Everyone was stunned. Pen Fun Pavilion wWw. ｂiquge。 ｉｎfo

-- Didn't we just finish talking about our ideals and ideas, and now we should not enter the scene where you ascend to the heights and call me to bow down? Why is there such a thing as a "trial"? This script is wrong?

- No, no, no, before this, you even shared your "thoughts", and clearly entered the rhythm of "dividing meat and eating", why do you suddenly want to brush people?

"You don't really think that I don't have a test at all, do you?" Wang Qi smiled: "Don't worry, it's not difficult." ”

Zhao Qingtan said: "This ...... Brother, something is wrong. Shouldn't you take the exam in the first stage and then tell us about your ideas after the exam?"

- Now everyone finally has the collective concept of "we are a family that loves each other", but you have to start driving people away...... Wouldn't it look at the atmosphere, bastard!

Wang Qi smiled: "Because I like it." ”

"As you just knew, I'm still using 'axiomatization' as the basic method. Therefore, there are high requirements for the level of set theory. Then there's algebraic topology. You know, I'm working on this right now. Then there's the functional analysis ......"

He grinned, "It may be a little wide, but remember to do your best." ”

Wang Qi shook his hand and threw those test papers in front of everyone with the standard secret weapon technique. Originally, some people still held the mentality of "what if", thinking that the neuropathy in front of them might really come up with a simple topic, and even if they had done it. Soon, however, they began to scold their mother.

Every question in this -- every question! all! is the most cutting-edge question!

And! It's very wide! It covers most different areas!

Problems that have just been solved, or are still being studied. Or very advanced theorems.

"You just need to write some of your own opinions, I don't ask for much, really, one opinion. Wang Qi seemed to have a wicked smile. This gives some people hope.

- As long as it's better than everyone else!

With this in mind, these people began to work the questions.

The monk's physical body was already very powerful, and the speed of his hands was beyond the imagination of mortals. Basically, you only need to go through it in your head, and you can write it quickly in your hands. Therefore, the amount of the question is not a problem for them.

The key is the scope and difficulty of the question.

Even if it is an exam, the teacher will usually make a focus.

But Wang Qi doesn't. The scope of his topics is simply drawn from countless fields.

Wang Qi sat in his chair, calmly closing his eyes and recuperating.

"The most important of these questions is set theory, because the 'structuralism' view of the Bourbaki school, which is in the same vein as the arithmetic, also requires a considerable level of set theory. After that, it was firmly arranged according to the ideas of the Bourbaki school. ”

When Wang Qi talked about the ideas of the Bourbaki school, he did not say it all. There are some things that are more mature and have a high degree of perfection, but he didn't talk about them.

For example, the core of the Bourbaki school is the "three parent structures", or the "three origin structures". The algebraic structure with "group, ring, and domain" as the core, the order structure with "partial order and full order" as the core, and the topological structure with "neighborhood, continuity, limit, connectivity, and dimensionality" as the core.

These three origin structures should not be all origin structures, and on top of this, there should be more fundamental structures. However, the path of the Bourbaki school also ended here: the first, second, and even some third generations of Bourbaki mathematicians died or retired, and the successors gradually lost the ambitions of their predecessors.

Although the Bourbaki School still exists, the Bourbaki Mathematics Seminar continues, and the Principia Mathematica is being followed, they no longer have the initial ability.

Perhaps it is because these successors also found that the ambitions of their predecessors were too terrible and beyond their means.

In addition, the ideas of the Bourbaki school cannot explain everything. There are some areas that cannot be included in the system of the Bourbaki school.

Take, for example, number theory.

This is a bit of a comical thing to say. The Bourbaki school followed the ideas of the Göttingen school and replaced "calculation" with "concept", which is the standard "deviant" according to the division of China. However, the most representative branch of the sect, "number theory", was not spoken of by the Bourbaki school.

In the Bourbaki conception, "integers" are "commutative rings of integer sets", and it is impossible to penetrate into the properties of specific numbers. The calculation of the pearl [Goldbach conjecture] and the calculation of the prime [twin prime conjecture], don't try to get any useful advice from the Bourbaki school.

Another embarrassment comes from Wang Qi himself.

The other area of his exercises, which is also the arithmetic extension of mathematical logic, the two-phase exercise of virtual and real, and the cybernetic ideas embodied in it, are also incompatible with the ideas of the Bourbaki school. Recursive theories cannot be incorporated into this system.

If Wang Qi continues to do this, he may have to face an embarrassing situation. He started a school of his own, and another school with his teacher, a Turing person, and then the theories on the two lines could not be integrated at all.

"Still, that's good. Wang Qi's thoughts drifted away: "It's just a good time to test your ability to control a variety of different ways of thinking......"

He glanced again at the monks who were struggling to write.

Someone has already wavered. Several Jin Dan broke down in a cold sweat, and then left here without saying a word.

Wang Qi didn't stop either.

The topics studied by the Bourbaki school are vast and numerous, but they are characterized by "unity". There is not a single theoretical idea that is not reflected in other fields.

This kind of thinking is also reflected in their discussion classes.

At nightfall, Wang Qi announced the handing in of the papers.

"Alright guys, the trial is over, let's hand in our things. ”

All the monks wept and gritted their teeth, and handed in the papers in their hands.

Wang Qi quickly flipped through the thick answers. The content of these answers may have been as much as a book, but he could finish it in a few moments.

This made the monks who answered seriously very unhappy. Anyone who sees what they have worked so hard to write is so belittled, will be dissatisfied in their hearts. In addition, such thoughts were born in their hearts.

- No matter how talented you are, can you surpass each of us in so many fields?

The reaction of a monk like Feng Xingchong was much simpler.

- Definitely...... Be sure to pass ......

Wang Qi said: "First of all, I want to congratulate everyone, you are all qualified." ”

"Huh?" no one reacted: "This is ......"

"It's just a test of your basic skills. Have a correct understanding of set theory, have a fairly broad thinking about arithmetic, and then there are ...... That's pretty much it. So much is enough. Wang Qi said: "So, as long as you can write most of it, and then there are no fundamental or logical errors, forget it." ”

Feng Xingchong almost sat down on the ground. He said, "This ...... It's also a bit of a test of the heart......"

——Can you pass the full write-up?Where does this come from?

- The people who left just now are all because of ...... Because the heart is not good?

"And then, number two, there's one more thing about you that I'm not happy about. Wang Qi picked up the test questions he had come out with both hands. Suddenly, a flame appeared, and all the test papers were burned out in an instant.

"None of you have said 'there may be a problem with the theory' or 'the existing theory may not be able to be answered'. Wang Qi shook his head: "You have disappointed me." ”

Once again, the crowd was petrified.

"Generally speaking, those who dare to write this kind of answer are all prepared to be scolded...... Su Junyu said dissatisfied.

"Ahem, that's the general situation. But what we have to do is different, what are we asking for? It is the foundation of recasting arithmetic! It is to break and then stand!" Wang Qi said solemnly: "You should have this kind of consciousness -- if there is a problem in the existing theory, if you can't figure it out, you should use our thinking to go through it yourself and push it over." ”

This is also the Grothendieck method.

Grothendieck's environment was not very good in high school or university, and the math teachers he could find were not as good as him. When he was in high school, he strongly believed that "the math textbook was not deep enough" and firmly believed that "it was the textbook that had a problem, not me". Then, when he first entered college, he independently redefined many concepts in his math textbooks.

Actually, that's not a math textbook problem, but the average high school student simply doesn't cover that deep concepts. They only need to know the length, width and height, know how to find the volume area, mass density, and don't need to know what "length" is called "area" and what is "volume" from a mathematical point of view - for the average person, this is self-explanatory.

He actually spent three years after the war rediscovering and defining the concepts of measure theory and the Lebesgue integral – by self-study.

The Bourbaki school had some similar styles, but they were not as extreme as Grothendieck's.

Grothendieck was not interested in the work of other mathematicians. As long as he thinks it is interesting and crucial, Grothendieck prefers to rediscover and prove the results himself—for him, most of the time, it takes little effort.

It's just that this won't bring any fame and fortune. Of course, Grothendieck didn't care.

The Bourbaki School, on the other hand, is constantly smashing and redefining the achievements of others, incorporating them into its own "structured" system.

That's what Wang Qi is asking of his new partner now. (To be continued.) )