I have heard a lot of "economic crisis" in my life, but I have heard of "mathematical crisis" for the first time. Similar to the cause of the economic crisis, the mathematical crisis is also due to the inherent contradictions of the mathematical foundation and framework, which are gradually revealed in the process of mathematical development.

In these three mathematical crises, I saw that mathematics and philosophy, whether personal philosophy or philosophy of the times, are inextricably linked. As philosophy says, "the world outlook determines methodology."

A person's view of a matter determines his way of dealing with it. For example, if Hibersos found that the diagonal of a square with a side length of 1 could not be expressed by any number at that time, Hibersos was brave enough to ask questions and decided that this problem was a defect in mathematics at that time.

I hope it can be solved in the discussion, but his view is considered "absurd" and contrary to common sense. He was suppressed by others and even drowned in the sea. This tragedy depends to a great extent on people's lack of comprehensive and in-depth understanding of numbers at that time, so those "deviant" "aliens" were executed.

At the same time, we can see that every mathematical crisis is a struggle between tradition and frontier. Enlightened people constantly challenge the authority of the old times, and die-hards constantly try to stifle new flames, but a single spark has already started a prairie fire, burning all decadent and backward things and rolling forward with the waves of the great river.

Therefore, we should cultivate the spirit of pioneering and innovating, learning and exploring, not afraid of authority and pursuing truth, and break a new world in our own field. Three mathematical crises are also three mathematical revolutions. When problems are found and raised, they need to be solved.

After years of unremitting discussion and research, people have overcome one difficulty after another. The impetus brought by the mathematical crisis to the development of mathematics has continuously promoted the perfection and maturity of the theoretical basis of mathematics. The new era should be an open and inclusive era, with the mentality of allowing different opinions to exist: "Although I don't agree with what you say, I will defend your right to speak to the death.

Only when everyone has the opportunity to express their views can we spark in the collision, inspire new inspiration and promote the development of the times. A hundred schools of thought contend, seeking common ground while reserving differences, and * * * progress are the proper ethos in the cultural field.