Enter the Immortal Cultivation

"After listening to this story, you seniors must have known the content of my paper. Regarding this point, I think it is difficult to say whether this is a blessing or a curse."

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

"Fortunate?" Ikeman looked up at Wang Qi, smiled bitterly, and then shook his head: "I don't see what makes people feel lucky."

Wang Qi smiled slightly: "If one day, we can really sort out a set of logic to judge the truth or falsity of a mathematical proposition like the puppet judge in my story judges the mechanical man himself, then do we mathematicians still have meaning to exist? I am afraid that by then, Shenzhou will no longer need any Wanfamen. An ultimate calculator will be better than all of us."

All the monks of Wanfamen lowered their heads, with divine light flashing in their eyes.

If it really comes to that point, then there is really no need for Wanfamen to exist. An ultimate calculator - the ultimate magic weapon that can explain any mathematical problem in a short time. That is simply a shortcut.

At that point, mathematics has come to an end.

So, has mathematics come to an end now?

I am afraid it is far from it.

On Earth, there were countless scholars who clamored that "physics has still come to an end" and "humanity will master the ultimate truth." That era was the heyday of classical physics - yes. Just classical physics.

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

This is just because they can't see the next step.

If they can't see the next step, they think they have reached the limit. In fact, they haven't, and they are still at the initial stage.

How similar is the mathematics of Shenzhou today to that time?

Now it seems that how far the way of the flow of heaven in Shenzhou is from the true way of heaven, how far the way of mathematics is from the true way of heaven.

After listening to Wang Qi's words, all the mathematicians finally regained some enthusiasm. However, some people still sighed: "It's true... but who will dare to seek the way of mathematics in the future?"

Wang Qi's incompleteness and undecidability almost put a label of "nothingness" on the entire way of mathematics.

In this case, who would dare to explore the way of mathematics? You don't even dare to believe that the way you seek is meaningful.

This is not a problem of "unsteady heart for the way". Because Wang Qi's incompleteness and undecidability are all derived from mathematics itself, and the proof process is impeccable.

It's like saying that the Buddha suddenly started killing and eating human flesh at a Dharma meeting. He turned into a green-faced and fanged figure. No matter how firm the heart of Buddhists is for the way, they probably can't withstand such stimulation.

Wang Qi stripped off the gentle mask of mathematics and exposed its terrifying nature.

Seeing the erratic expressions of the crowd, Wang Qi smiled bitterly in his heart.

After experiencing this twists and turns, the mathematics community on Earth was depressed for 20 to 30 years. In the past two or three decades, there have indeed been some mathematical achievements. But it is no longer as grand as before.

It is indeed difficult to ask these free and easy monks to immediately accept the two principles of incompleteness and undecidability.

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

"In fact, I actually have some ideas about how mathematics should go from now on."

Wang Qi's words. The people who listened to it fluctuated slightly again.

Looking forward to the future, not everyone is qualified to do it. What is being done here are all the top mathematicians in Shenzhou. In addition to the Lord of Mathematics and the Master of Mathematics, is there anyone in the world who can point fingers at them and say "you should do this next"?

This is not for the general public, for low-level monks, but for these top mathematicians.

What he did was not an irresponsible prophecy, but something similar to the programmatic "Five-Year Plan". Those who can do this are all people 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 arithmetic school, is not far from it.

Ke Lanyin, the former leader of the Goting School, the former God and Prince of Yunduan, also integrated the modern and ancient geometry and transformation groups with a program, and created the era of "one law is all the laws" in the Wanfa School. It is precisely because of this that he is considered to be able to compete with the Lord of Calculation. [Here refers to the Erlangen Program]

And what he summarized are only two fields, geometry and group theory.

When Wang Qi opened his mouth, he was talking about the entire mathematical world.

If ordinary people said this, even if they thought they were free and easy monks, I am afraid that these top monks would start to rebuke.

However, only Wang Qi, no one dared to criticize.

The second and tenth questions of Ximen's twenty-three questions are too important. Many free and easy monks of the Goting School have never seen any hope of solving them. But this young man solved them.

In terms of magic power, he may still lack a little accumulation. However, in the field of mathematical logic, he is a top number.

"In fact, I neither can nor intend to point out a path for the future development of arithmetic - I am not even qualified to do so, and I also know that doing so will definitely be futile and in fact a ridiculous thing. I always firmly believe that the mathematicians of the future, just like the mathematicians of the past, will never follow the same old path. They will use new perspectives to solve the big problems we leave them through connections that we have never thought of. It is just a matter of lack of knowledge. ,we do not know."

"But at least I know what I can do."

"Incompleteness and undecidability are not terrible things. The Misty Way proves that certainty is lost in the microscopic realm. However, this has no impact on the macroscopic world. We still prevail in a world of cause and effect. "Wang Qi said: "Although I have proved the lack of completeness and decidability of arithmetic, I have only proved their existence, but I still don't know where they occur. We are far from touching the edge of arithmetic. .Incompleteness and undecidability have little meaning in the known field of arithmetic."

"At least for now, the arithmetic we know 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 microscopic world, we have to face 'uncertainty'. But that day is not now."

"That kind of research has not been carried out in the past, and it is still too early. At least the existing mathematics is not enough to touch that area. I believe that when we touch that realm, the need for proof has already reached the level of consciousness. , and the technology with this need has evolved – but not now.”

"Beyond this field, we still have many meaningful problems to study. For example, the fifth of Ximen's twenty-three calculations - the formula for changing the sky and the transformation group; Rie's conjecture - when we give up the previous After using Changtian Shi as a weapon to overcome it, new hope is in front of us; the quadratic reciprocity law of the senior mathematician... We can see that arithmetic is still making progress. "

"Actually, for fellow Taoists who don't seek Yuansuan, incompleteness, undecidability, or absence are the same and have no impact on their work."

"And for fellow Taoists of Yuan Suan Dao, our journey has just begun! We still have a lot to do!"

Some people in Li Zong were dissatisfied: "What else can we do?"

——What we pursue has been destroyed by you.

"I have completed Senior Xi's question, so you think there is no problem to solve?" Wang Qi shook his head.

In academia, solving problems is basically equivalent to "stealing jobs." Once a conjecture is verified, countless mathematicians who point to this conjecture will lose their jobs. These free monks here are not only shaken in their Taoist hearts, but also deprived of the goal they strive for.

It's just that the way he used to achieve these goals was completely opposite to these people's ideal way, so they couldn't accept it for a while.

but……

"The Calculator once said that only when there are problems does it mean that this subject is developing." Wang Qi sighed: "Incompleteness and undecidability are the huge problems that I have exposed. As for the idea of ​​​​getting around this problem - in fact, I am I said that six years ago.”

"Six years ago..."

Some mathematicians showed complicated expressions. Six years ago, Wang Qi did talk about some "ideas" at the Banquet of Making Things. But at that time, no one cared. All of them regard it as this junior's personal experience - just a personal research idea. No matter how perfect it is, what's the point?

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

Now look at this young man.

Rebellion?

The future leader of Li Zong?

Many free monks vaguely saw this. But emotionally, they couldn't accept it for a while.

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

Wang Qi nodded, followed the standard by 60%, and began to talk about his paper "On Computable Numbers and Their Application in Determination Problems".

Suanjun was still not very interested in this, he shook his head and said: "It's useless."

The paper "On Computable Numbers and Their Application to Decision Problems" is also not very long. Like "On the Formally Undecidable Statements and Related Systems in the Arithmetic Chapter of Volume 1 of "Wanfa Suanzang"", its proof process is actually very simple.

Simple, but full of wisdom.

All Xiaoyao are unconsciously immersed in this piece of paper, which itself exudes the alluring brilliance of wisdom. Even if they knew that this river of logic would flow into the abyss, those mathematicians could not help but listen.

Soon, a monk stood up and cheered loudly: "Okay!"

The person standing is the master of Qianji Pavilion, Master Turing. (To be continued ~^~)