Ready to Make a Move

Ou Ye asked, "How many people are in your team?"

"Mary, a married woman, German, she's a PhD. Jonas, an older single man, Swede, he's a PhD student like me. Professor Muller, I've told you about him, my advisor. The three of them, plus me, make up a team." Shen Qi briefly introduced his team.

"Are they all from Princeton University?" Ou Ye asked again.

"Yes," Shen Qi said.

"But I'm not from Princeton University," Ou Ye with some concern.

"You're my girlfriend, you're the most important." Shen Qi pulled Ou Ye out of bed and to the desk. "You're also a member of my team, even more important than them. You have to work hard, Little Yezi. The proof of the Riemann Hypothesis depends on you."

"Mmm." Ou Ye was in high spirits. Being able to tackle the Millennium Prize Problem with her boyfriend was just too wonderful.

Shen Qi and Ou Ye sat side by side at the desk. Shen Qi guided Ou Ye step by step, imparting core technologies. He made full use of all available resources. His girlfriend also had to contribute. Shen Qi's woman never did anything for free.

Ou Ye was very clever and understood immediately. "So, what I need to do is, for this set of equations, the critical line, Rez equals 1/2."

"Yes, you're great. Let's go eat." Shen Qi finished explaining most of what needed to be explained and went out to eat with Ou Ye.

After dinner, Shen Qi continued to teach Ou Ye core technologies in her room. The two understood and supported each other, striving for a common goal.

Having mastered the core technology, Ou Ye talked a lot with Shen Qi —about mathematics, life, ideals, the future, and even menstruation.

"Oh, Little Yezi, you've started your period?"

"Soon..."

"It's almost done, about 3 days later."

"Shen Qi, you actually plotted against me..."

"Ou Ye, don't you know what I studied?"

"Then... then come downstairs and buy that for me... my stomach hurts..."

What should I buy? Sanitary napkins?

"Um..."

"I'm a man, and in front of everyone, you're asking me to go to the supermarket to buy sanitary napkins!"

"Never mind then."

"Buy it! I'll buy it!"

"Hmm, Qi, you're so kind. This is my card; the PIN is your birthday."

"You have hundreds of thousands of dollars in that card, how many packs of sanitary napkins could you buy?"

"You don't need to finish it all, you idiot."

Then Shen Qi went downstairs and bought five packs of sanitary napkins for Ou Ye. After spending the night there, he left.

At Princeton, Shen Qi's team is operating efficiently.

At Columbia University, Ou Ye is conducting research on core technologies under the remote guidance of Shen Qi.

With the entire team working together, Shen Qi's small goal is to showcase his team's preliminary research results at the Breakthrough Prize & New Horizons Prize conference next month.

Everyone is busy and full of energy.

There is one person who seems to have been forgotten: Zhou Yu'an.

Zhou Yu'an chose Differential Geometry as his main focus. Unlike Shen Qi, he wasn't as well-rounded and could handle any branch of mathematics with ease.

Zhou Yu'an couldn't help with the Riemann Hypothesis or number theory, and he felt isolated.

"Differential Geometry has no future, I see no hope, I want to switch to another field." Zhou Yu'an found Shen Qi and poured out his troubles.

Shen Qi: "Go talk to your advisor and see if he agrees to let you switch."

"I haven't even met my advisor a few times, I'm already doomed." Zhou Yu'an was full of vigor and ambition when he first arrived at Princeton two or three months ago, but now he is a little discouraged.

"Who's your advisor?" Shen Qi asked.

"Professor Faltings," Zhou Yu'an said.

"Professor Faltings has been flying all over the world lately, giving lectures everywhere. It's normal that we don't see him. He's a strong contender for this year's Fields Medal," Shen Qi said.

In Fields Medal year, the hottest topic in the mathematics community is the Fields Medal. Shen Qi encouraged Zhou Yu'an: "Study hard with Professor Faltings. He comes from a background in Differential Geometry. He is your role model. So Differential Geometry is not without a future, but rather has a bright future."

Zhou Yu'an: "Yes, Professor Faltings's background is in Differential Geometry, but he's now obsessed with elliptic and parabolic PDEs. It's difficult to win the Fields Medal if you only study Differential Geometry."

"You understand the principles, so go ahead and do it! Elliptic and parabolic PDEs are popular research topics in the field of Partial Differential Equations. The current popular combination is Differential Geometry + Partial Differential Equations, with the two branches intersecting and complementing each other. I just told you, Professor Faltings is your model, and he is known as an 'enhanced version of Terence Tao.' So Zhou Yu'an, don't doubt your initial choice. The path of Faltings and Terence Tao is the path you will follow." Shen Qi comforted Zhou Yu'an, calming him down and reminding Zhou Yu'an not to forget his original aspirations.

"Differential Geometry + Partial Differential Equations, elliptic and parabolic PDEs, okay, I'll develop along this path." After chatting with Shen Qi for a while, Zhou Yu'an was no longer confused. He was also very curious whether his mentor, Professor Faltings, could win the Fields Medal this year.

Zhou Yu'an cannot help Shen Qi at present, but he holds a special place in Shen Qi's heart.

Number theory is only a part of mathematics, a side job for Shen Qi, and his current team members are all number theorists. He needs fresh blood to cultivate talent for a greater cause in the future.

Based on the first expression of the Riemann Hypothesis ζ(s) derived by the "Shen matching method", Shen Qi improved it within this month, with Mary and Jonas helping him a lot.

"The first expression is crucial; at least we can declare that we have found the correct way to prove the Riemann Hypothesis," said Jonas, a single man in his late thirties from Sweden.

"What about the second expression, Qi? Have you finished the derivation?" asked Mary, a married German woman who was having a fight with her husband but had not yet divorced.

"It's basically complete," Shen Qi said.

"That's great! Then we can declare that we have made a preliminary proof of the Riemann Hypothesis!" Mary exclaimed excitedly. She asked, "When will the manuscript be finalized?"

"I'll handle the final draft. Mary, Jonas, please send me the complete, editable electronic version of the derivation and proof of the first expression," Shen Qi said. "Let's meet again before we go to Washington for the Breakthrough Prize conference."

After repeated confirmation by Shen Qi, the first expression of ζ(s) has become nearly perfect and flawless.

Shen Qi approached Professor Faltings: "Grader, I think the second expression is fine now, and we can combine it with the first expression to complete the draft."

Faltings handed Shen Qi a USB drive. "Qi, just as we discussed last time, I've finished my work on deriving the second expression for ζ(s) using the 'Shen matching method,' making appropriate adjustments to your work."

"Grader, thank you very much." Shen Qi and Professor Faltings worked together to advance the derivation and proof of the second expression, and their collaboration was quite pleasant.