Enter the Immortal Cultivation

With the help of Master Turing, this question-and-answer session was passed without any danger.

Before Wang Qi "traveled through time", the research on modern mathematical logic was far beyond the era of Gödel. There were countless mathematical systems that were equivalent to Turing machines and lambda algorithms. As far as Wang Qi knew, they included the cellular automata that Wang Qi had made in Shenzhou before, as well as the Post correspondence problem, counter machine, Markov algorithm, and recursive function.

On this issue, his vision was inherently higher than that of everyone in Shenzhou.

And his own talent was not weak, and he had the help of Master Turing. Naturally, a lot of things could be accomplished in half a year.

For ordinary free-spirited people, the preparations of Wang Qi and Master Turing were flawless and impeccable.

So impeccable that just thinking about it could make them lose their courage.

In the end, it was Feng Luoyi who interrupted the communication between Wang Qi and Master Turing. He looked around and said, "If no one continues to ask questions now, then the time for questions is over."

Turing Zhenren was still not satisfied: "Wait a moment, wait until we finish discussing this issue..."

"You can chat privately." Feng Luoyi glanced at the master and the master, and then announced: "Now, let's wait for midnight."

This is one of the few details of the current law. This subversive summary must be conducted at midnight.

The intersection of the old and the new, yesterday's things died yesterday, today's things are born today.

The spirits of those free and easy monks are still immersed in the shock brought by the incomplete theorem. Only now did they realize that so much time has passed.

Starting at noon and ending at midnight. This sermon has lasted for a whole half day.

After discussing with Turing Zhenren, Wang Qi sat back on the edge of the podium again. Close your eyes and rest. It is obviously just the little monk in the Jindan period just now. But for some reason, the free and easy monks felt that he seemed to have an aura as majestic as a mountain and a deep abyss.

——Psychological effect?

Some people had a little doubt.

Even the Suanjun school, which did not approve of Wang Qi's theory, had to admit that Wang Qi was very talented.

No one could ignore him anymore.

"As soon as he entered the immortal path, he dominated the world..." Someone whispered, "I seem to have seen another national master of the common people."

"He is like Suanjun... They both destroyed the Tao heart of a generation of Ge Ting leaders to achieve a great reputation..."

"Shut up!"

That sentence seemed to cause a little commotion. Most of the fortune tellers looked at the fortune teller with concern.

In a turmoil, the fortune teller was the one who suffered the most. Wang Qi bred a weapon to deny him from his thoughts and his ideas. His lifelong pursuit was also broken. Now. It would not be surprising if this top free man died immediately.

However. The fortune teller remained motionless and silent.

The midnight bell rang soon. Wang Qi walked onto the podium again. This time, his expression was filled with unparalleled confidence.

"In a past sermon, Master Pang Jialai talked about the future of mathematics. He said: 'There were some half-immortals who could tell fortunes. They kept saying that all problems had been solved, and the only thing left was to polish the answers.' Then he added: 'But. Those who are sad about the spring and autumn will never die well... I think no one still holds this idea today.'"

"This sentence from the senior is really appropriate at this time. Now, our belief in progress and our confidence in our immortal way are no longer so firm. These views have been shaken by extremely severe blows. For us, it seems not so reasonable to extrapolate the past, present and future without hesitation like Master Suanjun - we don't even know what we will know, what we will know, and what we need to know."

Wang Qi's words are like opening the curtain of a dark age. He is explaining the destructive power of incompleteness and indeterminability. Wanfamen was almost devastated by the blow. Except for some low-level monks, no one's Taoism is unshakable.

Outside the venue, the Wanfamen disciples who were still paying attention to this sermon were still sobbing. They cursed in a low voice: "Exiled immortal! Heavenly demon! Evil heretic!"

Even the Shaoli Sect members in the venue felt lost.

"If you ask mathematicians about their views on the future of mathematics, then most mathematicians would like to raise a more fundamental question: What kind of immortal path does the human race want to create for themselves? After 80,000 years of accumulation by the human race and 2,000 years of seeking for modern methods, is our way of thinking just a flash in the pan in the universe? If we are worried about being trapped in a mysterious discussion and would rather stay in the current unreliable historical materials, we will encounter the same problem. It's just expressed in a different form: Are we watching our immortal path grow old and turn from prosperity? Should we abandon entrepreneurship, at least abandon entrepreneurship for the path in our hearts, and turn to preservation?"

The Lizong mathematicians headed by the Ge Ting Sect also fell into confusion.

From finite to infinite, is it the barrier of our cognition?

Will we never be able to reach the other side of infinity?

Is this barrier insurmountable?

Or is it, as the ancients said, that the universe is not infinite?

However, Wang Qi chose this speech not to brag, but to express his own views.

—— Mathematics must be reborn from the ashes!

The Bourbaki school was the nirvana that stood out when many new generation geniuses led by Gödel and Turing were bloodbathing the entire mathematical world. It was also the one who went furthest in the second half of the twentieth century.

"Why is this happening? There is no doubt that we have encountered a big problem, a very huge problem. This problem may take my entire life to solve. However, at this time, I always think of what Lord Ximen once said - —A branch of science is full of life as long as it can provide a large number of problems, and a lack of problems is a sign of death. I think we at least need not worry about witnessing the death of arithmetic. What a terrible problem we have encountered. ah!"

Someone cursed in a low voice: "You speak lightly..."

"That's right. There are also seniors who want to say that I, this golden elixir-level monk who has not yet established himself, can stand and speak without pain. But, but! Are our arithmetic and our Wan Dharma Sect afraid of crisis?"

There was a hint of excitement in Wang Qi's voice.

"When ancient mathematicians first defined the ratio of two quantities with sufficient precision, they raised the question of the existence of incommensurable quantities. They seemed to believe and required that all ratios be rational numbers, and based their first sketches of geometric reasoning on this On the basis of provisional assumptions, some of the greatest advances of medieval mathematicians were connected with their initial errors on this point."

——The first mathematical crisis, the discovery of irrational numbers.

"Also at the beginning of the era of variegation theory and infinitesimal calculus, it was expected that every analytic expression would define a categorization, and that each categorization would have a derivative; today we know that these requirements are mutually exclusive— —And Mr. Wei Er, who solved this problem, is sitting among us now!"

——The second mathematical crisis. Calculus operates on infinitesimals and infinitesimals. resulting in conflicts.

"The latest crisis has been caused by the bizarre way of argumentation provided by the emergence of naive set theory, which has led us to results so good that we can think of it as finally established. We have learned to put the whole Arithmetic goes back to a single source, consisting of a few symbols and a few rules for the use of these symbols. It is undoubtedly an impenetrable barrier, although it is difficult for us to be imprisoned in it without running the risk of starvation. But you can always decide to retreat when the situation is uncertain and there are external dangers.”

——The third mathematical crisis, the contradiction caused by the self-reference of set theory.

Wang Qi closed his eyes. There was a pause here. Then, he expressed his thoughts firmly and resolutely: "Only a few people with backward thinking still insist on the position that mathematicians must rely on his 'intuition' to arrive at new 'non-logical' or 'previous ideas'." The reasoning elements of logic. If some branches of arithmetic have not been axiomatized, they are reduced to such statements in which all nouns are defined by the basic concepts of set theory and all axioms are clearly expressed by the primitive concepts of set theory. , that’s just not enough time for us to do this. Of course, it is very likely that one day our descendants will ask for the introduction of reasoning methods that we are not allowed to introduce into set theory, and it is even very likely that we will use the reasoning models we use now to discover today. We have not yet seen the beginning of a contradiction, although the work of modern logicians shows that it is very unlikely that a general revision of the arithmetic will be required by then. The most essential elements will not be affected.”

After hearing the first sentence, all the Shaoli monks, including Suan Jun, became furious.

Wang Qi is equivalent to pointing their noses and scolding them!

However, Wang Qi must say this.

This is the foreshadowing of his subsequent thoughts.

"He is still a disciple of Li Zong after all..." A complex expression appeared on Fairy Ruo Che's face, which was not just relief but resentment.

"Even among the twenty-three questions, there are still several problems that are far away from us, although they are not unattainable goals. They may continue to provide research topics for more than one generation. Among them, the fifth problem about Lie groups Just an example..."

"The Riemann Hypothesis, after people gave up their intention to prove it with a heaven-changing method, now seems to have new light. It shows that it is closely related to a certain heaven-changing conjecture, which makes the two problems become Two aspects of the same arithmetic-algebraic problem, for which the simultaneous study of all cyclotic expansions of a given number field undoubtedly plays a decisive role..."

"...the arithmetic of Gao Si, the arithmetic king, centered around the law of quadratic reciprocity; we now know that the law of quadratic reciprocity is only the first special case of the 'like field' laws that determine algebraic number fields Agrarian expansion theorem, we also know how to formulate these laws so that they appear to be a compact whole..."

Questions were raised one after another. Many mathematicians are not stupid. They quickly realized that this was a mature ideological system.

It includes not only the logic and formalization of Li Zong, but also the low-dimensional topology and algebraic topology represented by Lian Zong. Vaguely, there is something more than that.

He Weier's eyes became eager.

"This Wang Qi really seeks the nirvana of arithmetic!" (To be continued ~^~)