first, so the tortoise must always run ahead. This argument is the same as the dichotomy paradox, except that it is not necessary to divide the required distance equally again and again. "The arrow doesn't move": It means that the arrow must be in a certain position at any time during the movement, so it is stationary, so it can't be moving.
3. Impact: This crisis not only did not hinder the rapid development and wide application of calculus, but let calculus gallop in various scientific and technological fields, solved a large number of physical problems, astronomical problems and mathematical problems, and greatly promoted the development of the industrial revolution. As far as calculus itself is concerned, after the baptism of this crisis, it has been systematized and integrated and expanded to different branches, becoming the "overlord" of mathematics in the18th century.