Into the Immortal Cultivation

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With the help of real Turing people, this question and answer is considered a risk-free pass.

In the years before Wang Qi "traversed", the study of modern mathematical logic is far from comparable to that of Gödel. Mathematical systems that are equivalent to Turing machines and Lambda algorithms do not know much. As far as Wang Qi knows, including the cellular automata that Wang Qi made in Shenzhou before, as well as the Post correspondence problem, counter machine, Markov algorithm, and recursive function.

On this issue, his vision is inherently higher than that of the people in China.

And his talent is not weak, and he has the help of Turing real people. Within half a year, naturally many things can be accomplished.

For the general Xiaoyao, the preparation of Wang Qi and Turing live-action is seamless and impeccable.

If you think about it, you can make them lose courage.

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

Turing's true intentions are still not exhausted: "Wait, wait for us to discuss this issue ..."

"You just talk privately." Feng Luoyi glanced at the fortune-teller and forehead, and then announced: "Now, let's wait for the midnight."

This is one of the few particularities in this practice. The summary of this subversive approach must be carried out midnight.

At the intersection of the old and the new, all of yesterday died yesterday, and today are born today.

The spirits of the monks who were carefree were still immersed in the shock brought by the incomplete theorem. It was only now that I was shocked that time had passed so long.

It starts at noon and ends at midnight. This preaching has actually lasted for half a day.

After discussing with the real Turing man, Wang Qi sat back on the edge of the pulpit again, closing his eyes and raising his mind. Obviously it was just that little monk of the Jindan period. But somehow, a group of Xiaoyao felt that he seemed to have a breath like Yue Ruyuan.

——Psychological effect?

Some people have a trace of doubt.

Even if he does not recognize Wang Qi's theory, he has to admit that Wang Qi is very talented.

No one can ignore him.

"Fang enters the fairy road, and then presses the world ..." Someone whispered: "I seem to have seen another living country hand."

"It's like saying he's like a monarch ... It's all about destroying the morality of a generation of court leaders to achieve great reputation ..."

"To shut up!"

That sentence seemed to cause a little commotion. Most fortune-tellers looked at the fortune-teller worriedly.

Amidst the turmoil, the fortuneteller was the one who suffered the most. Wang Qi gave birth to a weapon that denies him from his thoughts and ideas. His lifelong pursuit was also broken. Now, it's not surprising that this top Xiaoyao died immediately.

However, the fortune teller remained motionless and said nothing.

The midnight bell rang quickly. Wang Qi returned to the rostrum. This time, in his look, with unparalleled confidence.

"In the past sermon of Pang Jialai, he talked about the future of mathematics. He said this at the time: 'There used to be so many half-cents of mathematics. They repeatedly said that all problems have been solved, The rest is just to polish the answer again, 'then he added:' However, this kind of sad spring and autumn people always have to die well ... I want to come, no one still holds this today An idea. '"

"This sentence of the predecessors, when used at this time, is really in context. Now, our faith in progress and our confidence in our fairy tales are no longer so firm. These views have been shaken by extremely fierce blows. Yes For us, it does n’t seem reasonable to push the past and present into the future without hesitation, like Senior Jun Jun. We do n’t even know what we will know, what we will know, and what we need to know. . "

This sentence by Wang Qi is like opening the curtain of a dark age. He is exposing incomplete and undecidable destructive power. Wanfamen was almost beaten down. Except for some low-level monks, no one ’s heart is unshakable.

Outside the court, Wanfamen disciples who were still paying attention to this sermon were still sobbing. They whispered in a low voice: "Fairy Fairy! Heavenly Demon! Evil Demonway!"

Even the Shaoli people in the field felt frustrated.

"If you want to ask a mathematician about the future of mathematics, then most of the mathematicians will want to ask a more fundamental question: What kind of fairy road do the human races want to create for themselves? The human race has accumulated over 80,000 years, and the law has been sought for two thousand years. Is n’t our way of thinking just a flash in the universe? If we are worried about getting caught in the discussion of Xuan Zhixuan, we would rather stay in the historical materials that are not so reliable now, we will also encounter the same problem, just change Expressed in various forms: are we watching our fairy tales grow old and turn from Thai to Thai? Should we abandon entrepreneurship, or at least abandon entrepreneurship for our own way of mind, and turn to conservatism? "

Lizong, headed by the Geting School, was also lost in confusion.

Is there a limit to infinity, is it a barrier to our cognition?

Will we never be able to reach the endless shore?

Is it impossible to break through this barrier?

Or as the sages said, there is no end to this universe?

However, the purpose of Wang Qi ’s choice of this speech was not to brag, but to express his views.

——Study, it is necessary to rebirth Nirvana!

The Bulbaki School was the Nirvana who stood out when many new generations of geniuses, led by Gödel and Turing, washed the entire view of the mathematical world. They were also the furthest away in the second half of the twentieth century.

"Why is this? There is no doubt that we have encountered a big problem, a very huge problem. This problem may be solved in my entire life. But at this time, I always think of what Ximen once said- —A branch of science is full of vitality as long as it can provide a large number of problems, and lack of problems is a sign of death. I think we at least do n’t have to worry about witnessing the death of mathematics. What a terrible problem we have encountered what!"

Someone whispered, "You speak lightly ..."

"Yes, there are also seniors who want to say me-this unprepared Jindan monk stood up and spoke without backache. But ah, but! Our mathematics, are our Falun Dafa afraid of crisis?"

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

"The first time the ancient mathematicians defined the ratio of the two quantities accurately enough, it caused the problem of unfair measurement. They seemed to believe and required all ratios to be rational numbers, and laid their initial sketches of geometric reasoning on this On the basis of temporary assumptions, and some of the greatest developments of the Middle Ages were linked to their initial mistakes at this point. "

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

"Similarly at the beginning of the era of variable-day theory and infinitesimal calculus, people also hope that every analytical expression defines a variable-day formula, and each variable-day formula has a derivative; today we know that these requirements are mutually incompatible— -And Mr. Wei Er, who solves this problem, is sitting among us now! "

——The second academic crisis, the contradiction caused by the operation of calculus on infinity and infinitesimal.

"The most recent crisis was due to the weird argumentation provided by the emergence of the naive set theory, which led us to quite good results so that we can think that it has finally been established. We have learned to put the whole Mathematics is traced back to a single source, which is composed of several symbols and several rules of use of these symbols. This is undoubtedly an unbreakable mountain protection array. Although it is difficult for us to be imprisoned without being exposed to the risk of hunger, we But they can always decide to retreat in the face of uncertainty and danger. "

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

Wang Qi closed his eyes and paused here. Then, he firmly and resolutely expressed his thoughts: "Only a few people with backward thinking still adhere to this position: the mathematician must rely on his" intuition "to draw a new" non-logical "or" pre Logical 'reasoning elements. If some branches of arithmetic have not been axiomatized, that is, reduced to such a statement, where all nouns are defined by the basic concepts of set theory, and all axioms are clearly expressed by the original 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 us to introduce inference methods that we do not allow into set theory, and it is even more likely that we will use the inference model we are using to discover today. We have not yet seen the germination of contradiction, although the work of modern logicians shows that the possibility of this situation is very small. By then, a general correction will be required, but even now we can be sure to learn The most essential elements in it will not be affected. "

Only the first sentence was heard, and all Shaoli monks including Shujun suddenly changed their colors.

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

However, Wang Qi must say so.

This is the foundation of his subsequent thoughts.

"Whether he is still a disciple ..." Ruo Che fairy had a complex expression on his face, not just comfort or resentment.

"Even among the twenty-three questions, there are still several questions that are far away from us. Although they are not unachievable goals, they may continue to provide research topics for more than one generation. The fifth question is about Li Qun. Is an example ... "

"Riemann's conjecture, after people abandon their plans to use the sky-changing method to prove it, now there seems to be a new light. It shows that it is closely related to a sky-changing conjecture, so that these two problems become There are two aspects of the same arithmetic-algebra problem, and for this problem, it will undoubtedly play a decisive role for the simultaneous study of all the expansions of a given circle in a given number field ... "

"... Arithmetic Wang Gaosi's arithmetic is concentrated around the law of quadratic reciprocity; now we know that the law of quadratic reciprocity is just the first special case of the laws of the" domain ", and these laws determine the algebraic number field As for the theorem of Aschalt expansion, we also know how to express these laws so that they appear to be a compact whole ... "

Questions were asked one by one. Many mathematicians are not stupid. They are quick to realize that this is a mature ideological system.

It includes not only the logic and formalization of the sect, but also the low-dimensional topology and algebraic topology of the representative of the sect. Indistinctly, there is something above it.

He Waier's eyes were eager.

"This Wang Qi, really is the nirvana of learning!"

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