Warm-Up
"Oh, Qi, you've finally solved the Hodge conjecture?" Faltings asked, looking very interested.
"I knew you could do it," Director Feierman said.
"Let's begin," Deligne said succinctly.
Shen Qi began his presentation by playing the PowerPoint slides. "Okay, let's begin. Unlike other teams that attempt to directly prove the Hodge conjecture, our approach is to first establish a system composed of Algebraic Geometry, Mathematical Analysis, and topology, and then prove that the Hodge conjecture is part of that system. The overall idea is similar to Perelman's proof of the Poincaré conjecture..."
The report was extensive and lengthy. Although the recipients were three Fields Medal winners, Shen Qi tried to be as detailed as possible, as this was a completely new report.
Shen Qi's original plan was to finish the report within five hours, but five hours have passed and he still hasn't finished the first part, the AG section.
During the presentation, the three Fields Medal winners asked numerous questions, with the most frequent question concerning Shen Qi's unique definition of "S-type characteristic surface".
Shen Qi had to repeatedly explain the relevant properties and derivation process of the "S-type characteristic surface". He had to make the three Fields Medal winners from Princeton and the Princeton Institute for Advanced Study fully understand his solution.
If even Deligne, Faltings, Feierman couldn't understand Shen Qi's SLW system, then there was no point in holding math lectures for the general public, because it would be even more difficult for others to understand.
Theories that most people cannot understand will not be officially recognized by IMU.
The Hodge conjecture is one of the conditions for Shen Qi to advance to level 15 in mathematics. If he reaches the maximum level, then it doesn't matter. Whether you understand it or not, I, Old Shen, will just do what I love.
However, he hasn't reached the maximum level yet, so Shen Qi needs to make his system public as soon as possible and make most people understand his theoretical system.
The AG team finally explained things to the three bigwigs of the Fields Medal; it was already 10 p. m.
Deligne was old and tired. The old man was exhausted, but he still couldn't hide his excitement. "Qi, let's stop here for today. We'll continue tomorrow. I'm really looking forward to your report."
After seeing off the three bigwigs, only Shen Qi and Ralph remained in the conference room.
Ralph, who was responsible for serving tea, water, and coffee, breathed a sigh of relief. The presence of four Fields Medal winners in a closed conference room created a considerable sense of pressure for him.
"The three of them understood, what about you, Ralph?" Shen Qi asked.
"I'm quite familiar with the AG section, except for the 'S-type characteristic surface'. But after Professor Shen's explanation, I completely understand it. I can only say, wow, what a brilliant and ingenious idea!" Most of the content in the AG section was completed by Ralph and Yu Lei, and after Shen Qi's later refinement, it is already perfect.
"That's good. Ralph, you also deserve credit for the AG section." Shen Qi was relieved. Ralph represented the working class of Mathematics Community; everyone's success is truly the best outcome.
Ralph: "So we're the fastest, right? I've been following the progress of Schultz's team in Germany, and they haven't published any new research results recently."
Shen Qi nodded. "Yes, we should be the fastest."
The following day, Shen Qi continued to explain the TP and AN sections, as well as the SLW system built by integrating the three major sections of AG, TP, and AN.
"Does anyone have any questions about the SLW system?" Shen Qi asked with concern, as this was a very crucial question.
"All the doubts have been resolved. This new system, which includes Algebraic Geometry, topology, and Mathematical Analysis, is without problems." Deligne stood up, walked to Shen Qi, and shook hands with him. "It's a pity that a mathematician can only receive the Fields Medal once in his lifetime. Otherwise, your name would be on the Fields Medal list again next year, Qi."
"Would the IMU make an exception?" Director Feierman said.
"No, they won't. They're even more conservative than this old fogey." Deligne shrugged and walked toward the conference room door.
"Hey, Professor Deligne, my report isn't finished yet. The last part is proving that the Hodge conjecture is a special case of SLW," Shen Qi shouted to Deligne's back.
"No need to prove it to me. In my opinion, the SLW system makes more sense Hodge conjecture." Deligne turned back, smiled, waved, and left.
Shen Qi returned to his reporting position and asked, "Director Feierman, Professor Faltings, would you be willing to listen to the last part of my presentation?"
"Listen, why won't you listen?"
"Continue, Qi."
Deligne, the grand slam Deligne of the Fields Medal, the Wolf Prize, and the Abel Prize, has a higher level of understanding; he came with high expectations and left when he was satisfied. Director Feierman and Professor Faltings, on the other hand, are more down-to-earth; they are itching to see the final outcome.
Next, Shen Qi demonstrated to Director Feierman, Professor Faltings, and Ralph why the Hodge conjecture is part of the SLW system.
"... In conclusion, Hodge conjecture has been fully proven." Shen Qi concluded his departmental report.
"Beyond imagination yet perfectly reasonable," Faltings clapped his hands in praise.
"The Mathematics Department will immediately arrange a mathematics lecture, inviting mathematicians from IMU and other research institutions to attend," Feierman said, looking excited but also a little reluctant. "Qi, as I said, you will always be Princeton's best alumnus. Thank you for your contributions to Princeton over the past five years."
During his studies and tenure at Princeton, Shen Qi proved the Wash Conjecture, the Muller -Shen theorem, Shen Proximity Theorem, the Riemann Hypothesis, Goldbach Conjecture, and three other related conjectures, winning ten Math Prize and achieving remarkable results.
Hodge conjecture has just been proven by Shen Qi and will soon be announced to the world.
As his colleagues all know, the Hodge conjecture is Shen Qi's last gift to Princeton. Shen Qi will announce to the world as a Princeton mathematics professor: The Hodge conjecture has been solved.
If someone wants to go home, no one can stop them.
Everyone knows this principle; it's human nature.
Faltings said to Director Feierman, "Charles, there are too many 'best alumni' awards. Shouldn't you give Qi a special gift, like Honorary Professor at Princeton?"
"The department head cannot appoint Honorary Professor; that requires a decision from the university board of trustees." Dean Feierman shook his head, indicating his limited authority.
"However..." Feierman then changed the subject, saying, "Solving two Millennium Prize Problem in succession is unprecedented in the History of Mathematics. It's remarkable. Although I am not qualified to directly award you the title of Princeton Honorary Professor, I have the right to propose it to the Board of Trustees."
"Hurry up and make the proposal, Charles. You'll be stepping down as department head in a few months." Faltings meant that if you don't have the power, you'll be struck by lightning.
"I will make the proposal immediately after Qi's public presentation." Feierman suddenly realized something: if Princeton offered Shen Qi some incentive, such as a tenured Honorary Professor, then Shen Qi would be inextricably linked to Princeton for life. "Qi, get ready. Your public presentation on the Hodge conjecture will take place in as little as a week. I assure you, this will be the largest academic conference in the history of Princeton."
"Received!" Shen Qi rubbed his hands together, eager to ensure the success of the meeting. To this end, he sent the condensed version of the paper on the SLW system and the proof of the Hodge conjecture to arVix.
The full paper is 221 pages, while the abridged version is 103 pages. The abridged version serves two purposes: first, to claim that the team led by Professor Shen Qi of Princeton has been the first to prove the Hodge conjecture.
Secondly, it gives the international Mathematics Community some advance time to preview the main content of this paper, so that everyone is well-informed and avoids feeling like they are listening to gibberish at the presentation, which would be very embarrassing.
Feierman, on behalf of the Princeton University Mathematics Department, issued a wide invitation to renowned figures in the international Mathematics Community to travel to Princeton soon to discuss important matters, and the organization of the conference was proceeding intensively.