Enter the Immortal Cultivation

Everyone was confused.

——Didn’t we just finish talking about ideals and concepts, and now shouldn’t we enter the scene where you ascend to a high place and I greet you with my head bowed? Why does "trial" happen? Is this script wrong?

——No, no, no, before this, you even shared your "ideas" and clearly entered the rhythm of "dividing the meat and eating it". Why do you suddenly have to brush people off?

"You don't really think that I have no test at all, do you?" Wang Qi smiled: "Don't worry, it's not difficult."

Zhao Qingtan said: "This...junior brother, something is wrong. Your order is wrong. Shouldn't you take the exam in the first stage, and then tell us about your concepts after the exam is over?"

——Now everyone finally has the collective concept of "we are a family that loves each other", but you are starting to drive people away... Do you think it depends on the atmosphere, you bastard!

Wang Qi smiled: "Because I like it."

"As you just knew, my method here is still based on 'axiomatic'. Therefore, there are very high requirements for the level of set theory. Then there is algebraic topology. You understand, I am here now Study this area. The next step is functional analysis..."

He grinned and said: "The scope may be a bit wide, but please remember to do your best."

Wang Qi shook his hand and threw the test papers in front of everyone using standard hidden weapon techniques. Originally, some people still had a "just in case" mentality, thinking that the lunatic in front of them might actually give a simple question, and if they did it, they would pass. But soon, they started to curse.

Every question here - every question! all! All! Cutting edge issues!

and! The range is huge! Covers most different areas!

Problems that have just been solved recently or are still being studied. Or a very advanced theorem.

"Everyone just needs to write down some of their own opinions. I don't ask too much. Really, it's just an opinion." Wang Qi seemed to be laughing in a wicked way. This gives some people hope.

——As long as you are better than others!

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

The monk's physical body is already very powerful, and his hand speed is beyond the imagination of ordinary people. Basically, you only need to go through what you want to write in your head, and you can finish it quickly by hand. Therefore, the number of questions is not a problem for them.

The key is the scope and difficulty of the questions.

Even if it is an exam, teachers will usually focus on it.

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

Wang Qi sat in his chair and calmly closed his eyes to rest.

"Among these exam questions, the most important one is set theory, because the 'structuralist' view of the Bourbaki school is in the same vein as the calculation master, and it also requires a considerable level of set theory. After that, we will firmly follow the ideas of the Bourbaki school Arranged."

When Wang Qi described the thoughts of the Bourbaki school, he did not explain everything. There are some things that are relatively mature and highly complete, but he didn’t talk about them.

For example, the core "three parent structures" of the Bourbaki school, or the "three original structures". Algebraic structures with "groups, rings, fields" as the core, order structures with "partial ordering, total order" as the core, and topological structures with "neighborhood, continuity, limit, connectivity, dimensionality" as the core.

These three original structures should not be the entire original structure, and above these, there should be a more fundamental structure. However, the path of the Bourbaki school has reached this point where the first, second and even some third generation mathematicians of the Bourbaki school died or retired, and the successors gradually lost the ambition of their predecessors.

Although the Bourbaki school still exists, Bourbaki mathematics seminars continue to be held, and "Principles of Mathematics" is also being followed up, they no longer have the original capabilities.

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

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

For example, number theory.

This is a bit funny to say. The Bourbaki School adheres to the ideas of the Göttingen School and replaces "calculation" with "concept". According to China's classification method, it is the standard "leaving the sect". However, the Bourbaki school had no way of talking about the most representative branch of Li Zong's discipline - "number theory".

In the concept of the Bourbaki school, "integer" is a "commutative ring composed of a set of integers", and it is impossible to go into the specific properties of numbers. For the calculation of pearls [Goldbach's conjecture] and the calculation of prime numbers [twin prime conjecture], you can't even hope to get any useful opinions from the Bourbaki school.

Another embarrassment comes from Wang Qi himself.

Another area of ​​his skills is also the calculator that extends mathematical logic, the virtual and real two-phase skills, and the cybernetic ideas embodied in them, which are also incompatible with the ideas of the Bourbaki school. Recursion theory cannot be incorporated into this system.

If Wang Qi keeps doing this, he may have to face an embarrassing situation. He established one school of thought by himself, and another school of thought with his teacher, Turing, and the theories on the two lines could not be integrated at all.

"However, this is good." Wang Qi's thoughts drifted away: "It's just a test of his ability to control many different ways of thinking..."

He took another look at the monks who were writing furiously.

Some people have already wavered. Several Jindans were sweating coldly, and then left here without saying a word.

Wang Qi did not stop them.

The Bourbaki School's research topics are complex and numerous, but their characteristic lies in "unity". There is no theoretical idea that is not reflected in other fields.

This kind of thought is also often reflected in their discussion classes.

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

"Okay, everyone, the trial is over, everyone hand in your work."

All the monks turned in their papers with sad faces and gritted their teeth.

Wang Qi quickly flipped through the thick answers. The contents of these answers added together may be as much as a book, but he finished flipping through them in a moment.

This made the monks who answered the questions seriously very dissatisfied. Anyone who sees that the things they worked hard to write are so despised will be dissatisfied. In addition, they also have such thoughts in their hearts.

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

The reactions of Jindan cultivators like Feng Xingchong were much simpler.

——Must...must pass...

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

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

"This is just a test of your basic level. You need to have a correct understanding of set theory, have a fairly extensive understanding of mathematics, and...basically that's all. That's enough." Wang Qi said: "So, as long as you can write most of it, and there are no fundamental or logical errors, you will pass."

Feng Xingchong almost fell to the ground. He said: "This...this is too much of a test of your character..."

——You can pass if you fill it all in? Where did this free exam come from!

——So all the people who left just now were because...because their character was not good enough?

"And, secondly, there is one thing that makes me very dissatisfied." Wang Qi held up the test questions he had given with both hands. Suddenly, a ball of fire appeared with a "bang", and all the test papers were burned in an instant.

"None of you actually said 'there may be problems with the theory' or 'existing theories may not be able to answer'." Wang Qi shook his head: "You disappoint me."

Everyone was petrified again.

"Generally speaking, those who dare to write such answers are prepared to be scolded..." Su Junyu said dissatisfiedly.

"Ahem, that's the general situation. But what we want to do is different. What do we want? To recast the foundation of mathematics! To break and then build!" Wang Qi said seriously: "You should have such awareness-if there is a problem in the existing theory that you can't figure out, just use our ideas to go through it yourself and force it through."

This is also Grothendieck's method.

Whether in high school or college, Grothendieck's environment was not very good, and the math teachers he could find were not as good as him. In high school, he strongly believed that "the math textbook was not in-depth enough" and firmly believed that "there was a problem with the textbook, not me." Then, when he just entered college, he independently redefined many concepts in the math textbook.

In fact, it was not a problem with the math textbook, but that ordinary high school students would not involve such in-depth concepts at all. They only need to know the length, width and height, and know how to calculate the volume, area, mass and density. They don't need to know what "length", "area" and "volume" are from a mathematical perspective - for ordinary people, this is self-evident.

He actually spent three years after the war to rediscover and define the concepts of measure theory and Lebesgue integral - by self-study.

The Bourbaki school also has some similar styles, but they are not as extreme as Grothendieck.

Grothendieck is not interested in the results of other mathematicians. As long as he thinks it is an interesting and critical problem, Grothendieck would rather rediscover and prove those results himself - for him, this is not much effort most of the time.

It's just that this will not bring any fame and fortune. Of course, Grothendieck doesn't care.

The Bourbaki school is constantly crushing and redefining the results of others and incorporating them into its own "structural" system.

This is what Wang Qi is asking his new partner to do now. (To be continued ~^~)