Make a Little Trouble?

Shen Qi quickly wrote down a blackboard full of formulas. He explained, "Regardless of whether it's the first or Second Kind Reciprocal Sequence Relation, we can perform a summation transformation. Consider the influence matrix on the sequence (f), then substitute it into the expression of f(n) and change the order of the summation..."

"... After some simplification, using the First Kind Reciprocal Sequence Relation, we can obtain g(k) = (a; q)k/(b; q)k(b/qa)k. In other words, this special case also applies to the Second Kind Reciprocal Sequence Relation, so the Second Kind Reciprocal Sequence Relation holds."

"Does anyone have any questions?" Shen Qi asked, facing the audience.

"Impressive." Xiao Tao had no choice but to admit defeat. He was most familiar with this topic of Infinite Series, and he was completely convinced.

Today was the first time Shen Qi had seen this topic. He immediately came up with a new solution and even conjectured and proved the Second Kind Reciprocal Sequence Relation.

Shen Qi is a few years younger than me, and this operation is amazing... Xiao Tao understood immediately, and the problem that had been bothering him for more than a year was solved on the spot by Shen Qi.

"The Second Kind Reciprocal Sequence Relation holds true, so by letting a and b take special values, we can easily obtain the transformation formulas for the two basic Hypergeometric Series!" Xiao Tao exclaimed, suddenly enlightened.

"I see." Director Wu stroked his chin and breathed a sigh of relief; the problem was finally solved.

Director Wu earnestly said, "Since Professor Shen is here, why don't you stay at our center for a few more days? We still have many questions we'd like to ask you."

Shen Qi nodded. "Let's spar."

Over the next few days, Shen traveled back and forth between the hotel and the Morning Star Mathematics Center.

Director Wu and the researchers were highly enthusiastic about their studies. They divided into several groups according to the nature of their projects and took turns seeking advice from Shen Qi.

"Engineer Zhu, why didn't you stay at Hunan University or find a job at another university after you graduated with your doctorate? Why did you come to the center as a researcher?" Shen Qi would chat with the researchers while solving problems, which would help them get to know each other better.

Engineer Zhu said, "There's a lot of infighting in schools, it's really upsetting. Actually, I worked at a university for two years, and it was incredibly frustrating. At that time, the center was recruiting researchers, so I simply quit my job at the university and came here for some peace and quiet. The academic atmosphere at the center is much purer. Including Director Wu, there are only about twenty of us who are dedicated to front-line Mathematical Research. Each of us is responsible for a specific area, and we can't even cover everything. If there's no need to fight for positions, there won't be any infighting."

"That's right, you've hit the nail on the head." Shen Qi understood Engineer Zhu's indifferent attitude towards worldly affairs very well. Where there is a struggle for interests, there will inevitably be competition and even struggle. Some people choose to fight their way out, while others retreat to a quiet life. Everyone has their own ambitions.

"Professor Shen, I study topological linear spaces. Could you take a look at this topic for me...?"

"No problem, no problem, it's like this, it's like this..."

"Master, you truly are a master! Listening to Professor Shen's words is worth more than reading books for ten years!" Engineer Zhu benefited greatly.

"Engineer Qin, you're only a few years older than me, and you already have two children. That's impressive!" Shen Qi met another researcher surnamed Qin.

"I'm a very boring person. All I do is math and take care of kids." Engineer Qin was in his early thirties, with thinning hair and a kind face.

Shen Qi asked, "With two children at home, the financial burden must be quite heavy, right?"

Engineer Qin smiled, tired but happy. "It would be a lie to say I have no pressure, it's the pressure of happiness."

"Engineer Qin, your research topic is in the field of Probability Theory." Shen Qi flipped through the materials that Engineer Qin had brought.

"This problem has troubled me for many years. Bernoulli's law of large numbers, Chebyshev's law of large numbers, and Khinchin's law of large numbers—these three laws of large numbers, set according to the limit model, I still can't figure them out. Is it because I haven't mastered the trick?" Engineer Qin humbly asked for advice.

Shen Qi gave him instructions. "I have some insights into the law of large numbers, especially Bernoulli's law of large numbers. Here's how, and so on..."

Engineer Qin was initially shocked, then clapped his hands in delight. "Wonderful, wonderful! Professor Shen, you are no ordinary person!"

The researchers at Morning Star Mathematics Center are a relatively simple group of people, Shen Qi quite enjoys interacting with them.

Within a few days, Shen Qi demonstrated remarkable proficiency in numerous fields, including Infinite Series, topological linear spaces, Probability Theory, and Harmonic Analysis, covering a very wide range of areas.

Researchers privately commented on Shen Qi: "Shen Qi's mathematical ability is almost unparalleled; he's a once-in-a-century all-around mathematician!"

The last question was raised by Director Wu himself, "When a, b, and c are Advanced Mathematics, there is a problem that remains unsolved. This Diophantine equation only has positive integer solutions: x=y=z=2. Professor Shen, what are your thoughts on this problem?"

This... Old Wu, so you're also studying the Yesmanovich Conjecture... Shen Qi frowned and pondered, seemingly stumped.

Old Wu asked a good question, a brilliant one. The Yesmanovich Conjecture was Ou Ye's doctoral research topic.

Director Wu closely followed the popular research directions in the international Mathematics Community. His research topic overlapped with that of a doctoral student at Princeton University Princeton Mathematics Department, who happened to be Shen Qi's girlfriend.

Great minds think alike. The Morning Star Mathematics Center invites renowned mathematicians to give lectures every year, and Director Wu and the researchers have an international perspective, which is commendable.

After proving the Lê Conjecture and the Goldbach Conjecture, Shen Qi hadn't touched number theory for a long time; the Yesmanovich Conjecture is a number theory problem.

Even though he lived with Ou Ye, Shen Qi never gave her any specific technical guidance on Ou Ye Yesmanovich Conjecture. He only knew that Ou Ye was studying the Yesmanovich Conjecture.

If Shen Qi goes all out, proving the Yesmanovich Conjecture wouldn't be difficult for him. He could easily do it by giving his girlfriend, a PhD student at Princeton University, or the director of the Morning Star Mathematics Center a little hint.

"It's tough, really tough." Shen Qi was conflicted. Earning these 2 million from you guys was really hard. If I sell my girlfriend, she might fall seriously ill.

Director Wu knew that many number theory teams were studying the Yesmanovich Conjecture, but he was unaware that Shen Qi's girlfriend was one of them.

"Actually, it was our fault. Professor Shen has been working too hard these past few days. Everyone gets tired and exhausted. More than twenty of us have been asking you questions every day, exhausting your inspiration. It was our fault, and we are very sorry. Professor Shen, I have no more questions. Let's put the Jesmanovich conjecture on hold for now." Director Wu was an honest and soft-hearted man.

"Understanding is everything," Shen Qi said. "I'm human, not a god. I have my limitations too. I really can't solve the Yesmanovich Conjecture, please forgive me, Director Wu. Apart from the Yesmanovich Conjecture, I can help your center solve any other problem."

Director Wu looked troubled. "But we have no problems for now. You've solved everything that needed to be solved... except for the Yesmanovich Conjecture."

Shen Qi said resolutely, "If there are difficulties, we must overcome them; if there are no difficulties, we must create them and overcome them!"

Director Wu boldly asked, "Then... then shall we create some difficulties?"