Qin Ke's manuscript was roughly sorted out initially. Later, Ning Qingyun spent nearly half an hour sorting it out again before practicing the Eastern Secret Code. At this time, Ning Qingyun went up to the second floor to take it down and let everyone in the research group

Read carefully.

By the way, the official members of the research team are still only Qin Ke, Ning Qingjun, Edward Witten and Lao Tao, and the rest are Faltings, Deligne, Mr. Qiu, Wiles, and Lindenster

Rouse is a non-staff member of the research team. He has made it clear that he will not sign the author's name on the project results. He firmly refused even if it was a second author, but readily agreed that his name should appear in the "acknowledgments" at the end of the paper.

In their words, being able to witness and participate in such a process of research on the unification of mathematics is the greatest spiritual enjoyment. Moreover, they only participated later and made limited contributions, so they firmly refused to agree to be listed in the author column.

However, although they are "non-staff members", these five mathematical masters have devoted considerable energy. In the past two or three weeks, they have basically been discussing "new geometry" all day long, and their contributions cannot be ignored.

At this time, they got Qin Ke's manuscript. Although there was only the last part of dozens of pages, they could still easily understand which part was which content. In order to facilitate subsequent scanning and inputting into the computer and write the paper directly, Qin Ke wrote it in English.

, which makes it easier for everyone to read.

Considering that there were a lot of people and it was a bit troublesome to read the manuscripts scattered, Ning Qingyun asked the artificial intelligence Xiaoguang to scan all the manuscripts into electronic versions and play them on the 108-inch LCD TV in the hall.

No one was in the mood to have breakfast. They each took out pens and papers and prepared to follow Qin Ke's ideas to calculate and verify.

For a while, the living room was extremely quiet, with only the sounds of excited breathing and the occasional sound of pen scratching on paper.

Qin Xiaoke couldn't understand the paper, so he played the role of pouring coffee, and then sat next to him and recorded this interesting scene with quick sketches.

After reading a few pages, Tao and Lindenstrauss came to the living room to have breakfast after washing up. Only then did they realize that something "big" had happened. They quickly came over to sit down and read the TV screen together.

Time passed bit by bit with such concentration, and it was not until noon that everyone finally finished reading the contents of these dozens of pages of manuscript paper.

The eldest gentlemen all looked tired. After all, such high-intensity thinking was too mentally taxing and a bit too heavy a burden for the elderly. However, everyone's faces were full of excitement.

"It's great, the creativity in many places is simply genius-like and unconstrained!" Wiles was the first to sigh.

Edward made no secret of his admiration: "Well, there is no doubt that the answers to the 11 questions we have discussed for a long time in the past three weeks have all been found in these manuscripts. Qin Ke is indeed an amazing genius.

All the results discussed in Tianlai were integrated and pushed to a whole new level, solving all these problems in one go."

Deligne blinked his sour eyes and sighed: "I didn't find any problems. I can see such a perfect new geometry. I have no regrets in this life. I believe that if Teacher Grothendieck sees it in heaven, he will also

Will be full of praise.”

"Full of imagination. Some of the content I found incomprehensible when I first read it, but when I thought about it more carefully, I couldn't help but marvel. For example, the application of the triple inversion of the outline on this page in the moduli space of parameterized algebraic varieties can be transformed directly.

For the geometric topology problem, the cleverness of the idea is amazing!" Lao Tao said excitedly.

Mr. Qiu said, "No, I think there is another problem that is not a problem."

Qin Xiaoke was listening with great joy. She liked hearing others praise her brother most. Seeing that Mr. Qiu seemed to have some objections, she couldn't help but mumbled: "Grandpa Qiu, what do you mean by a problem that is not a problem?"

Mr. Qiu smiled slightly: "Don't worry, it's not that there is something wrong with your brother's manuscripts, but... they are too difficult. You need to pay attention to secondary optimization when writing the papers."

He looked around at everyone: "We have been involved in the perfection of 'New Geometry' in the past few weeks, so we can understand it, but it is also a bit difficult to understand. Many details need to be thought over and verified to understand. Except for us

What about other people? I estimate that there are no more than a hundred mathematicians in the world who can understand this 'new geometry', and if they want to fully understand this 'new geometry', it will not take them several years.

It can’t be done.”

"Is it a problem that it's too difficult? But this is something you great mathematicians came up with together. Isn't it normal? It would be weird if I could understand it, right?" Qin Xiaoke still didn't understand.

Linden Strausch had a good temper. He had a good impression of Qin Xiaoke, so he explained warmly: "It is indeed a problem that the difficulty is too high. If the final papers are of this difficulty, I guess I will want to find reviewers."

It is extremely difficult for everyone. The last paper by Qin Ke and Xiao Ning on the Yang-Mills equation gave the reviewers a headache for a long time. This 'new geometry' is even more difficult. I want to verify all the papers and get the approval.

The conclusion of the manuscript will take at least two or three years. After all, almost all the people who are most qualified to review the manuscript are concentrated here, and we have to avoid suspicion and cannot participate in the review."

"That's it..." Qin Xiaoke finally understood.

"And it's too difficult, which is not conducive to promotion." Lao Tao said.

Seeing Qin Xiaoke blinking in confusion again, Ning Qingyun next to her explained: "If this 'new geometry' is too advanced, it will not have the conditions to be promoted to the general public. It will only be spread among the top

Among mathematicians, their influence on the mathematics world will be greatly reduced. One of the goals of the "Unification of Mathematics" is to unify various mathematics sub-subjects with a unified "language" and allow more mathematicians to

Master, break the divide between different sub-disciplines.”

Modern mathematics has developed to this day and has become a "big family" with more than 100 branches and sub-disciplines. However, if roughly divided, mathematics is mainly divided into three major categories.

This chapter is not finished yet, please click on the next page to continue reading the exciting content! The first category studies "numbers", which is represented by algebra, including advanced algebra, number theory, abstract algebra (groups, rings, fields), etc.

The second type of research is "shape", represented by geometry, including mapped geometry, non-Euclidean geometry, Euclidean geometry, analytic geometry, and topology evolved from geometry, etc.

The third category is the study of the relationship between numbers and shapes, as well as extreme operations, etc., represented by analysis, the most common ones are calculus, differential equations, function theory, functional analysis, etc.

These three major classifications constitute the ontology and core of the entire mathematical system, and the three major classifications interpenetrate and blend with each other, giving birth to many sub-disciplines and cross-disciplines, such as algebraic geometry, algebraic topology, differential geometry, etc.

Just as what is combined must be divided over time, and divided over time, it must be combined. With the development of mathematics, each sub-discipline continues to extend in depth. The result is that it becomes more and more abstract and difficult. The boundaries between each sub-discipline become increasingly blurred and blurred.

They are becoming more and more alienated, those who are blurred merge into each other, and those who are alienated almost never interact with each other until death.

The excessive separation of connections between knowledge theories makes it increasingly difficult for mathematicians to understand "mathematics". Mathematics masters who study two different sub-disciplines have even reached the point where they are as separated as a mountain. This is true for students studying mathematics.

, or mathematicians who use mathematics to solve problems in other disciplines such as physics, chemistry, and biology, have caused great trouble.

More and more people are turning their attention to the ultimate direction of "unification of mathematics" and want to use a unified "language" to realize the mutual transformation of the three major classification problems and provide as many solutions to difficult problems in a certain subject as possible.

For this reason, the "language" of "mathematics unification" must be easy to understand, at least for senior mathematics professors to understand, teach students, and promote its application.

Now the "new geometry" integrated by Qin Ke has successfully "unified" algebraic geometry, topology, and mathematical analysis, laying a solid foundation for the unification of mathematics.

But when Qin Ke wrote these manuscripts, he did it in the most concise and refined way, striving to write the "new geometry" with the most mathematical beauty, rather than the best-understood "new geometry". The starting point was different.

, the results are naturally different.

Edward Witten smiled and said: "It's just a small problem that the difficulty is too high. As long as we and Qin Ke spend some time to add more details to make it better understood. In any case, let's celebrate the birth of 'new geometry' first.

!This will be the most outstanding achievement achieved by the unification of mathematics in the past hundred years!"

Everyone raised their coffee cups and bumped them together vigorously!

…

Qin Ke's paper on "New Geometry" "New Geometry - New Expanded Exploration and Thinking Based on Algebraic Geometry" was repeatedly optimized to make it easier to understand, and it finally took nearly ten days to complete.

Ning Qingyun finished typing the last character and checked it carefully again before taking a long breath and showing a proud smile on her pretty face.

It was not easy to write this paper. It can be said that it took several drafts.

In the previous seven days, Qin Ke, Ning Qingjun, Edward Witten, Tao Zhexuan, Faltings and other eight partners have been optimizing the "new geometry" to reduce the difficulty as much as possible, at least to make it accessible

Senior mathematics professors at the university can read it, which will facilitate the promotion and application of "new geometry" and lay a solid foundation for the future promotion of "Qin's Unified Framework Theory of Mathematics".

The final author was Ning Qingyun. Edward Witten was too old to write such a long paper, and Lao Tao was also a little tired of such writing work, so the writing task naturally fell on Ning Qingyun.

Ning Qingyun lived up to his high expectations and spent about three days completing the paper and then submitted it to everyone for review.

For this great paper, which is destined to go down in history and influence the development of the entire mathematical community in the next hundred years, everyone has devoted all their attention and energy, studying every word and every deduction step of the paper repeatedly, striving to avoid any problems.

In the end, except for some fine-tuning of a few words, the paper was unanimously approved by everyone.

The total length of the paper exceeds 300 pages, which is enough to produce a mathematical monograph. Of course, compared with Mr. Grothendieck's 7,500-page "Fundamentals of Algebraic Geometry" which took 7 years to write, it is just

It seems very "thin".

On June 9, the night when the paper on "New Geometry" was officially completed, everyone opened a bottle of champagne to celebrate.

"cheers!"

The nine mathematicians and Qin Xiaoke who joined in the fun gently clinked ten wine glasses together. Old Tao drank the most generously. He raised his head and drank it all in one gulp, and then breathed out: "Happy! These people who came to Xia Kingdom

These months are the happiest months for me. The experience of working on the project with you is really unforgettable and cherished. I don’t want to go back to the United States. Unfortunately, it’s too laborious to access foreign websites here!”

Qin Ke smiled and said: "If you really want to stay, I think Qingmu University will be extremely happy."

"My family are all in the United States. My wife is very happy working at NASA, but she is not willing to resign. It seems that it is impossible to continue this kind of cooperation in the future, and we can only connect remotely through video." Lao Tao was helpless, remote video

Of course, online cooperation is not as convenient as face-to-face communication, and there is also the problem of time difference:

"Let's not mention this somewhat disappointing topic. Team leader Qin Ke, what are our plans next? The new geometry is completed, which is to improve string theory, especially Edward's high-end version of M theory, to solve the problem of radioactive elements.

Harm issue?”

As Lao Tao said, he saw that Lao Qiu's wine glass next to him was empty, so he picked up the champagne next to him and filled it up for him.

Qin Ke briefly thought for a moment, then blinked and said: "So to speak, our 'new geometry' is all theory and derivation. Although it is full of useful information, it is still a little less convincing. I will not add some content to prove it.

Its use. Well, how about choosing a simpler direction, such as using it to prove the Hodge conjecture? You should be able to prove the Hodge conjecture in two days, and spend another day to write a paper, which is consistent with this "New

"Geometry - New Expanded Exploration and Thinking Based on Algebraic Geometry" was submitted together. What do you think?"

The lively atmosphere suddenly fell silent.

Ning Qingyun, who knew in advance, suppressed her laughter. The scene in front of her was exactly the same as when she said on the morning of May 30, "Qin Ke has solved the problem of high-dimensionalization of the Riemann-Rohe theorem." She was explaining to Mr. Qiu

Tao Zhexuan, who was pouring the champagne, even forgot to lift the champagne bottle in his hand. As a result, the champagne in the glass overflowed and soaked Mr. Qiu's clothes.

Only then did Lao Tao react. He quickly put down the champagne and hurriedly got a tissue to wipe Mr. Qiu's face.

Qin Xiaoke acted the fastest, picked up the tissue box and handed it over.

Mr. Qiu joked while wiping the wine stains on his body: "This shirt of mine has made a contribution to solving the Hodge conjecture. Don't forget to include this shirt of mine when you write your thanks."

This humorous remark naturally caused a lot of laughter.

The laughter stopped and Professor Wiles coughed lightly: "Um... Qin Ke, you said you can prove the Hodge conjecture within two days, do you mean you have a specific idea?"

Everyone present knew the new geometry very well. People like Lao Tao, who was an active thinker, had already tried to use it to solve the problems encountered in his previous research, but no one had ever used the new geometry.

Learn to prove the Hodge Conjecture!

Especially listening to Qin Ke's tone proved that millennium-level mathematical problems were as easy as chopping melons and vegetables. Even though everyone present was used to seeing wind and waves, the corners of their mouths couldn't help but twitch.

That's the Hodge's conjecture! Many mathematicians believe that the difficulty of the Hodge's conjecture is even higher than the Riemann's hypothesis!

Qin Ke nodded and said: "Yes. In fact, the relationship between the algebraic topology of non-singular complex algebraic varieties and the geometry expressed by the polynomial equations that define sub-varieties is already included in the 'new geometry'. I want to prove it and

It won’t take too much time and effort, but the proof process will be a bit more complicated, and there is no way to make it as simple as possible like writing a paper on new geometry.”

Lao Tao spread his hands: "I don't have any objections, but I will not participate in this proof process. You and Xiao Ning can complete it."

Edward Witten also nodded and said: "Tao and I will first improve M theory through new geometry. This 'simple' problem will be left to you and Xiaoning."
Chapter completed!