Three crises in the history of mathematics revealed the mystery of scientific development. These three crises urge people to break through the limitations of existing theories and move towards a broader field of knowledge.

The emergence of irrational numbers

The first crisis, the emergence of irrational numbers, challenged the rules of integer division, but was eventually brought into the field of real numbers, which gave birth to the glory of Euclidean geometry.

The imprecise definition of calculus

The second crisis originated from the imprecise definition of calculus, and the argument caused by infinitesimal promoted the establishment of real number theory and limit theory, which laid a solid foundation for mathematical analysis.

Challenges faced by set theory

The third crisis is the challenge of set theory. Russell's paradox reveals the flaw of set definition, but it is solved by axiomatic system, which promotes the progress of mathematical logic and other disciplines.