I really just want to be a scholar

Given an Abelian variety over a global field, it is conjectured that the rank of its Modal group is equal to the zero order of its L function at 1, and that the leading coefficient of the Taylor expansion of its L function at 1 is the same as that of the Modal group There is an exact equational relationship between finite part size, free part volume, period of all prime sites, and sand clusters.

——This is the BSD conjecture, the full name is the Birch and Swinnerton-Dyer conjecture (Birch and Swinnerton-Dyer conjecture). If you think the above description is too complicated, it can be roughly described as:
"The relationship between the arithmetic information of the finitely generated Abelian group formed by the rational point set of the elliptic curve E and the corresponding analysis information of the Hasse-Weil L-function L(E, s) in the Taylor expansion of s=1 contact."

Is this easier to understand?
To put it simply, the BSD conjecture is a number theory conjecture about the structure of rational points on elliptic curves. It is also an important conjecture in congruent numbers, and its difficulty is still higher than Fermat's last theorem.

Although in terms of mathematical significance, the BSD conjecture is not as good as the Riemann conjecture, but the difficulty is relatively a little lower, so many mathematicians turned to study the BSD conjecture after attacking the Riemann conjecture to no avail. A large number of mathematical tools, such as the Gross-Zagier formula, is one of the most powerful tools to promote the proof of the BSD conjecture, and it is also the preferred tool for the mainstream research on the BSD conjecture in the mathematics field. At present, [-]% of the results related to the BSD conjecture rely on Gross -Zagier formula.

Now Professor Huffman studies the BSD conjecture from an unprecedented new perspective, from the perspective of matroids and group theory, how can it not arouse the strong curiosity of the audience?
Although Professor Huffman is a great expert in matroids and group theory, and has done in-depth research on the Hodge conjecture, would it be too abrupt to suddenly turn to the BSD conjecture?

In the eyes of countless doubts and curiosity, Professor Huffman stepped onto the podium.

Professor Huffman, who is nearly forty years old, is a typical example of "the less hair you have, the greater your knowledge". Almost all the hair on his forehead has fallen out, leaving only a few sparse strands of hair.He stood still and spoke:

"As we all know, the BSD conjectures of order 0 and order 1 have almost been solved, and for higher order BSD conjectures, it mainly depends on continuing to explore the potential of the Gross-Zagier formula, but there is not enough Brilliant results, obviously using the Gross-Zagier formula to study high-order BSD conjectures is very difficult. I think so, proving that BSD conjectures are inseparable from group theory and elliptic curves, can it be combined with matroids? It took me It took more than half a year to do this research, and then I will talk about my understanding."

Professor Huffman is a typical mathematician who never talks nonsense, and he went straight to the topic without even exchanging greetings.

"Everyone here should know the relationship between the Hasse-Weil function and the Euler product. I just skipped this part and directly used the Euler product..."

Professor Huffman's research results are excellent. He studies the high-order BSD conjecture from another brand-new perspective. Although there is still a long way to go to prove it, he starts with a matroid and combines group theory and Riemann zeta The Gauss conjecture of function and quadratic domain shows a promising new direction.

When the one-hour report was over, there was thunderous applause from the audience, including Faltins, Professor Tao and others, who applauded vigorously while nodding in admiration.

Ning Qingjun sighed softly: "Professor Huffman is so powerful, he is worthy of being called the mathematician who is most likely to win the Fields Medal besides you. Just now he skillfully quoted our hypergeometric mapping method , I have won the essence of it, and there are indeed many strong people in the international mathematics world, and I feel that I still have a lot of gaps with him."

Qin Ke said with a smile: "He is indeed a genius. At least from the report just now, his research on the BSD conjecture has been ranked among the top five in the world. This is the result of his research for only half a year. But you don't have to He underestimates himself. He is a super expert in matroid and group theory. He uses the tools he has studied all his life to think about the BSD conjecture. Of course, there will be more obvious results. If you use the three lime number theory methods to study the BSD conjecture, you will also An impressive result has been achieved.”

Ning Qingyun nodded, and his confidence recovered a little bit. It is true. Professor Huffman has achieved very dazzling results starting from matroids and group theory, but whether this direction is correct and whether the BSD conjecture can be completely proved is still a question. unknown number.

Just like the original "Hardy-Ramanujan System" and "Jacques Solomon Adama System", they have been used by countless people to study the Riemann Hypothesis for more than half a century, and have achieved many amazing results. But in the end it was overthrown by Qin Ke. The direction of these two systems can only be very close to the end of Riemann's conjecture, but what is wrong is wrong. No matter how close it is, it is impossible to reach the real end.

Generally speaking, Professor Huffman's report was very successful, and the biggest highlight was innovation and the profound mathematical foundation shown in it.

From the enthusiastic applause of the audience, it can be inferred that Professor Huffman has more than [-]% chance of locking in a Fields Medal.

In the face of Professor Huffman's "beads and jade", the following academic reports all turned into "bricks", which made people feel lacklustre.

The academic reports on the second and third days were also no such amazing reports. Until the fourth day, Professor Lepe, a famous German mathematician, gave a report entitled "Research on P-ary Hodge Theory". There was a sensation.

This outstanding mathematician, who has won the highest Leibniz Award in the German scientific community and is highly expected by the German mathematical community, made a breakthrough in Hodge's conjecture with his original "p-adic analysis technique". , won almost as much applause as that of Professor Huffman.

A succession of two heavy-weight seed contestants have launched a charge to the seven millennium mathematics problems, and they have achieved excellent results with innovative methods. It can be seen that Qin Ke proved that the Riemann Hypothesis had a great impact on them-now that the seven millennium problems are not the subject of the report, it seems that they are embarrassed to stand on the stage to receive the award with Qin Ke.

The performance of Professor Huffman and Professor Leippe also made many mathematicians who originally wanted to compete for the Fields Medal almost give up, including Professor Maynard of Eagle Country.

Speaking of which, Professor Maynard is indeed a little unlucky. Every time he suffocates his energy and wants to defeat Qin Ke, he is hit again and again, especially at the last Steele Award academic report meeting, he was directly deduced by Qin Ke on the spot Riemann guessed that the situation of the fifth group of expressions was completely devoid of confidence, and he has not been able to fully recover until now.

Facing the excellent performances of the two competitors at this time, Professor Maynard's confidence in winning the award was shaken again. The saddest thing is that his report was just after Qin Ke's report. When he saw the meeting schedule When the schedule was arranged, Professor Maynard even thought about going home.

What supports him to stay now is only the idea of ​​"everything has come" and his last stubbornness as a mathematician.

In the next two days, the mathematicians who presented their reports competed with each other. The Hungarian mathematician Professor Emily Bolivar, who won the Cher Tibor Memorial Medal, and the female mathematician who won the National Science Award Professor Mary Siegel, both of whom performed equally well.

The strong fighting spirit and "big moves" shown by the popular candidates for the Philippine Awards this year overshadowed the performance of the other speakers.

Under such tremendous pressure, Ning Qingyun ushered in her 45-minute report.

Judging from the grades of the report time, the young Ning Qingyun only has the second file of 45 minutes, compared with the first file of the one-hour reports of popular candidates such as Huffman, Lepe, Bolivar, Siegel, etc. inferior.

But Ning Qingyun had already been aroused to fight. She clapped hands with Qin Ke lightly, took a deep breath, moved her legs that were trembling slightly due to nervousness, and walked up to the reporting platform with firm will.

"Hello everyone, I'm Ning Qingyun from Qingmu University in Xiaguo. The topic of my report today is "Research on NS Equations Using Infinite Flow Algorithms for Nonlinear Partial Differential Equations"!"

The girl's soft and melodious voice echoed in the auditorium that could accommodate thousands of people. The audience was slightly startled, and then exploded.

Another Millennium Conjecture!
The report made by Ning Qingjun is not the previous wave guessing, ice guessing, nor the three lime number theory processing methods, but a brand-new, never-before-published research on NS equations!
No one expected that Ning Qingyun would release such a hidden big move!
Professor Siegel, who had been paying attention to Ning Qingyun, changed his face.

At present, many media and academic figures are speculating on the list of winners of this year's Fields Medal. Among them, there are only two female mathematicians in the top ten, namely Marie Siegel, a female mathematician from China, and Xia Guo, a female mathematician. Ning Qingyun!

Among them, the 37-year-old Professor Siegel ranked sixth, while Ning Qingyun ranked ninth.

Professor Siegel understands that when it comes to academic achievements and the number of awards, he is slightly inferior to Ning Qingyun, and his biggest advantage is his age.

This is the last International Congress of Mathematicians where she can win the Fields Medal, and among the female mathematicians of the same age, no one is her opponent.

In addition, no female mathematicians have won awards in the past three sessions.

From the perspective of gender balance and the fact that IMU has always encouraged women to devote themselves to mathematics research, the probability of her winning the Fields Medal is much higher.

In order to stabilize Ning Qingyun, Professor Siegel spent countless efforts and recruited the best graduate students in the school to do research together, and finally formed the "Geometric Analysis and Low-Dimensional Topology in Shimura" reported yesterday. The application of Andre Oort's conjecture in clusters", the applause made Professor Siegel see that the Fields Medal was already waving towards him.

But at this time Ning Qingyun suddenly released a big move, and it was a big move related to the NS equation, which made Professor Siegel feel a chill in his heart.

Andre Oort guessed that both fame and significance were inferior to the NS equation. If Ning Qingyun made any major breakthroughs in the NS equation, her winning rate would drop drastically!

Under Professor Siegel's apprehensive and even terrified eyes, Ning Qingyun began his 45-minute academic report.

This is the first time for Ning Qingyun to stand on such a high-end stage. Almost the most famous mathematicians in the world gather here to listen to her share her latest research results.

Recalling that a few years ago, she didn't even have enough confidence to enter the Olympiad provincial competition, but now she has stood on the stage of the International Congress of Mathematicians, which made her feel as if she had been a lifetime away.

Ning Qingyun knew that it was because Qin Ke had been pulling her away, and she also gritted her teeth and followed closely behind Qin Ke, paying unimaginable hardships and efforts, and countless days and nights of burning light to study hard. Only in exchange for the results.

"Don't worry, I will always be behind you and try my best to be your No.2."

Ning Qingyun met Qin Ke's eyes in the audience, and a strong determination surged in her heart, and her nervous and trembling voice became fluent. She looked around the dark audience, combined with a stylus and PPT display, and presented The lecture script that has already been memorized fluently speaks out.

Non-linear partial differential equations are also the direction that Ning Qingjun is very good at, which is mainly due to studying Goldbach's conjecture with Qin Ke.

The NS equation is a new direction that she has been focusing on for the past six months. The knowledge imparted by Qin Ke with "thinking resonance" and the experience of participating in the "turbulent flow" research group of the old academician Jiang Weixian in the past two months are exhaustive. It turned into a row of gorgeous and eye-catching mathematical formulas at this time.

Qin Ke nodded secretly when he heard this. The outstanding science talent inherited from academician parents, which had been hidden in Ning Qingyun before, has been fully discovered in the past few years of hard work and study, and has made her surpass it again and again without knowing it. My own limit finally bloomed with colorful light at this moment!

After 45 minutes, Ning Qingjun bowed slightly: "...According to the above derivation, I have come to the following conclusion, through the nonlinear partial differential equation infinite flow algorithm, can solve about a quarter of the normal NS equation solving problems. I will continue to study new mathematical methods in the next three years, and strive to achieve greater breakthroughs in NS equations, thank you all, this is the end of my report!"

Responding to Ning Qingyun was a warm applause resounding from the audience.

Although Ning Qingyun, like Professor Huffman and Professor Leippe, failed to crack the Millennium Conjecture, all three of them have achieved important results that no one can ignore in different Millennium Conjectures.

Originally, many people had the impression of Ning Qingyun as "the partner with Qin Ke" and "the girl who was taken away by Qin Ke", but her wonderful performance this year almost made everyone admire her.

This extremely young girl is indeed a mathematician who has reached the top international level!Especially in the direction of number theory and partial differential equations, it will never be inferior to senior mathematics professors in the same direction!
Professor Siegel's face was unconcealably pale. When it comes to her performance at the academic report, she was still inferior to Ning Qingyun after all.

Now there are only two chances for her to win, one is age, the other is nationality...

Professor Siegel was confused, and everyone present was actually thinking about the same problem as her.

"Will the IMU resist the age pressure and give the 20-year-old Qin Ke a Fields Medal, and then give another Fields Medal to Ning Qingyun, who is also only 20 years old from the same country?"

Ning Qingyun walked off the stage, and Qin Ke gave her a light high-five again: "It's great, as expected of my Yun'er."

Ning Qingjun blushed and said in a low voice: "It's your turn next, come on!"

"Don't worry, your excellent performance has given me a lot of motivation."

Qin Ke stood up with a smile and walked to the edge of the stage.

At this time, the host has already read out: "Next, I would like to invite Professor Qin Ke from the Department of Mathematics of Qingmu University and Qiuzhen Academy to give you a one-hour report. The topic of his report is "Conjecture from Hailstorm , Goldbach's conjecture, and the proof of Riemann's conjecture, thinking about the future direction of the unification of mathematics"!"

The auditorium that had just calmed down was like hot oil poured into boiling water, and it boiled instantly!

Math Unity!The No. [-] candidate for the Fields Medal this year actually chose the theme of the unification of mathematics, which has made countless people yearn for and discouraged!