With the help of Turing's real people, this Q&A can be regarded as a thrilling pass.

Wang Qi "traveled" through the era before the study of modern mathematical logic was far from Gödel's time. I don't know much about a mathematical system that can be equivalent to a Turing machine or a Lambda algorithm. As far as Wang Qi knows, it includes the cellular automata that Wang Qi made in Shenzhou before, as well as the Post correspondence problem, the counter machine, the Markov algorithm, and the recursive function.

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

And his own talent is not weak, and he has the help of Turing real people. In half a year, I can naturally accomplish a lot of things.

For the average carefree, the preparation of Wang Qi and Turing is seamless and impeccable.

Invulnerable, just thinking about it can make them lose their courage.

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

Turing was still unsatisfied: "Wait a minute, wait until we finish discussing this issue......"

"Just talk to yourself privately. Feng Luoyi glanced at the Counter and the Counter, and then announced, "Now, let's just sit back and wait for midnight." ”

This is one of the few things that is emphasized in the practice of the Fa today. The summary of this subversive way must be carried out in the middle of the night.

The old and the new are friends, yesterday's kinds of yesterday died, and today's kinds of today's life.

Those carefree monks were still immersed in the shock of the incomplete theorem, and only now did they realize that so much time had passed.

From noon. Sub-time. This sermon. It's been going on for half a day.

After discussing it with a real Turing. Wang Qi sat back on the edge of the pulpit again, closed his eyes and rested. Obviously, he was just the little monk of the Jindan period just now. But for some reason, everyone felt that he seemed to have the aura of Yue Ruyuan.

- Psychological effects?

Some people have a hint of suspicion.

Even if you don't agree with Wang Qi's theory, you have to admit that Wang Qi is very talented.

No one can ignore him anymore.

"When you enter the immortal path, you will dominate the world...... someone whispered: "I seem to see another national player." ”

"Let's say he's like a king...... They all destroyed the Dao heart of a generation of leaders in the Song Court to achieve great fame......"

"Shut up!"

That sentence seemed to cause a bit of a commotion. Most of the calculators looked at the arithmetic with concern.

In the midst of a tumult, the Reckoner was the one who suffered the most. Wang Qi gave birth to a weapon to deny him from his thoughts, his train of thought. His lifelong quest was also shattered. Right now. It would not be surprising that this top escapee would die immediately.

However, the master remained motionless and did not say a word.

The clock of midnight soon rang. Wang Qi re-stepped onto the pulpit. This time, there was unparalleled confidence in his expression.

In a past sermon, Pang Jialai talked about the future of arithmetic. He said at the time: 'Once upon a time, there were some half-immortals who told fortunes. They repeatedly said that all the problems had been solved, and that all that remained was to polish the answers again,' and then he added: 'But such sorrows are always not good to die...... I don't think anyone else thinks that way today. ’”

This sentence from the seniors. At this point, it's really appropriate. Now, our belief in progress. Our faith in our immortal path is no longer so strong, and these perceptions have been shaken by the extremely violent blows. It doesn't seem so reasonable for us to extrapolate the past and the present all the way to the future without hesitation, as our predecessors did—we don't even know what we'll know, what we'll know, and what we need to know. ”

Wang Qi's words are like opening the curtain of a dark era. He is illustrating the incomplete, unpredictable destructive power. Wanfamen was almost crushed by the blow. Except for some low-level monks, no one's Dao heart was unshaken.

Outside the venue, the disciples of Wanfa Sect who were still paying attention to this sermon were still sobbing. They scolded in a low voice: "Immortals, Heavenly Demons, Evil Demons!"

Even the Shaoli faction in the audience felt stunned.

"If we were to ask arithmetic scholars their views on the future of arithmetic, then most arithmetic scholars would like to ask more fundamental questions: What kind of immortal path does the human race want to forge for itself? After 80,000 years of accumulation by the human race and 2,000 years of searching for the present law, is our way of thinking just a flash in the pan in the universe? If we are worried about falling into the discussion of the mysteries and prefer to stay in the historical materials that are not so reliable now, we will also encounter the same problem, but in a different form: Are we watching our immortal path grow old and turn from Tai to Tai? Should we abandon entrepreneurship, or at least abandon entrepreneurship for the way in our hearts, and turn to keep?"

The renegade led by the Geting faction also fell into confusion.

Is being poor to infinity a barrier to our cognition?

Will we never be able to reach the infinite shore?

Is this barrier impossible to break through?

Or, as the sages said, there is no infinity in this universe?

However, the purpose of Wang Qi's choice of this speech is not to boast, but to express his own views.

- arithmetic, you will be reborn in Nirvana!

The Bourbaki school was the one who stood up at a time when many new generation of geniuses led by Gödel and Turing were bloodbathing the entire mathematical world, and they were also the ones who went furthest in the second half of the twentieth century.

"Why is this happening? There is no doubt that we have a big problem, a very big problem. This problem may be solved in my lifetime. However, at this time, I am always reminded of what Lord Hymon once said that a branch of science is full of life as long as it provides a large number of problems, and the lack of problems is a sign of death. I think we don't have to worry about witnessing the death of arithmetic. What a terrible problem we have!"

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

"That's right, there are also seniors who want to talk about me - this Jindan monk who has not yet stood up does not have a backache when he stands and talks. But ah, but! Have we ever been afraid of a crisis?"

Wang Qi's voice was in the middle of it. There was a hint of excitement mixed in.

"For the first time, an ancient arithmetic defined the ratio of two quantities with sufficient precision. As for the question of the existence of non-measurability, they seem to believe and demand that all ratios be rational numbers, and to base their first sketches of geometric reasoning on this provisional assumption, to which some of the greatest advances of the Middle Magometrials are linked to their first errors. ”

- The First Mathematical Crisis, the Discovery of Irrational Numbers.

"Also at the beginning of the era of variable celestial theory and infinitesimal calculus, it was desirable that every analytic expression define a variable celestial formula, and that each variable celestial formula has a derivative; Today we know that these requirements are incompatible with each other - and Mr. Wei Er, who solved this problem, is sitting among us right now!"

- The Second Mathematical Crisis. Calculus's manipulation of infinity and infinitesimal causes contradictions.

"The most recent crisis was caused by the strange way of argumentation provided by the advent of naïve set theory, which led us to such good results that we can consider it finally established. We have learned to trace the whole of arithmetic back to a single source, which consists of several symbols and several rules for the use of those symbols. Undoubtedly, this is an impenetrable mountain guard, and although it is difficult for us to be confined to it without the risk of starvation, we can always decide to retreat to it at our own discretion when the situation is uncertain and there is danger from the outside world. ”

The Third Crisis of Mathematics, the contradiction caused by the self-referential nature of set theory.

Wang Qi closed his eyes and paused here. And then he was determined. He resolutely spoke his mind: "Only a few backward minds still hold the position that the arithmetic must rely on his 'intuition' to arrive at new 'illogical' or 'prelogical' elements of reasoning. If some branch of arithmetic has not yet been axiomatized, it is reduced to such a statement. All of these terms are defined in terms of the basic concepts of set theory, and all axioms are clearly expressed in terms of the original concepts of set theory, but there is not enough time for us to do so. Of course, it is quite possible that one day our descendants will demand that the methods of reasoning that we do not allow to be introduced into set theory, and that it is even very possible that later we will discover the germ of contradictions that we do not see today with the mode of reasoning we use today, although the work of modern logicians suggests that such a situation is very unlikely. At that point, a general correction will be required, but even now we can be sure that the most essential elements of arithmetic will not be affected. ”

Hearing only the first sentence, all the Shaoli sect monks, including Shujun, changed color.

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

However, Wang Qi must say so.

This is the foreshadowing of his subsequent thoughts.

"Is he still a disciple of the Sect ......" A complicated expression appeared on Fairy Ruoche's face, not just relieved but resentful.

"Even among the twenty-three questions, there are still a few that are far away from us, and although they are not yet unattainable goals, they may continue to provide research topics for more than one generation, and the fifth question about Li Qun is an example......"

Riemann conjectures that after people have given up their intention to prove it by the transtemporary, there now seems to be a new light. It shows that it is closely related to a conjecture of a variable nature, which makes the two problems two sides of the same arithmetic-algebraic problem, which undoubtedly plays a decisive role in the simultaneous study of all the circular expansions of a given number field......"

“...... The arithmetic of the high heir of the king is concentrated around the law of quadratic reciprocity; Now we know that the quadratic reciprocal law is only the first special case of the laws of the 'class field', which are the theorems that determine the expansion of algebraic fields, and we know how to formulate these laws so that they appear to be a compact whole......"

One question after another was asked. Many calculators are not stupid. They are quick to realize that this is a mature system of thought.

It includes not only the logic and formalization of the deviant sect, but also the low-dimensional topology and algebraic topology of the representative of the lianzong. Vaguely, there is something more than that.

He Weier's eyes became eager.

"This Wang Qi is really seeking the nirvana of arithmetic!" (To be continued.) )