Visiting His Senior and Seeing His Girlfriend
Columbia University, Gong Changwei's office.
"Shen Qi, you come to our school quite often." Gong Changwei leaned back in his chair, twirling a pencil between his fingers with practiced ease. His hair was thinning, but his pencil-twirling technique was becoming increasingly refined.
"First of all, congratulations, senior! I think you have a good chance of winning the Fields Medal this year." Shen Qi poured himself a glass of water; he and Gong Changwei were quite familiar with each other.
"Let nature take its course," Gong Changwei said, but his eyes told Shen Qi that he wanted to win the Fields Medal.
This year, three Chinese mathematicians received invitations from IMU to give 45-minute presentations at the International Congress of Mathematicians. The three mathematicians are Gong Changwei, Yun Wei, and Xu Yang. All three graduated from the Mathematics Department at Yenching University, where they completed their undergraduate studies.
The International Congress of Mathematicians, held every four years, is the highest-level conference in the Mathematics Community. Mathematicians who are eligible to receive this year's Fields Medal will inevitably have to give a presentation at this International Congress of Mathematicians.
The report specifications are divided into four levels, from highest to lowest: 1 hour, 45 minutes, 30 minutes, and 15 minutes.
According to convention, mathematicians who have given a presentation at the previous or the one before that International Congress of Mathematicians, and are invited by the IMU to give a one-hour presentation at the highest level at this congress, have a very high chance of winning the Fields Medal.
Rumor has it that nine mathematicians worldwide received invitations to give a one-hour presentation at IMU this year.
This year's four winners of the Fields Medal are very likely to be chosen from these nine people, all of whom have been speakers at the previous two conferences.
Why does Shen Qi believe that Gong Changwei, who qualified for the second-tier 45-minute report, also has a chance to compete for the Fields Medal?
Among mathematicians under the age of 40, Gong Changwei has reached the pinnacle in the field of number theory.
Yun Wei and Xu Yang both specialize in Algebraic Geometry, a very popular field. In previous Fields Medal, more than one-third of the awards have been given to mathematicians in Algebraic Geometry.
Popular fields mean fierce competition. Among the nine mathematicians who received the highest level of treatment (one hour) at this conference, three specialize in Algebraic Geometry. Yun Wei and Xu Yang face extremely fierce competition.
Therefore, Shen Qi felt that Gong Changwei had a chance to cause an upset, and of course he hoped his senior would win the award.
If Senior Brother Gong can pull off this impressive feat and become the first Chinese mathematician to win the Fields Medal, Shen Qi will congratulate him.
"Sigh, it's actually quite difficult. All the breakthroughs in number theory have been made, and the breakthroughs that can't be made remain elusive." Gong Changwei stopped twirling his pen. This year is his last time competing for the Fields Medal. In the next four years, he will be over forty.
"Never give up hope, senior brother, maybe we'll pull off an upset," Shen Qi said. "Ou Ye has become your apprentice, and if you win the Fields Medal, Ou Ye will benefit too. On behalf of Ou Ye, I sincerely wish you success in winning the Fields Medal."
"I'm not eating this dog food!" Gong Changwei laughed and asked, "By the way, Shen Qi, what did you want to see me about? You didn't come all the way from Princeton University just to show off your love here, did you?"
"No, no, I came here specifically to ask you about some professional questions." Shen Qi casually picked up a piece of white paper from the table, pulled out a pencil, and wrote down his "Shen matching method" and the first expression. "Senior, please give me your guidance."
Gong Changwei took the blank paper and looked at it. He was shocked by what he saw. "This... this... this is what you came up with?"
"I came up with the initial idea, and now there's a team in our Mathematics Department at Princeton University working on this project. I'd say I'm the actual person in charge of it," Shen Qi said.
Gong Changwei took off his glasses, wiped them, and put them back on. He then carefully studied Shen Qi's manuscript, becoming increasingly surprised as he studied it. "So, Shen Qi, by taking two non-obvious zeros that match the features and cleverly handling variables and complex variables, you derived an important expression for the Riemann Hypothesis ζ(s) in a completely innovative way. This expression is very convincing! And what about the second one? There should be a set of similar expressions, right?"
My senior colleague is indeed a top expert; his words hit the nail on the head. Shen Qi became excited. "We haven't gotten the second one out yet!"
"You're still so happy even though you didn't finish it?" Gong Changwei returned the manuscript to Shen Qi.
"So you agree with my approach, senior brother," Shen Qi said. Columbia University and Princeton University's Mathematics Department each have their own strengths, and the top number theory experts at both Columbia and Princeton University agree with Shen Qi's approach, which makes Shen Qi even more confident.
"Why didn't IMU invite you to give a presentation? With this piece of paper in your hand, even if it's a half-finished proof of the Riemann Hypothesis, you'd be qualified to attend the conference. I, Gong Changwei, have been studying number theory for so many years since graduating from Yenching University, only to find out that my biggest competitor is actually you, Shen Qi!" Gong Changwei was both amused and exasperated, yet he was also deeply impressed by Shen Qi's ingenious ideas.
"Senior, we'll never be rivals. This year's Fields Medal is impossible for me, and next year..." Shen Qi stopped abruptly, realizing he had said the wrong thing.
"I won't be eligible to compete for the Fields Medal next year," Gong Changwei said. "But it's okay. We mathematicians don't study mathematics for the sake of winning awards, but because we love mathematics. The younger generation surpasses the older, and I look forward to Shen Qi and your team finally proving RH. As a contemporary mathematician, it's a privilege to witness RH being conquered."
"Senior, for the next hypothesis, I hope to collaborate with you." Shen Qi said sincerely. RH had no choice; this was a key project of Princeton University, and it would be awkward to explain to the organization that they had brought people from other universities into the research group, unless they were family members.
"Take care of RH first. Hey, Shen Qi, do you need me to ask IMU for you? I think you should be on the meeting. Even though you're young, you can make an exception. You should at least get 15 minutes to perform."
"Your new proposal hasn't been officially published yet. A conference report is the most suitable opportunity to showcase it. By the time the journal finishes its review, it will be ages. Can a problem like RH be solved in less than a year or two?" People who study science and engineering generally have one advantage, or rather, one disadvantage: they are honest and like to help others, like Gong Changwei.
"Director Feierman went to inquire for me," Shen Qi said.
Gong Changwei felt he was overestimating himself. "Fine, never mind. The IMU president was a student of your director Feierman. Feierman was already teaching at the University of Chicago when he was your age."
"Even Fei the Boss has students like this, the president of IMU?" The longer Shen Qi stayed at Princeton University, the more he realized how immense Princeton University's connections and influence were. In theory, it was possible for such an organization to mobilize the entire university to either promote an academic star or bury an unknown genius.
The international academic and Mathematics Community also have their own circles, and fortunately, Shen Qi is doing quite well in them. He respects professors, unites with classmates, and treats students in the tutoring program kindly. His reputation has spread, and he is well-liked by everyone. Big shots appreciate and support him.
After all, Princeton is a place where academics are paramount. As long as you're not too unlikeable or have extreme religious beliefs, young people with strong academic abilities are more likely to succeed.
Shen Qi checked the time; Ou Ye would be out of class in two minutes. He asked, "Ou Ye, it's been a month since you enrolled. Have you caused any trouble for me, senior?"
"She won't cause any trouble. She's quite well-behaved; she hasn't left the campus in the month since she arrived at Columbia."
A few minutes later, in the girls' dormitory.
Columbia University's graduate student dormitories for women don't have any dormitory supervisors or similar positions. You need to scan your fingerprint to enter through the main door on the first floor, so it's relatively safe, unless a female student brings a criminal into the dormitory.
Ou Ye swiped her fingerprint and led Shen Qi into the girls' dormitory, to her room.
"How have you been feeling lately?" Shen Qi asked, sitting at Ou Ye's desk, his head down as he wrote something.
"I'm taking my medicine on time, and everything is normal," Ou Ye said.
Shen Qi: "I have a new set of equations. Can you help me solve them?"
"A degree equation?" Ou Ye asked.
"A quadratic equation." Shen Qi wrote down a set of equations in Ou Ye's notebook.
"A quadratic equation..." Ou Ye took a few steps back, retreated to the bed, hugged the blanket, covered her head and face, looking very nervous.
"What are you doing under the covers? Come on, Little Yezi, come out and solve the equations." Shen Qi turned around, picked up his notebook, walked to the bedside, and patted Ou Ye under the covers.
Ou Ye peeked out and saw the equation in the notebook. "Ah, solve this quadratic equation?"
The notebook contained a system of quadratic equations based on the "Shen matching method." Shen Qi explained, "To analyze the Riemann Zeta function, I need you to do an extremely important task: starting with the zero-point equations, find the third expression. The calculations are extensive, which is why I'm asking how you are feeling."
Ou Ye peeked out, clearly interested in the zero-point equation Shen Qi had written, "The second expression, is it finished?"
"After I return to Princeton University, I will work with Professor Faltings to solve the second expression, and you, Ou Ye, will assist me in completing the third expression." Shen Qi held Ou Ye's small hand and encouraged her, "Although you have just entered graduate school, I believe that under my guidance, you can perform at the level of a doctoral student. Even Mary is not as good as you at pure prime number calculations."
"And who is Mary?" Ou Ye asked.
"Mary is my colleague, anyway, you're better than her," Shen Qi said.