The auditorium of MIT has a long history. It is said that many modern and contemporary historical celebrities have given speeches here, including the Fields Medal, the Turing Award, and the Nobel Prize.

The old gentleman also stood on the podium of this auditorium.

On the afternoon of August 12, the sun was shining brightly, and fine dust was flying in the light coming from the window.

Qin Ke stepped on the beams of lights, stepped over the steps step by step, and stood where countless celebrities had stood.

The commotion and chaos in the audience finally stopped temporarily after repeated persuasion by the staff.

There were two to three thousand spectators in the venue. These spectators included mathematics professors from famous universities around the world, as well as invited mathematicians from mathematics research institutions, as well as the top ten in the world, including "Annals of Mathematics" and "

The editors-in-chief of professional academic journals such as Journal of Mathematics and New Advances in Mathematics, as well as the editors-in-chief of many academic publishing houses, the HR of some well-known large companies, the president of MIT, and all the teachers of the Department of Mathematics

Staff and student representatives.

Of course, media reporters from various countries also account for more than 200 places, but they generally do not have seats and can only observe and shoot.

From the time Qin Ke walked to the podium to when he stood still, the cameras in the hands of these reporters never stopped making a slight "kacha" sound. Fortunately, the venue did not allow flash, otherwise Qin Ke's eyes would have been blinded by the flash.

As Qin Ke stood on the podium, slight commotions and whispers broke out again among the two to three thousand spectators present.

"Is what Dr. Ning Qingjun said just now reliable? Dr. Qin Ke derived the last set of expressions of the Riemann Hypothesis? I just checked on arXiv and didn't find any new pre-collected papers uploaded by "".

"

"I don't know, I haven't heard anything about it before."

"Three nights ago, Dr. Qin Ke ran a long-distance run on the sports field of this school. He ran 30 kilometers and then passed out from exhaustion. Could it be that he got the inspiration at that time? I heard that running to preach was his stunt.

.”

"No way? Dr. Qin Ke seems to have been sleeping. I heard a reporter asked the staff at noon and said that Dr. Qin Ke was not awake yet and was not sure whether he could attend the afternoon report meeting. Even if he had inspiration, he would not

Maybe the derivation can be completed so quickly?”

"Shh, be quiet. Stop guessing. Everyone is standing on the podium. We will know the answer soon."

I only heard the host loudly say: "Now, let's invite this year's Steele Prize winner, Dr. Qin Ke from the Department of Mathematics of Xia Guoqingmu University, to give us an hour-long academic report! Everyone welcomes it with applause!"

The audience burst into thunderous applause, and the host immediately walked off the podium, leaving only Qin Ke standing on the podium.

Qin Ke lowered his hand and the applause quickly subsided.

Facing countless eyes, Qin Ke turned to the microphone and began his great report in English that was destined to shock the world.

"n, good afternoon everyone, I am Qin Ke, a Ph.D. from the Department of Mathematics, Qingmu University, Xia Guo. Thank you all for coming to listen to my academic report. The topic of my report today was originally the proof of Goldbach's conjecture, but more than an hour ago

, I temporarily changed my mind and changed the topic of the report to "Complete Proof of the Riemann Hypothesis"..."

There was a commotion in the audience again, and Qin Ke pressed his hand again and continued: "I also said it at the previous academic lecture of the Crafford Prize. In my research system, the Riemann Hypothesis has a total of five sets of expressions.

expressions, the later expressions involve a wider range of topics, and the derivation becomes more and more difficult. I have completed the derivation of the first four sets of expressions, but I encountered great difficulties in the last set of expressions. Various methods and

No way of thinking can go deep into the essence of the Riemann Hypothesis."

"In order to solve these difficulties, I decided to learn German on my own and found all the academic works and original handwritten notes of Riemann that I could find in the world to study. In order to find inspiration, I also went for a night run three days ago.

"

"When my physical strength was close to the limit but my mind was extremely clear, I finally grasped the most critical key to unlocking the mystery of the Riemann Hypothesis. Unfortunately, I fell asleep directly because I was too tired, and I slept until noon today. Now, I

My spirit has been fully restored, and I decided to use this key here to complete the derivation of the fifth set of expressions of the Riemann Hypothesis on the spot!"

"To be honest, I'm not 100% confident whether it can be successfully deduced, but I want to try it!"

boom!

The whole place exploded again!

It turns out that Qin Ke had not completed the derivation before. He had just woken up, and he wanted to deduce the last set of expressions of the Riemann Hypothesis live here!

Countless people were stunned, and countless others were dumbfounded.

No one has ever tried to prove a conjecture on the spot with just one possible idea on such a serious and important occasion, let alone the most important and famous conjecture in the world!

The reporters excitedly took pictures and the cameras recorded the whole process.

Qingmu University originally arranged to go abroad with Qin Ke, associate professor Sun Liwen, who was Qin Ke’s old partner. However, Sun Liwen’s child happened to be born, and he took parental leave to take care of his wife and young son, so the school sent another one named Feng

Wanhua’s accompanying teacher.

Feng Wanhua was also checking the camera in his hand repeatedly at this time. Because he was too nervous, his hands were shaking. He kept praying in his heart that his camera must not malfunction, otherwise he would miss such a historical moment.

He was about to become the sinner of Qingmu University. At the same time, his heart was so excited that he almost burst out of his chest. If he could record such precious historical materials, it would be of great benefit to him when he was promoted to associate professor in the future. He didn't see Sun Liwen because of the filming.

After downloading the videos of Qin Ke’s lectures, he was promoted to associate professor!

Not only the media and reporters, but also everyone among mathematicians was surprised.

Faltings stood up in disbelief: "He...he wants to deduce it on the spot?"

Professor Tao was equally surprised and delighted. He clapped his hands and said softly with a smile: "Professor Wiles guessed it right. This guy is really going to have a big surprise, and a big surprise for the whole world!"

Wiles calmed down instead. He frowned and said worriedly: "Qin Ke is reckless this time. It can even be said to be reckless. If the on-site derivation fails, it will be a huge blow to his honor and reputation!"

When Professor Andrew Wiles was proving Fermat's Last Theorem, he did encounter a hurdle that was almost impossible to pass. Because of a small problem that arose during the proof, he spent half a year unable to solve it. Later, he failed to solve it in the huge problem.

Under pressure, he was so depressed that he wanted to publish an apology in the newspaper, admit failure, and give up the honor of being the first to prove Fermat's last theorem. Only with the encouragement and support of his colleagues did he return to research, and finally succeeded a year later.

Using a new mathematical method that combines Iwasawa theory and Fletcher's method, this small gap was solved, completely and perfectly proving Fermat's conjecture, turning it into "Fermat's Last Theorem".

No one knows better than him the difficulty of proving a great conjecture, and a small problem may cause the train of thought to be interrupted.

Now Qin Ke's report will only last about an hour. Even if he only derives the last set of expressions, it is also the most difficult expression in the Riemann Hypothesis!

I don’t know how many mathematicians have followed Qin Ke’s ideas in the past six months and conducted arduous research on the basis of the first four sets of expressions that have been published, trying to derive the last set of expressions, but no results have been published yet.

Since then, not even one mathematician has publicly claimed to have achieved certain results.

The difficulty of the last part of the Riemann Hypothesis is evident.

In Wiles' mind, even if Qin Ke had a clear idea, he would have to spend at least a month or two carefully pondering the details before he could complete the entire derivation, rather than under such immature conditions.

Under the pressure of countless people watching, I forced myself to complete the entire derivation process within an hour!

As a senior mathematician who cared about Qin Ke and appreciated Qin Ke, Wiles really did not want to see Qin Ke take such a risk.

But Linden Strausch next to him smiled and said: "Professor Wiles, you have a psychological shadow because of your experience back then? If you hadn't been forced into a desperate situation, I'm afraid you wouldn't have been able to prove Fermat so perfectly.

Theorem. I think Qin Ke is imitating you, planning to fight against the odds and unleash his full potential. Look at his expression, his fighting spirit is burning in his calmness. This is a real full-out attack."

Wiles observed Qin Ke's expression, still unable to conceal his worry: "I hope he can succeed."

Not only Faltings and others, but also many mathematicians

Analyzing Qin Ke's probability of success in a low voice.

Especially those who come to "find out the enemy's situation" and are popular candidates for this year's Fields Medal.

The famous Chinese mathematician Professor Lai Pei, the American Professor Huffman, the Hungarian mathematician Professor Emilie Bolivar, the American female mathematician Mari Siegel, and the American mathematician Mei Mei from the Department of Mathematics of the University of Oxford.

Professor Nader and others were all present. At this moment, several of them had serious expressions on their faces, staring at the stage without blinking, with only one thought in their minds: "Can he succeed?"

Seeing that the situation was about to get out of control again, Qin Ke hurriedly pressed his hand for the third time, and the buzzing in the audience finally subsided.

"Okay, everyone, please sit down, sit down where you are, and please be quiet. Next, I will start the derivation of the fifth set of expressions."

Qin Ke held the writing pen in his hand and took a deep breath. The huge pressure from behind made him subconsciously close his eyes.

Yes, just as Professor Linden Strausch guessed, Qin Ke is forcing himself to unleash his full potential.

If the first four sets of expressions are mainly due to the knowledge provided by the system, then Qin Ke plans to complete the derivation of this last set of expressions entirely by relying on his own mathematical knowledge and mathematical thinking.

But he is not in the special state of "inspiration amplification" now. He can only capture the remaining ideas and key keys from that time to carry out this derivation.

To this end, he must stand on the edge of the cliff and stimulate his full potential to complete this most difficult and greatest derivation process.

In addition to the huge pressure, Qin Ke could not hide his excitement.

It has been more than three years since he was exposed to the Riemann Hypothesis in the third year of high school. During this period, he received a notebook recording erroneous attempts from his teacher Shi Cunyuan and read countless materials in order to understand the "Complete Explanation of the Riemann Hypothesis" given by the system.

”, the notes he took and the draft paper he wrote were probably piled up to more than two meters.

And now, today, here, he is very likely to bring a perfect conclusion to this most difficult and meaningful pure mathematical proposition in human history.

Let's get started, officially reach the pinnacle of mathematics, and pick that extremely bright and extremely sweet fruit!

Qin Ke opened his eyes, holding a pen in his hand, and his eyes fell on the writing board.

When he focused all his thoughts and energy on the derivation, everything disappeared. The noise and gazes around him, the possible consequences of success and failure, all disappeared in his mind.

There is nothing else but the Riemann Hypothesis!

Qin Ke slowly and firmly wrote the first line of calculations.

"dy∫(?X/?x)·∑ (X)ds..."

In the audience, countless attentive eyes were focused on the big screen, following the movement of his pen tip. Many people also took out paper and pens to do calculations and deductions on the spot.

As the lines of calculations were written out like a flowing stream, the mathematicians in the audience couldn't help but whisper to each other.

"Hey, this is the spherical representation of complex numbers? Riemannian geometry is also used."

"Yes, the previous dozen calculations are all based on the Riemann sphere. They are just connected with the fourth set of expressions, and they gradually begin to involve the fields of complex numbers and differential geometry."
To be continued...