I really just want to be a scholar

The public review meeting of "Proving the Hodge Conjecture" will be held in the auditorium of the University of Miami, scheduled for 11 a.m. on November 3.

Because the International Congress of Mathematicians was the next day, basically all the guests attending the conference had arrived in Miami, making this public review meeting gathered almost all the world's top mathematicians.

If the "Little Ice Age" hadn't arrived as scheduled and attracted a lot of attention, this review conference might have become the focus of global media coverage.

"Hodge's conjecture" is not as well-known among the public as Goldbach's conjecture and Riemann's conjecture, but it is still a well-known big conjecture.

In the 1950s, William Valens Douglas Hodge, a master of mathematics in the Eagle Country, discovered that these groups reflected the topological properties of geometric objects when he was studying cohomology groups in algebraic geometry in the 1950s. "Hodge's Conjecture".

The Hodge conjecture has attracted great attention since its birth. If this conjecture can be proved, it will provide a theoretical framework foundation for the two mathematical sub-subjects of algebraic geometry and topology, and enable them to successfully establish a relationship. This will be of great significance to the development of algebraic geometry. In addition, it can also solve some number theory problems. Even in physics, the Hodge conjecture is closely related to the spatial dimensions of string theory.

For decades, countless mathematicians have been studying the "Hodge Conjecture", and research on the connection between algebraic geometry and topology has made great progress. However, before Qin Ke, mathematicians could only use computers to Algorithmic and algebraic geometry methods have successfully verified the validity of Hodge's conjecture in some special cases, but there is still a long way to go before completely proving it.

It is precisely because the Hodge conjecture is so difficult that it is almost impossible to prove it before new mathematical tools are developed. The Hodge conjecture has been designated as "one of the seven major mathematical problems of the millennium" by the Clay Research Institute. At the same time, it is also called "the first difficult problem of algebraic geometry" by countless mathematicians.

Now, this century-old problem that has troubled the mathematics community for more than 80 years is finally about to usher in a historic moment and come to a perfect end. How could the mathematics community not be sensational, and how could mathematicians not flock to it? Listen to this report?

What's more, this is also the first time in recent years that Qin Ke and Ning Qingyun have publicly given an academic report to mathematicians. What a rare opportunity!

In addition, there are also many tourists who do not understand mathematics but come here because of the purpose, either for the purpose of "checking in", or to "post online to attract traffic", or simply to join in the fun and watch rare world events. They are trying every means Come and listen to this report.

The huge market demand has caused the two thousand tickets originally issued for free to be wildly hyped to US$100000 - even the concert tickets of the most famous singers in the world are far from this price!

The most exaggerated thing is that such a price demand was speculated on the premise that the public review will be broadcast live on the Internet for free.

In other words, even if you are not on site, you can comfortably watch the entire report meeting through the Internet at home.

This has caused a lot of controversy on the Internet.

Some people say that the audience is crazy. Free tickets for an academic lecture that they don’t understand are so expensive.

Some people say that tickets for those singers’ live concerts also cost thousands of dollars, and they sing old songs that fans are tired of singing. Aren’t there still countless fans willing to pay for this fanaticism and rush to buy concert tickets? Now it's just chasing academic stars, so why not?

Some people also say that this proves the charm of academics and the celebrity effect of Academician Qin Ke and Academician Ning Qingjun of Xia State, who have achieved "out of the circle".

Regardless of the comments on the Internet, it was later proven that the transaction volume of high-priced tickets was actually only two to three hundred. The vast majority of mathematicians who could obtain tickets were unwilling to sell their tickets and miss this rare opportunity. Given their status, There is no shortage of this mere hundred thousand dollars. Among the students at the University of Miami who were lucky enough to get tickets, only some couldn't stand the money offensive and sold their tickets.

This lecture also made the attending mathematicians feel that their trip was worthwhile and they benefited a lot.

Qin Ke was the first to take the stage and gave a report on "New Geometry" for about half an hour. He also showed his amazing imagination and profound mathematical knowledge. He picked up and applied mathematical knowledge in all sub-disciplines. The explanation of "New Geometry" also fully demonstrated the endless changes of "New Geometry" and its huge potential to connect several major mathematics disciplines.

Then Ning Qingyun stood on the stage. This young mother with great oriental beauty still wore a high ponytail. Her pretty face was just like her innocent girlhood. She was still flawless under the spotlight, but she The light of wisdom shining on his body attracts the attention of mathematicians.

Ning Qingyun spent an hour extending the "new geometry" that Qin Ke had previously explained. He transformed the Hodge conjecture into countless "projective algebraic arrows" like a puzzle, and then used "new geometry" to Then he re-harmonized the differentials to form a smooth multi-dimensional surface whose dimensions are continuously superimposed and does not exist in the world, and then successfully used closed rational cohomology classes of the differential forms of each non-singular projective complex algebraic arrowhead. A rational combination method of algebraic form is constructed.

For mathematicians in algebra and geometry, this is simply a grand visual feast that makes people reluctant to blink during the whole process.

Under Ning Qingjun's dancing pen tip, she inherited the excellent scientific talent from her academician parents. Qin Ke has continuously instilled in her a scientific and huge mathematical knowledge system through "thinking resonance" every day for several years, as well as her own countless hardships and sweat. , a unique mathematical thinking ability that only belongs to her, formed by combining some of the mathematical thinking of her teachers, Academician Tian Jianlan, Academician Wang Henglao, Professor Karen Uhlenbeck, and Qin Ke, in the process of proving the Hodge conjecture. Show it vividly!

At the same time, she also showed that except for Qin Ke, her super mathematical strength is not inferior to any young and middle-aged mathematicians under the age of 40!

When Ning Qingjun wrote the last sentence, "It can be seen from the above derivation that every harmonic differential form on a non-singular projective algebraic arrow is a rational combination of the cohomology class of an algebraic closed chain, that is, Hodge Conjecture has been Proven (Hodge's conjecture is proven)!", then turned around and bowed slightly towards the audience, the audience was silent for a few seconds, and then thunderous applause drowned the entire auditorium.

Not everyone present could understand it, especially those who came to join in the fun. Listening to it felt lonely, and the whole process was like listening to a book from heaven.

But at this moment, the light of confidence and the beauty of wisdom exuded by Ning Qingyun really made people feel excited and crazy that they couldn't suppress when they saw the truth! Everyone present could not help but clap their hands vigorously and express their most sincere admiration to this young female mathematician who has reached the top of the world.

Academician Tian Jianlan and Professor Karen Uhlenbeck also clapped vigorously with relief.

Tian Jianlan's eyes were filled with mist. Standing on the stage was her most outstanding disciple. He was already outstanding at a young age, and he represented the future of Xia's mathematics community and even the world's mathematics community!

What moved her most was that from Ning Qingyun's proof process just now, she could see the mathematical inheritance of herself and her teacher Mr. Chen Jingrun. She couldn't help but look up at the sky outside the window, and silently said to the teacher in her heart: "Teacher Chen, have you seen it in Tianzhiling? Your mathematical life has been best extended by Xiao Ning. What you have thought about mathematics throughout your life is now being displayed on the world's most advanced mathematics stage. With..."

Professor Karen Uhlenbeck also had hot circles under her eyes. She has wanted to prove to the world all her life that women can learn mathematics and science well and are no worse than men. Now, Ning Qingyun has done it for her. At this time, the audience is full of people The applause shattered the stubborn notion that "science is only suitable for men".

In the future, more and more girls will surely follow Ning Qingyun's footsteps and embark on the path of becoming mathematicians driven by their interests!

She firmly believes this!

The applause that lasted for nearly five minutes slowly stopped, and then the regular expert review process entered.

In order to be able to review such extremely difficult mathematical conjectures, and because the subjects of the questions are top mathematics masters like Qin Ke and Ning Qingyun who have won the Fields Medal and the Wolf Prize in Mathematics, the judges who came to serve as judges this time are basically They are all mathematics masters who have also won the Fields Medal, the Wolf Prize in Mathematics, and the Abel Prize. The average age is 72 years old. The original most suitable judges, such as Faltings, Deligne, Wiles, Edward Witten, Tao Zhexuan, etc., were unable to become judges because they avoided suspicion. In order to make up for the 30 judges, IMU had to invite them again and again. Some old mathematicians who have not been involved in the world for a long time. Although their level is no longer what it was back then, their status and reputation are still there - yes, in fact, this time IMU also believes that the review is just a process, and the criteria for selecting experts are more More is "fame" so that this review meeting can "convince the public".

A group of elderly experts worked hard to ask seven or eight questions, and then passed the collective vote without any suspense, announcing that the review was successfully concluded, and Hodge's conjecture was successfully proven.

The media reporters who had already written the press release rushed to publish the news in the next second.

"The IMU jury officially recognized that the Hodge conjecture has been jointly proven by Academician Qin Ke and Academician Ning Qingjun! 》

"Following the Riemann Hypothesis, NS equation, and Yang-Mills equation, the fourth millennium Hodge Hypothesis was also conquered by this young couple! 》

"Unstoppable, the most genius mathematician couple successfully proved the Hodge conjecture!" 》

"Their pace of creating miracles has never stopped. Hodge guessed where they will point their swords in the future?" 》

"The light of Xia's best mathematician shines over the United States again!" 》

However, the response to this news was not too intense. After all, since Qin Ke uploaded the paper "Using New Geometry to Prove the Hodge Conjecture" to arXiv, many mathematicians have been working on the premise that "it is correct" Studying it - with Qin Ke's excellent academic reputation, academic resume that has never made mistakes, and a group of mathematics masters appearing in the "acknowledgments" of the paper, no one doubts its correctness.

Compared with these news, the fifteen-minute press conference after the review meeting attracted more attention from the public and mathematicians.

A reporter asked: "Academician Qin, you and Academician Ning have solved four millennium conjectures so far. Do you have any plans to follow up on the remaining two millennium mathematical conjectures - the NP-complete problem and the BSD conjecture?" Solve it? We all believe that you two have such strength."

Qin Ke thought for a while before replying: "I have no intention of solving both conjectures at the moment. At most, we will only solve one of them and leave the other."

Another reporter immediately asked curiously: "Why should one be left behind?"

Qin Ke smiled and replied: "First of all, there is insufficient time and energy. It takes a lot of time and energy to solve the Millennium Mathematics Conjecture. It took us four years to prove the Riemann Hypothesis, and it took us three years to prove the Hodge Hypothesis. It took us five years to prove the NS equation, and it took us a shorter time to solve the Yang-Mills problem, but it also took more than two years. There is something more we want to do next, and cracking the Millennium Mathematics Conjecture is just As a way to play games to rest and relax in your spare time, it may take longer, as fast as three to five years, or as slowly as ten or eight years. Therefore, only one of the conjectures can be solved during this period."

All the reporters and the audience were speechless.

Prove that the Millennium Conjecture is just a way of entertainment after work? Can you, old man, say something humane?

And even if it takes ten or eight years, being able to solve a millennium mathematical conjecture is already super invincible, right?

Just listen to Qin Ke continue: "As for leaving a mathematical problem, I want to leave a thought for future mathematicians. We have a saying in the Xia Dynasty, which is called 'One flower blooming alone is not spring, and a hundred flowers blooming together fills the garden.', Mathematics It is a very charming language. I hope that more and more people will fall in love with this language and work together to make the world a better place through mathematics. A mathematical conjecture that has received countless attention is to attract young mathematicians to continue to The best reward for reaching the pinnacle of mathematics.”

In fact, the most fundamental reason is that the "Please continue to solve more millennium mathematics problems" issued by the system only requires solving the Hodge conjecture, Navier-Stokes equation, NP-complete problem, and the existence of Yang-Mills property and quality gaps, and any four of the BSD conjectures. Now Qin Ke can complete the task and get a big reward as long as he solves the NP-complete problem or any one of the BSD conjectures.

The "NP-complete problem" can be regarded as a mathematics + computer algorithm problem, and the "BSD conjecture", namely Behe ​​and Svenaton-Dyer conjecture, is a number theory problem in the direction of Diophantine. Both are areas that Qin Ke is good at, but even He is already the de facto god of mathematics. It is not easy to conquer NP-complete problems or BSD conjectures. It is estimated that if he really wants to solve it, he will have to devote himself to research for three or four months.

Now that the "Little Ice Age" has arrived and the first sign of "world collapse" is just around the corner, how can Qin Ke spare so much time?

It was difficult for him to even spare three days of free time to absorb the vast amount of knowledge at the "god level of physics".

Moreover, the reward for this task is S knowledge "A New Program for the Unification of Mathematical Theory". Qin Ke wants to use his own wisdom to develop his own unified theory of mathematics after saving the world, so he is not in a hurry. Got rid of these millennium conjectures.

As he said, it is most appropriate to regard solving the Millennium Conjecture as a hobby to relax your mind and take the time to delve into it slowly.

The press conference was over, and a new round of news headlines was released rapidly, this time obviously much more attractive.

"Academician Qin: Solving the Millennium Conjecture is just a way of entertainment after work"

"Mathematicians can breathe a sigh of relief, because Academician Qin Ke will leave you with a millennium conjecture"

……

After the public review meeting for proving the Hodge conjecture that burned many brain cells, Qin Ke and Ning Qingyun ushered in the major event of IMU every four years, the International Congress of Mathematicians.

This time, the two of them will serve as important guests and each will give an academic report on stage. However, there is no time limit or topic limit, so they can express themselves as they wish.

Qin Ke was slightly interested in whether his and Ning Qingyun's names were included in the final Fields Medal list. (End of chapter)