An Invitation from the Courant Institute
"To prove the Hodge conjecture, I designed three sections. The other two sections, which start from topology and Mathematical Analysis, are mainly tackled by teams from Yenching University and the Morning Star Mathematics Center. This joint approach was only decided half a month ago, but this idea has been in my mind for a long time."
Shen Qi explained the overall framework of the Hodge conjecture project. Ralph and Yu Lei felt that this project was getting bigger and bigger, and it was very exciting.
For the next period of time, Shen Qi spent every day on the lawn in front of the mathematics building engaging in outdoor academic exchanges with Ralph and Yu Lei, discussing project advancement plans and specific technical details.
With their thinking becoming clearer and clearer, Ralph Yu Lei made rapid progress and were full of enthusiasm under Shen Qi's careful guidance.
When lecturing outdoors, he can be seen by the students and faculty coming and going at Princeton.
The news spread like wildfire, and soon the entire Princeton knew that Shen Qi and his two doctoral students were working on the Hodge conjecture.
At an internal exchange meeting of the Mathematics Department, Shen Qi reported to the department on his overall ideas regarding the Hodge conjecture, with Princeton University as the lead academic institution and Yenching University and the Morning Star Mathematics Center as the collaborating academic institutions.
There's nothing to hide. At Princeton, each professor is responsible for their own area of expertise, raises their own funds for academic research, and collaborates with whomever they want. The school's main performance indicators for professors are the quality and quantity of their academic works, the amount of academic grants they receive, and the number of PhDs they receive.
Shen Qi served Princeton during the day and returned to his faculty dormitory at night, where he secretly studied the theoretical relationship between Riemann Theorem and quantum communication keys. No one could help him, and he didn't need anyone else's help; helping would only cause more trouble.
The Riemann Theorem and the theoretical system of the prime number distribution of the Riemann zeta function are widely known. Shen Qi elaborates on them in his academic monograph, "History of Number Theory." This book has been on the market for more than a year and has brought Shen Qi more than one million US dollars in revenue.
The theoretical framework of Riemann Theorem and the prime number distribution of the Riemann zeta function, and the quantum communication key system—how to establish an effective mathematical connection between these two systems—are important issues facing Shen Qi.
"This is really brain-teasing, this task is challenging." Shen Qi chewed on his pencil, staring blankly at a pile of messy symbols on the draft paper.
In another corner of the study, Ou Ye was biting another pencil, her brows furrowed, racking her brains over her Doctoral Thesis.
Shen Qi knew that Ou Ye's Doctoral Thesis was related to the Yesmanovich Conjecture, and Ou Ye also knew that Shen Qi was researching quantum keys in secrecy.
The two didn't inquire about the specific details of each other's research topics, and it would be pointless for Ou Ye to ask, as she wasn't an expert in Quantum Physics.
Shen Qi also did not provide Ou Ye with any technical details regarding the Yesmanovich Conjecture in number theory.
Because Ou Ye a goal: she would prove the Yesmanovich Conjecture on her own.
"Many concepts in Quantum Physics are completely different from those in classical physics, but there is only one thing in common: the mathematical language is universal in both Quantum Physics and classical physics," Shen Qi muttered to himself, seemingly having found a spark of inspiration.
"Jeremiah, positive integer solution, Luca number even," Ou Ye murmured, her inspiration striking.
"I've come up with a solution. In the Quantum Theory system, we can use Differential Equation as a breakthrough point to establish a new functional expression. It will serve as a bridge, ultimately connecting to the theoretical system of the prime number distribution of the Riemann zeta function!" Shen Qi was amazed by this stroke of genius and exclaimed with delight. He had finally found a directional solution. The next step was to derive and verify it.
"Luca number even, standard decomposition, algebraic integer ring!" Ou Ye was in superb form tonight; she knew how to prove the Yesmanovich Conjecture!
In the same study, the two men were researching completely unrelated topics, but this did not prevent them from doing their own research and making progress on their respective projects.
A few days after Shen Qi determined the research direction of Riemann Theorem and quantum key distribution, the Courant Institute of New York University called and invited Shen Qi to attend an academic exchange meeting at the Courant Institute. The theme of the meeting was "Application of Riemann Theorem and the theory of prime number distribution of Riemann zeta function".
Princeton Mathematics Department is a temple of fundamental mathematics, Courant Institute at New York University is a center for applied mathematics.
Shen Qi accepted the invitation and visited the Courant Institute at New York University.
The director of the Courant Institute warmly received Shen Qi, and then the "Riemann Theorem Application Research Group" conducted specific academic exchanges with Shen Qi. The group leader was American applied mathematician Kevin Stari.
Professor Kevin Stari is an applied polymath; he holds a PhD in mathematics and a PhD in communications engineering, and also has profound expertise in Computer Science and Material Science.
There were four people sitting in the conference room: Shen Qi, Stari, and Stari's two assistants.
Stari said, "Professor Shen, all members of our Riemann Theorem Application Research Group are here. Let's get to today's topic."
"Are you kidding me? You only have three people researching the applications of Riemann Theorem? That's far too few." Shen Qi felt that Stari was not being honest. According to international practice, research teams engaged in applied research often have more members than those engaged in basic theoretical research.
Back then, Shen Qi's team consisted of eight people. It took them one or two years to complete the proof of the Riemann Hypothesis, which was eventually renamed the Riemann Theorem Riemann Hypothesis.
Professor Stari now tells Shen Qi that our Courant Institute's application team has dispatched three people to study the application techniques of Riemann Theorem.
"OK, Professor Stari, let's begin," Shen Qi said calmly. In truth, he was also very interested in how far the Courant Institute, which had long held the top spot in applied mathematics rankings, had progressed in its research on his Riemann Theorem theory.
"Wait a minute, I remember now. I recently read a paper whose core idea was that quantum chaotic systems include all prime numbers as components of their systems. The institution listed was the Courant Institute at New York University, and there were three authors..." Shen Qi suddenly realized that one of the authors of that paper was named Kevin Stari.
"That's right, it's the three of us," Stari laughed.
"Are there no other researchers?" Shen Qi asked.
"It's just the three of us, Professor Shen." Stari maintained his polite smile.
Shen Qi looked surprised. "Wow, you three are Lujalig, Bebirus, and Gibela from the Courant Institute, the best lineup in history!"
Stari and his two assistants laughed heartily, "Thank you for the compliment. So Professor Shen is also a New York Yankees fan."
Arriving in New York, if you're running out of things to talk about, the New York Yankees are the perfect topic. Shen Qi just been idly flipping through a baseball magazine when he came across a list of some of the greatest players in New York Yankees history, and he immediately put his knowledge to use.
After some initial probing, the two sides moved on to the topic of academic exchange.
Shen Qi guessed that Stari's team had encountered problems in applying Riemann Theorem.
If there's trouble, they'll call on Shen Qi, the prover of Riemann Theorem. If everything goes smoothly, Courant Institute produces research results, they'll put them directly into application.
Stari said sincerely, "Professor Shen, we have encountered some trouble in the application research of Riemann Theorem. After repeated verification, we found that the root of the problem lies in the insufficient understanding of the theoretical prototype. Therefore, we sincerely invite you to come and hope that you can answer our questions about the theoretical prototype."
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