● The three mathematical crises in the history of mathematics are coherent and intrinsically related, which can be described as one after the other.
● Berkeley's ridicule of calculus prompted mathematicians to establish a rigorous theoretical foundation for calculus, and mathematicians such as Euler, D'Alembert, and Lagrange all attempted but failed.
● Cauchy redefined the limits and established a strict definition of concepts such as infinitesimal quantities, infinitely large quantities, continuous, derivatives, differentiations, and integrals, laying the foundation for the rigor of analysis.
● Weierstrass gives a ε-δ definition of the limit, which is strictly expressed by inequality intervals, completely free from the dependence on geometry and motion, and can be based on a clear definition of numbers and functions.
● The development of mathematics is inseparable from the rigor of basic theories, and the contribution of Cauchy and Weierstrass to the rigor of analysis is decisive.
● Every crisis in mathematics is an opportunity for progress, and it is because of these crises that mathematics continues to develop and improve. #漫谈数学史#
