No Possibility

"Our Princeton team's research topic is 'Algebraic Geometry Methods for the Hodge conjecture.' The core idea, as shown on the screen, is to decompose each projective variety into irreducible branches and consider the set of affine zeros..."

"... Professor Schultz's report was excellent, but I think the most brilliant part was the combination of Algebraic Geometry, Mathematical Analysis, and topology. First, the system was established, and then it was proven that the Hodge conjecture is a special case within that system." Shen Qi paused for a moment here.

The audience responded enthusiastically; building a system first and then verifying individual cases is the consistent approach of these masters.

Notable examples include Perelman's proof of the Poincaré conjecture and Wiles' proof of Fermat's Last Theorem.

Perelman first proved the Thurston's Geometrization Conjecture system, and then proved that the Poincaré conjecture is a special case of the system.

Wiles first established the Elliptic Curve model system, and then proved that Fermat's Last Theorem was a special result among them.

"This is a massive project, and we have made great strides every step of the way, but we have also achieved some results. I hope to share all our research findings as soon as possible, not today, but in the near future. Thank you, that concludes my report." Shen Qi finished his ten-minute report, having achieved his goal of making an appearance and generating buzz, as he had not spoken publicly on the international mathematics stage for quite some time.

After the meeting, a reporter interviewed Shen Qi: "Professor Shen, do you think your team will complete the proof of the Hodge conjecture before Professor Schultz's team?"

Shen Qi: "The order isn't the key issue; the key is to completely solve the problem. After all, the Hodge conjecture has puzzled us for decades, and it's time to give the correct answer."

Reporter: "Is it possible to collaborate with Professor Schultz's team on the Hodge conjecture?"

Collaborating with Schultz? Wow, this reporter has a broad perspective.

This reminded Shen Qi. Yes, cooperation? Why can't we cooperate? There's no irreconcilable hatred between me and Schultz, like killing my father or mother. Schultz's plan is quite innovative. Deep cooperation between two top teams will surely make us invincible.

"Impossible," Shen Qi said, shaking his head.

Forget it, let's not cooperate with Schultz. If everyone is invincible, wouldn't the world be in chaos?

Meanwhile, another group of reporters interviewed Schultz: "Professor Schultz, is it possible that you could collaborate with Professor Shen's team to jointly tackle the Hodge conjecture?"

Schultz answered without hesitation, "Impossible."

Related media reports covered the main content of this international mathematics conference, highlighting that three top mathematics teams —Shen Qi Team from Princeton, Schultz's team from the University of Bonn, and Viduka's team from the ENS Paris —are all making their attempt to solve the Hodge conjecture, Millennium Prize Problem.

The solutions from Shen Qi Team and Schultz's team have attracted the most attention. Although both teams only provided abstract versions, it was enough to garner significant attention from the international Mathematics Community.

Shen Qi and Schultz are renowned award-winning Mathematics Community, having won over 20 Math Prize combined, and their combined age is less than 60 years old—an astonishing statistic.

Both individuals, known for their excessive spending on prizes, stated that they would not cooperate with each other in any field.

Reports indicate that Schultz's ex-wife, Mary Schmidt, was a member of Shen Qi Team, and that she worked with Shen Qi to prove the Riemann Hypothesis.

When asked about his private life, Shen Qi generously said that he loves his girlfriend very much, the two will get married in the future, and he hopes to have two children, a boy and a girl, which would be the best outcome.

Schultz declined to discuss his private life, turned and left, refusing to answer any further questions.

Shen Qi and his two students returned to Princeton. Yu Lei and Ralph participated in their doctoral defenses as planned. Their Doctoral Thesis together were titled "Algebraic Geometry Methods Based on the Hodge conjecture," while when separated, they were two independent papers.

Yu Lei's strengths lie more in the combination of Complex Analysis and Algebraic Geometry, while Ralph incorporates Algebraic Geometry based on Abstract Algebra.

Independence is relative. There is inevitably some overlap between the two dissertations of Shen Qi's two doctoral students, with several pages being almost identical.

It's not a big problem. This situation between fellow students doesn't constitute plagiarism, and the Princeton defense committee members are aware of the background of the research topic.

The defense went very smoothly. Yu Lei and Ralph received their PhDs from Princeton in just two semesters. The entire graduate and doctoral program took six semesters, or three years.

The fastest record at Princeton is held by Shen Qi, who earned his PhD before the end of his fourth semester at Princeton, completing his master's and doctoral studies in less than two years.

The person who was faster than Shen Qi in the world was Schultz. Schultz did not go through a doctoral program; he obtained his doctorate directly from a master's thesis.

For Shen Qi at this stage, it doesn't matter whether he's fast or slow. Life is long, and the real test is yet to come.

Shen Qi mentored two PhD students in one go, which essentially completed his professorship in the Princeton Mathematics Department.

"I spent five and a half years in the Princeton Mathematics Department. The first two years were spent studying, the middle six months were spent as a lecturer, and the last three years were spent as a professor. I published in the Big Four accounting firms, published a monograph, proved several conjectures, won some awards, and mentored two PhD students. I have no regrets, and I hope you two will have bright career prospects," Shen Qi said to Yu Lei and Ralph.

"Professor Shen, are you trying to get rid of us?" Dr. Yu Lei didn't want to leave.

Shen Qi waved his hand. "Go back to where you came from."

"I came from Tsinghua University, so am I going back to Tsinghua University?" Yu Lei still has a lot of affection for Shuimu University.

"Has Tsinghua University sent you an offer? If not, I can arrange for you to work at Peking University." Shen Qi, Visiting Professor at Peking University, has this connection; arranging for a mathematics PhD from Princeton to work at Peking University would be a piece of cake for him.

Yu Lei said, "People from Tsinghua University have contacted me, saying they're going back through the overseas talent recruitment program, but we haven't discussed the specific details yet."

"Hmm, Tsinghua University has done a pretty good job. The talent introduction program provides housing, settlement allowances, and start-up funds for research projects." Shen Qi expressed his satisfaction. His students had returned to China, so they should enjoy certain benefits.

"Professor Shen, I owe everything I have today to you," Yu Lei said sincerely. He was very young, a year younger than Shen Qi.

"You've also put in your own effort." Shen Qi smiled, then asked Ralph, "And you, where are you going? Where do you want to go?"

"I've spent almost all of my adult life at Princeton, and I don't know where I would go if I left Princeton." Ralph completed his undergraduate, master's, and doctoral studies in the Princeton Mathematics Department, making him a true Princeton University mathematician.

"Did they send you an offer?" Shen Qi asked.

Ralph said, "Yes, I've decided to stay at the university and start as Mathematical Research."

"Good luck, Ralph." Shen Qi patted Ralph on the shoulder. He had many students, and the first batch of doctoral students he mentored all found good jobs.