"After listening to this story, you seniors must also know the content of my paper. On this point, I think it's hard to say whether this is a blessing or a misfortune. ”

Wang Qi's tone was very calm and peaceful, as if the astonishing theory just now did not come from his mouth, but someone else.

"Luck?" Ike Man glanced up at Wang Qi, smiled slightly bitterly, and then shook his head again: "I don't see anything in this that makes people feel lucky." ”

Wang Qi smiled slightly: "If one day, we can really sort out a set of logic, just like the puppet judge in my story to judge the truth or falsehood of an arithmetic proposition, then we, the arithmeticists, will there still be any meaning to exist? One ultimate calculator is better than all of us. ”

All the Ten Thousand Dharma Sect monks lowered their heads, and their eyes flashed with divine light.

If it really comes to that point, then there is really no need for the Ten Thousand Laws Gate to exist. An Ultimate Calculator - An ultimate instrument that can give explanations in a short period of time, no matter what problems are in arithmetic. That's a shortcut.

At that point, arithmetic has come to an end.

So, is arithmetic now coming to an end?

Far from it, I'm afraid.

On Earth, there have been countless scholars who have shouted that "physics is still coming to an end" and "mankind is about to grasp the ultimate truth". It was the heyday of classical physics -- yes, just classical physics.

People of that era even declared that "the sky of physics is sunny, but there are only two small dark clouds".

It's just because, they can't see the next step.

I couldn't see the next step, so I thought I had reached my limit. As a matter of fact. They haven't even stayed at the beginning.

How similar is today's Shenzhou arithmetic to that time?

Now it seems that how far the Heavenly Path of Divine Transformation is from the True Heavenly Dao, the Dao of Arithmetic is as far as the True Heavenly Dao.

After listening to Wang Qi's words, all the arithmetic artists finally regained a little enthusiasm. However, some people still sighed: "That's right...... But later. Who else dares to do the math?"

Wang Qi's incompleteness and undecidability are almost labeled as "nothingness" on the entire way of arithmetic.

In such a situation, who would dare to seek the way of arithmetic? You can't even believe that the way you are seeking is meaningful.

It's not a matter of not having a firm "heart to the Tao". Because, Wang Qi's incompleteness and undecidability are all deduced from arithmetic itself, and the process of proof is impeccable.

It's like saying that the Buddha suddenly went on a killing spree and ate human flesh at a puja. In the shape of a green face and fangs, no matter how firm the Buddhists' heart is to the Tao, it is estimated that they will not be able to withstand such stimulation.

Wang Qi, this is to strip away the gentle mask of arithmetic, and let its terrifying nature be exposed.

Seeing everyone's carefree expressions, Wang Qi smiled bitterly in his heart.

The mathematical community of the earth, after this twist and turn. Depressed for twenty or thirty years. In the past twenty or thirty years, there have indeed been mathematical achievements. But it is no longer the same pomp and circumstance as before.

It is indeed difficult for a strong man to ask these carefree monks to immediately accept the two truths of incompleteness and indecisiveness.

However, on the question of "how to study", Wang Qi still has some ideas.

"Actually, for how to go forward with arithmetic from now on. The younger generation actually has a little idea. ”

Wang Qi's words made the people who listened a little fluctuating.

Looking to the future, not everyone is qualified to do it. What is being done here are all the top arithmetic in China. In addition to the king and the master, there are people in this world who can point fingers at them. Say "what you should do next"?

It's not for the masses, for the low-ranking monks, but for the most elite arithmeticians.

What he did was not an irresponsible prophecy, but something programmatic similar to the "Five-Year Plan." Those who can do this are those who can lead the times and take the lead. This kind of person, even if he is not the leader of the school or the leader of the family, is not far behind.

The former leader of the Geting School, the former god and son of the clouds, Ke Lanyin, also unified ancient geometry and transformation groups with a program, creating an era of "one law is universal and ten thousand laws are connected". It is precisely because of this that he is considered to be a person who can be with the king for a long time. [This refers to the Erlangen Programme]

And what he summarized was only two fields: geometry and group theory.

As soon as Wang Qi opened his mouth, he was talking about the entire arithmetic world.

If ordinary people say this, even if they think that they are carefree monks, I am afraid that these peak monks will open their mouths to reprimand.

However, Wang Qi is the only one, and no one dares to accuse.

The second and tenth of Simon's twenty-three questions carry too much weight. The Geting faction has many carefree attacks, but they have never seen the slightest hope of a solution. But the boy solved it.

In terms of mana, he may still lack a little accumulation. However, in the realm of arithmetic logic, he is the top number of the highest number.

"In fact, I can neither nor intend to show a way for the future development of arithmetic - I am not even qualified to do so, and I know that it would be futile and actually ridiculous. I have always believed that the calculators of the future, like the calculators of the past, will never follow the old path. They will see things in a new way through relationships we don't think of, and solve the big problems we leave them with – but because of the lack of knowledge, we don't know it. ”

"But at least I know what I can do. ”

"Incompleteness and undecidability are not a terrible thing. The ethereal way proves that in the microscopic realm, certainty is lost. However, this does not have any effect on the macro world. We are still victorious in a world where there is cause and effect. Wang Qi said: "Although I have proved the lack of arithmetic completeness and decidability. However, I only proved that they existed, but I didn't know where they happened. We are far from touching the edge of arithmetic. In the known field of arithmetic, incompleteness and undecidability are of little significance. ”

"At least for now, arithmetic as we know it does not contradict the objective facts of the world. ”

"Perhaps, sooner or later, we will face all this. Just like if we want to explore the microcosm, we have to face 'uncertainty'. However, that day is not now. ”

"That kind of research hasn't been done before, and it's still too early, at least the existing arithmetic isn't enough to reach that area. I believe that by the time we reach that state, the need for proof has already reached the level of consciousness, and the technology for this need has been developed - but not now. ”

"And outside of this area, we have a lot of interesting questions to look at. For example, the fifth of the twenty-three calculations of the Hemon -- the Changing Heaven Formula and the Changing Group, the Li conjecture -- when we give up using the Changing Heaven Formula as a sharp weapon to overcome it, a new hope is just around the corner, and the second mutual reversal law of the king's predecessors...... We can see that arithmetic is still improving. We can still move forward. ”

"Actually, for Daoists who don't seek the Yuan Calculation, incompleteness and indecidability or non-existence are the same, and it has no effect on their work. ”

"And for the Daoists of Yuansuan Dao, our journey has just begun! We still have a lot to do!"

Some people who left the sect were angry: "What else can we do?"

-- What we are seeking has been destroyed by you.

"I've finished the problem of Nozomi senior, so you think there is no problem that can be solved?" Wang Qi shook his head.

In academia, solving problems is basically equivalent to "grabbing jobs". When a conjecture is verified, countless mathematicians who point to this conjecture are unemployed. These carefree monks here are not only shaken by the Dao heart, but also deprived of the goal they are fighting for.

It's just that the way he picks up these goals is diametrically opposed to the ideal way of these people, so they can't accept it for a while.

But......

"The master once said that if there is a problem, it means that the discipline is developing. Wang Qi sighed: "Incompleteness and uncertainty, this is the huge problem I exposed. As for the idea of getting around this -- I actually said it six years ago. ”

"...... Six Years Ago"

Some of the arithmetic had mixed looks. Six years ago, Wang Qi did say some "ideas" at the banquet of instrumentation. But at that time, no one cared. All of them thought of it as a little personal experience of this junior—a little bit of personal research ideas. What's the point of perfecting it?

However, no one expected that today, after he proved the fallacy of the main idea, the idea that no one cared about would become the direction of the future development of the sect.

Look at this teenager again.

Apocalyptic rebellion?

The future leader of the sect?

Many of the Monks of Freedom saw this vaguely. It's just that emotionally, they can't accept it for a while.

Feng Luoyi coughed lightly twice: "I believe that by this point, you will all have a general understanding of Wang Qi's thoughts and concepts." Now, Wang Qi, you can explain your thesis to everyone. ”

Wang Qi nodded, according to the standard, sixty percent, and began to talk about his paper "On Computable Numbers and Their Applications in Judgment Problems".

Shui Jun was still not very interested in this, shook his head and said, "It's useless." ”

The paper "On Computable Numbers and Their Applications to Judgment Problems" is also not very long. Like the formally indeterminable statements and related systems in the arithmetic section of Paper 1, the process of proof is actually quite simple.

Simple, but full of wisdom.

All the carefree are unconsciously immersed in this piece of paper, which itself exudes a seductive brilliance of wisdom. Even if they knew that this river of logic would flow into the abyss, those calculators couldn't help but listen.

Soon, a monk stood up, intoxicated, and shouted: "Good!"

The one who stands, the master of the Thousand Machines Pavilion, the real Turing person. (To be continued.) )