A large number of combinatorial mathematics problems that are booming are rarely systematized. For the Bourbaki school, it is a headache to analyze specific problems one by one. Although they can solve many problems at once, sometimes they can't handle small problems. Practical problems are often related to computational mathematics, which needs computers to implement, but bourbaki members are dismissive of it. In fact, there is nothing they can do about it. Because of bourbaki's great achievements, since 1960s, "New Mathematics" has been introduced into mathematics teaching in primary and secondary schools, which has caused huge social problems. Kindergarten children have to learn set theory, and middle school students have to teach environment and ideals. Students can't stand it, and even teachers are complaining. This kind of "new mathematics" education has been carried out in France, the United States and other countries for a period of time, and the effect is obviously not good, so some people took it out on bourbaki and formed a wave of anti-bourbaki. Of course, bourbaki's mathematical system is often criticized as extremely formal, abstract, axiomatic and divorced from reality, and some critics think that bourbaki's mathematics is not fruitful. In fact, these criticisms are unfair. Bourbaki really pursues form and beauty. However, their abstract concepts are not water without a source, and they never do anything for promotion and abstraction. However, works divorced from reality did exist at that time, even in some areas, and some people blamed it on bourbaki. In the final analysis, this is a trend away from bourbaki. In 1970s, analytical mathematics, applied mathematics and computational mathematics made great progress. The four-color theorem proved by computer has successfully opened a new chapter in the history of mathematics and opened up a glorious road of mechanical proof. At the same time, "Constructivism", which runs counter to bourbaki's spirit, has gained a new life from stagnation. In this way, the development of mathematics has been pushed from the abstract and structuralist road led by bourbaki to the concrete, structuralist, practical and computer-based road, thus ending the glorious golden age of Bourbaki School. Mathematics is a science for young people. Only by constantly injecting fresh blood can the tree of mathematics be evergreen. However, the Bourbaki school has completed its historical mission and was sent to the grave. But bourbaki's reputation is indelible, and his legacy will last forever! Scientific research needs the strength of the group. As a group, it will learn from others. Each member has his own expertise, and they may find something on different issues. Although his personal views will be biased, this defect can be made up by collective strength, so that we can conduct in-depth research on each specific problem and finally find the most satisfactory answer. This will promote the development of mathematics in a deeper and more systematic direction.
Of course, we should look at the influence of schools in the development of mathematics dialectically. On the one hand, mathematics has been socialized, which directly serves all departments of war and economic production. In addition, mathematics is also combined with many other disciplines (such as biology, economics, linguistics, etc.). ) formed a new branch and promoted the development of the whole country in many fields. On the other hand, schools are made up of like-minded people, whose views are the same to some extent, so there must be a side opposite to other schools' views. It can be said that schools are mutually exclusive. In other words, different ways have no common goal. This leads to the narrowness and conservatism of the school itself. In this respect, the school has limited the greater development of mathematics to some extent.