Enter the Immortal Cultivation

The focus of the competition between Go Ting, led by the Master of Calculation, and Li School, led by the Master of Calculation, is on mathematical logic. This field is the most basic part of mathematical logic. And a mathematician's understanding of this field determines his overall grasp of mathematics.

Chen Feng's mathematics is worse than Wang Qi's, but he still knows this.

Wang Qi smiled and said, "Senior Feng also ordered this, there is no harm in doing it."

Feng Luoyi and Xi Boche both thought that Wang Qi was very talented in mathematical logic. If he continued on the road of first-order logic, he would sooner or later reach Xi Boche's ideal realm.

But Wang Qi knew that this road was not impossible to take, but the result of the next step would only run counter to Xi Boche's expectations.

Gödel's incompleteness theorem, a terrible theorem that destroyed the sublime beauty of mathematics and drove mathematics off the altar.

In the history of the earth, Gödel's incompleteness theorem proved that Hilbert's second question was an unsolvable problem, which made Hilbert's plan bankrupt. If it were thrown out in Shenzhou, I'm afraid it would completely shake the prestige of the Go Ting school.

No matter what I say, I have been labeled as a "Götting School" in the eyes of others, so it is better to consider this aspect when doing theory.

By the way, I also have to guard against others following my ideas to come up with the incomplete theorem.

Although it only takes one year for a genius like Gödel to go from the complete theorem to the incomplete theorem, for ordinary mathematicians, the road that Gödel walked in one year is absolutely a chasm.

Not to mention that Gödel himself derived the completeness theorem by relying on a flash of enlightenment.

The ideas of the Li School monks and Gödel are not completely consistent, and their understanding of mathematics is different, so their ideas and methods are also different. It is unlikely that they will derive the incompleteness theorem based on Wang Qi's paper and follow Gödel's ideas. It seems that only Suan Jun is a relatively big threat now.

The real people to be vigilant are "our own people".

Wang Qi, who is familiar with the subsequent history, knows. The hope of the results of Hilbert's plan is not completeness and decidability, which are clearly denied. The only hopeful part of it is the consistency of the arithmetic system.

The second article of Gödel's incompleteness theorem states that for any mathematical system, if it contains an arithmetic system, then we cannot prove its consistency within this system. This is part of the answer to Hilbert's second question.

Using transfinite induction, which is not within the arithmetic system, to prove the consistency of the arithmetic system just bypasses the iron wall drawn by the incompleteness theorem.

"So the next step is to get transfinite induction from set theory and then substitute it into the explanation of the arithmetic system, and direct the key of the debate to the consistency of the arithmetic system."

This is Wang Qi's current plan.

Chen Feng frowned: "Do you know what it means to get involved in the debate between the Lord of Calculation and the Lord of Calculation? Don't think that you won't get involved in Mars just because you are in Shenjing."

"I will only throw out a few papers, and generally I won't directly respond to the other party's questions." Wang Qi smiled.

As long as the focus can be directed to the consistency of the arithmetic system, it will be enough.

Moreover, organizing the arithmetic system is also a big project. I don't have much time to complete it one by one. I just need to participate in part of it at my true level.

Chen Feng looked at Wang Qi in confusion and asked, "You seem to be very obsessed with this debate... illusion?"

Wang Qi shook his head: "This is not an illusion."

I really want to get involved in this debate.

When reading the biography of Henri Poincaré in his previous life, Wang Qi had a very strange feeling.

This person was born at the wrong time.

Most mathematicians like to get involved in the field of physics to show that they have excess IQ, but his era was when classical physics developed to the extreme, and there was not much for him to play with. When Einstein triggered a new round of revolution, he was already old; he and David Hilbert were exactly two generations apart. The era when he gradually aged was the era when Hilbert rose step by step. When Hilbert reached his heyday, he had already withdrawn from the front line of mathematics due to aging.

Henri Poincaré never really burned in his life.

But in this world, he has to face a genius who is blooming with all his brilliance, the Lord of Calculation Pang Jialai!

In the same camp with him are the Lord of Calculation Xi Boche and the national player Feng Luoyi! They are mathematicians of the same level!

Any mathematician with a certain level will be excited by such a debate.

Moreover, Wang Qi himself also has a little thought.

"I may not be as good as Gödel, who is about fifty years old and at the peak of his life... But I should be at the level of Gödel when he is about twenty years old, right?"

He is not participating in it himself, but representing Gödel to participate in this event that is impossible to happen on earth.

Just thinking about this matter is enough to make people excited!

At the beginning, Wang Qi was also shocked by his crazy idea. But after calming down, his desire to participate in this debate became stronger and stronger.

This debate is the flower of the soul that mathematicians bloom with all their lives and talents, and it is an affirmation and sublimation of life!

How can I miss it?

Never miss it!

Even if I only participate in it as a supporting role!

Perhaps sensing the passion burning beneath Wang Qi's calm exterior, Chen Feng high-fived and praised: "Interesting, that's the way it should be! You are worthy of being my valued partner - by the way, are you still going to do the work here?"

In the past few days, Chen Feng had visited Wang Qi several times and mentioned the theory he was working on. He vaguely understood the significance of Wang Qi's theory and was vaguely aware of Wang Qi's level. Now, he was afraid that Wang Qi would regret it.

Wang Qi said: "Do it, why not? Qi training disciples are not allowed to leave the sect without permission. They have to ask for leave to go out. That means I can't leave Shenjing before the new arrangement of Wanfamen is made. And Shenjing is the best place to earn merit points, right?"

Chen Feng breathed a sigh of relief. On the surface, he asked, "Are you going to pay me back now for the merits you owe me or are you working for me for nothing?"

Wang Qi scratched his head: "Let's do what we agreed to do. Senior Feng said that the benefits of my paper will only gradually appear after the second month. The first month's income will not be too much, and the second month will be better than the first month. I'm still penniless recently."

Chen Feng nodded: "Okay. So what are your recent plans?"

"Of course I'm busy with foundation building. When Suan Jun comes back and the debate begins, I guess I won't be able to rest in peace." Wang Qi sighed: "By the way, Boss, do you know how to refine weapons? I skipped the refining class in the Immortal Academy. Can I make up for it?"

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