Great Country Academician

At half past seven, the scholars who came to attend the lecture had already taken their seats.

The auditorium was packed with seats and was buzzing with people, stirring figures and whispering discussions.

For the mathematics community, today's report is definitely a grand event comparable to the National Congress of Mathematicians (ICM).

Breakthroughs in the two major millennium problems, whether it is P=NP? Conjecture or Riemann Hypothesis is crucial to the development of mathematics and even social disciplines.

Of course, the excitement in the auditorium was not limited to the scholars who came to participate in the exchange report.

Backstage in the auditorium, teachers and staff from the Administrative Affairs Office of NTU Xianlin Campus were busy and nervous doing final inspections.

From microphones to projections, from speakers to projections, all equipment during the exchange meeting must be ensured without any problems.

This is the first time that the Xianlin branch has held a grand event of this level. The school leaders have given a fatal order. If there is a problem with the link in charge, then there is no need to do it and just get out!

This is the top academic exchange meeting in the world, with more than 4,000 scholars present!

For academia, even internationally, such a grand event may not happen once in several years.

It can be said that half of the world of mathematics is here. As a joke, if someone dropped a bomb here, the development of the world of mathematics would be set back at least twenty years!

Time passed quickly amidst the discussion of the crowd. At eight o'clock exactly, Xu Chuan, wearing a formal suit, walked steadily and slowly to the front of the auditorium.

Standing on the reporting platform, he looked around at the audience who had quickly quieted down and focused their attention on him. Even after experiencing countless reporting sessions, Xu Chuan still felt a surge of emotion in his heart at this moment. Like an endless stream of magic power.

Without him, this is not the result he made long ago in his previous life, but the path opened up on the towering mountain of Riemann Hypothesis. It is another breakthrough for him and an expansion of the boundaries of human civilization knowledge.

Taking a deep breath, Xu Chuan glanced around the venue, then looked back at the curtain hanging on the wall behind him, as if he could see another person waiting quietly and nervously in the lounge through the curtain.

After briefly looking back, he breathed a sigh of relief and said slowly: "First of all, welcome to everyone who came to participate in the exchange report meeting. I am also very grateful to you for taking time out of your busy schedule to come here to listen to the academic report."

"As you can see, today's exchange report will be divided into two sessions. The morning session is a proof report on "Polynomial Algorithm for Factorization of Great Positive Integers". The afternoon session is a proof report on "Weak Riemann Hypothesis". "

"The report is tightly arranged, so I won't waste your time anymore. According to the process, I will invite Liu Jiaxin, the proof and reporter of "Polynomial Algorithm for the Factorization of Positive Integers" to give an academic report."

After a brief opening remarks, Xu Chuan stood on the reporting platform and clapped his hands. A wave of applause rang out from the audience, echoing in the auditorium with thousands of people.

Behind the reporting desk, Liu Jiaxin, who was wearing a dress suitable for attending a report meeting, had already stood behind the curtain. After hearing the call for invitation on the stage, she took a deep breath and controlled her steps to walk onto the reporting platform.

Looking at the nervous senior in front of him, Xu Chuan's eyes were encouraging and he handed over the microphone in his hand.

Liu Jiaxin nodded slightly and stood on the stage instead of Xu Chuan.

Under the lecture hall, many scholars who had never seen or even heard of this name before here poked their heads and looked curiously.

Many people are curious and curious about this young female scholar.

There are very few women in mathematics. In particular, there are very few female mathematicians who can produce top results.

Didn’t you see that the Fields Medal has been awarded for so many years? From the 1930s to now, which is almost a full century, there are only three female mathematicians who have received this honor.

The first one is Professor Mariam Mirzakhani who has passed away, and the second and third ones are Professors Amelia and Marina who received the medals just over a year ago.

From 1936 to 2022, only three female Fields Medal winners were awarded in the entire eighty-six years. This shows that their numbers are rare, a hundred times rarer than wild giant pandas.

After these three female Philippine Prize winners, the International Congress of Mathematicians to be held in Jinling three years later will probably usher in a new female Philippine Prize winner.

P=NP? Conjecturing the core issue of this millennium problem, "Polynomial Algorithm for Factorization of Positive Integers" proves that it is absolutely worthy of this honor.

Even if she didn't have much reputation in the mathematics community before, it was enough.

So after Liu Jiaxin appeared on the stage, all the eyes of the audience turned over, with curiosity and wait and see, wanting to see this legendary figure solve P=NP? Wonder what the female scholar at the heart of the puzzle actually looks like.

In the venue, when Liu Jiaxin stood on the reporting stage, there was a sudden commotion in the audience.

Many scholars are surprised by the youngness of this female reporter. Judging from her appearance, she may be only in her twenties, which is about the same age as the astonishing Professor Xu.

Even though mathematics itself is a young subject, being able to solve a world-class mathematical conjecture at this age is still an important part of the Millennium Problem, which still surprises many people.

After a brief moment of surprise, many people turned their attention to the young man who had walked off the stage and was sitting in the front row.

In the past, Amelia solved Bloch's conjecture, and later, Liu Jiaxin solved the polynomial algorithm problem of positive integer factorization.

If there is one thing the two of them have in common, besides being young, it is that they are related to Professor Xu who is sitting in the front row at the moment.

The former is his student, and the latter is said to be his senior sister, and some say it is his girlfriend, but no matter what, if the two people can hold their lectures together, their relationship must be quite close.

Perhaps, that young Professor Xu also has a level of education that is difficult for ordinary people to reach?

On the reporting table, Liu Jiaxin didn't think too much.

Being watched by thousands of people in the audience, she felt like her heart was going to jump out.

Taking a deep breath, her eyes fell on a certain figure in the front row. Seeing the other person's face smiling and nodding gently at her, Liu Jiaxin tried her best to calm down.

"Come on! Jiaxin, you can do it, everyone is watching you!"

After silently cheering herself up twice in her heart, Liu Jiaxin had a firm look in her eyes.

Soon, the report on the proof of "Polynomial Algorithm for Factorization of Positive Integers" began.

According to the previous rehearsal, after welcoming scholars from all over the world as usual, the report meeting got down to business.

"The 'P=NP?' conjecture is a core problem in computing theory. Among them, the complex class P includes all those decision problems that can be solved by a deterministic Turing machine in polynomial time. NP refers to the problem that can be solved by non- A decision problem that a deterministic Turing machine can solve in polynomial time."

".It exists in various fields such as mathematics, optimization, artificial intelligence, biology, physics, economics, industry, etc. If the relationship between the two problem classes of P and NP can be solved, the algorithmic complexity problem of these problems will be solved, with Very significant.”

"."

On the lecture stage, from being a little nervous and unfamiliar at the beginning, to being calm and responsive later on, Liu Jiaxin's voice became calmer when explaining.

Sitting in the audience, looking at the senior sister who was getting better, Xu Chuan nodded approvingly with a smile on his face.

Although the proof of "Polynomial Algorithm for the Factorization of Positive Integers" can be said to have been completed independently by Liu Jiaxin, without him, it would probably be impossible for today's mathematical community to see such an exquisite paper, right?

After all, if the historical trend is true, the senior who originally graduated from college will go out to work. No matter how talented she is, it will be almost impossible to achieve anything after leaving academia.

It can be said that Liu Jiaxin is the talent he personally discovered, and he is Bole! The achievements of this cultivation system brought him another kind of pleasure that was no less than solving a world problem.

Half an hour passed, and the report meeting gradually came to an end. However, Liu Jiaxin on the stage did not dare to relax at all.

Because the following question and answer session is the core part of the entire report meeting.

The first person to stand up and ask questions was Laszlo Lovaz, a famous math expert from Hungary.

This expert studies theoretical computer science and discrete mathematics, and served as the director of the International Mathematical Union from 2007 to 2010.

Although he has not won the Fields Medal, he has won all the top mathematics and computer awards such as the Wolf Medal, the Knuth Medal, the Gödel Medal, and the Kyoto Medal.

It can be said that in the intertwined subjects of computer science and mathematics, he is a true master.

After the expert stood up, he glanced at the reporting table, then lowered his eyes at the notebook in his hand, and said in a straightforward tone:

"On page 23 of the report paper, I noticed that when the reporter described the order h(K)=|C(K)| of the group C(K) called the ideal class number of the number field K, The proof is completed: h(K) = 1 if and only if every ideal in the ring OK is a principal ideal, and if and only if OK has the unique factorization property."

"Regarding this part, how did the reporter come up with it?"

After hearing the expert's question, Liu Jiaxin quickly laid out the proof papers on the lecture table and found the problem that Professor Laszlo Lovaz mentioned.

Looking at the above formula, she quickly replied: "For many types of number fields, for a given finite commutative group G, in all such number fields with the discriminant D(K) 6 x, the group is There are limits α for the proportions of G as x → +∞, and they give calculated values ​​of nonnegative real numbers α.

"And in the proof formula on page 23, I completed the proof that when D(K) passes through all prime numbers, the class number of all real quadratic fields of D(K) 6 x is 1."

Concise and clear words came out of Liu Jiaxin's mouth quickly. In the audience, László Lovaz had a thoughtful look in his eyes, which immediately turned into approval.

He smiled, nodded, and said, "Thank you."

After Laszlo Lovaz’s questions, the Q\u0026A session continued.

The second person who stood up to ask questions was also a master in the field of computer mathematics and the winner of the 2006 Newanglina Award.

"Polynomial Algorithm for Factorization of Great Positive Integers" proves that P=NP? The core problem of the conjecture is an important part of the Millennium Problem for the mathematical community. It is a world-class conjecture that is very difficult, but for the development of pure mathematics, it is not of great significance.

However, for the development of computer mathematics, it can be said to be the pinnacle level.

Just like the Yang-Mills existence problem completed by Xu Chuan before, to the mathematical community, it is just an extremely difficult differential equation to solve. Putting aside the tools and other gains created in the process, solving it What you get is an answer.

But for the physics community, it is an important cornerstone that supports theoretical physics to move forward again, and is the only way to complete a grand unified theory.

Therefore, many scholars stood up and asked questions in the venue.

Of course, not all scholars who stand up to ask questions are experts, and they can also ask precise and competent questions.

For example, a doctoral student from the University of Edinburgh asked a question that was embarrassing to the whole world.

"Excuse me, on page 47, the trade-off between the running time of the approximation algorithm and the approximation guarantee. The sum-of-squares hierarchy can be adapted to an exponential-time approximation algorithm. n means that the number of vertices of the graph r can be anything greater than 1. Positive real numbers (probably depending on n), how did the reporter of this question get this proof?"

As soon as this question came out, there was a commotion in the auditorium.

The rustling exchanges intertwined in the extremely spacious auditorium, and many people cast surprised, surprised, confused and even mocking looks at the doctoral student who stood up to ask questions.

Hearing the question, Liu Jiaxin was stunned for a moment at the reporting table. After confirming the question, she explained: "The moderate exponential time approximation algorithm for vertex coverage, uniform sparsest cut and related problems is not mine. Prove the results.”

"If I remember correctly, in the subsequent explanation, Professor Luca Trevisan's report paper at the 2018 International Congress of Mathematicians was quoted."

"You can look at number six in the quote line. Professor Trevisan has explained it quite well."

Hearing that he had raised a question that had already been solved by someone else, the doctoral student from the University of Edinburgh suddenly turned red. He said "thank you" in a mosquito-like voice and sat back with an embarrassed look on his face.

It's one thing to not be good at academics, but it's also another thing to have the courage to ask questions at the report meeting. Even if you ask the wrong question, it doesn't matter.

But obviously, this kind of person has doubts in his mind, and will not even read the cited papers, nor will he search in advance to see if there is an answer to the question. If he raises it, he will only be laughed at.