Equation

After a week's stay in New York, Ou Ye's parents prepared to return to China.

Before leaving, Old Ou spoke with Shen Qi alone.

Old Ou said, "Actually, I was firmly against Ou Ye coming to the United States, but she insisted on coming, so I had no choice but to go along with her."

Your objections are invalid, Comrade Old Ou. Your wife is the one who calls the shots in your family. Having grasped the main contradiction, Shen Qi is no longer afraid of Old Ou. Old Ou is just a troublemaker; Madam Ye is the real key figure.

If you anger Old Ou, you'll at most get a beating.

If Shen Qi offends Mrs. Ye, the real estate tycoon, he may never see Ou Ye again in his life.

"Uncle Ou, please rest assured, I will take good care of Ou Ye with my life. She is your daughter and my girlfriend." Shen Qi solemnly made his promise. No matter what, Old Ou was Ou Ye's father, and he had to respect him even if he wasn't afraid.

"Sigh, my daughter's grown up, she'll make her own choices eventually." Old Ou leaned against a tree with a sigh, took out a pack of Marlboros, lit one, took two puffs, and then stubbed it out. "American cigarettes, too hard to smoke."

Old Ou's attitude softened, and Shen Qi pressed his advantage. "I will give Ou Ye the happiest ending."

Old Ou asked, "Let's be realistic, how many years do you and Ou Ye plan to go back to China? You're both 22 this year, and you're not young anymore after you finish your studies."

Shen Qi said, "Actually, I can go back to China after I get my PhD from Princeton this September. It mainly depends on Ou Ye's study progress. Whenever she wants to go back to China, I will go back with her."

"How did you study so fast? You've only been in the US for less than two years, and you've already got your master's and doctorate? Are Princeton degrees that easy to obtain?"

"I don't have any special skills, Uncle Ou, all I can do is study."

"When I first met you, I admired you quite a bit. But after meeting you a few more times, I've developed some opinions about you. Although you have many flaws, I admit you're a genius when it comes to studying and quite clever as a person. My only request now is that you absolutely must not bully or let down Ou Ye, otherwise I won't let you off the hook." Old Ou's body trembled, his words a mix of kindness and severity.

Shen Qi raised a finger. "I swear to mathematics, I will only love Ou Ye for the rest of my life!"

"What's the use of swearing an oath? You have to put your heart into it!" Old Ou scolded, but he could also see that Shen Qi was sincere towards Ou Ye.

Old Ou pulled out a Marlboro and offered it to Shen Qi. This was the first time he had ever offered Shen Qi a cigarette. "Want a smoke?"

Shen Qi waved his hand and said, "No, no, smoking is bad for your health. Uncle Ou, you should smoke less too."

"It's good that you don't smoke." Old Ou put the cigarettes back in the pack and then asked, "Do you drink?"

"Having a little drink occasionally."

"Then I'm relieved. Eating, drinking, whoring, gambling, and smoking—every man has to do one of those. If you don't do any of them and just read books all day like a saint, then I'll think you have a big problem." Old Ou's way of testing Shen Qi was rather special, so it could be considered a final approval. But it still had to pass; Ou Ye had already come to America.

The following day, Old Ou left the United States. They would effectively monitor Shen Qi's commitments through irregular flight checks and random telephone checks.

Ou Ye's room in a Columbia University women's dormitory.

"Come here, let me hug you, Little Yezi." Shen Qi hugged Ou Ye and showered her with affection.

"Ugh... I need to take a shower first... You bad guy... My parents just left..."

"You know what, Little Yezi? I'm about to name a new theorem: Shen Proximity Theorem."

"Wow... amazing..."

"With you not by my side, naming a hundred theorems is meaningless. Thank God you're finally here. Shall we work on a Shen-Euclidean equation together?"

"Okay... in what way?"

"You're best at Diophantine equation, so how about we start with Diophantine equation?"

"Hmm... I can only solve linear equations at most today... I can't do equations of degree or higher..."

Shen Qi spent the night in Ou Ye's dormitory. The young couple, who hadn't seen each other for a year, were naturally very affectionate, and their unspoken understanding in solving equations needed no further explanation.

Ou Ye's physical condition only allows him to solve equations one at most, Shen Qi understands Ou Ye's limitations.

Using techniques to solve equations effectively can help strengthen a mathematical relationship and also promote blood circulation and metabolism.

After daybreak, Shen Qi took Ou Ye to see Ou Ye's mentor, Gong Changwei.

"Columbia feels like your home turf." Ou Ye held Shen Qi's hand. She was the official student in Columbia's Mathematics Department, while Shen Qi was a student's family member.

"I know Professor Gong very well. We've had meetings together, and he was one of my reviewers. He was the one who verified the Wash Conjecture." Shen Qi and Ou Ye walked hand in hand into the Columbia University Mathematics Department building and met Professor Gong Changwei, a number theory expert.

"Senior brother, Professor Gong, I'm entrusting Ou Ye to you. Please guide her in mathematics, especially number theory," Shen Qi said.

"Why should you, Princeton University, worry about our Columbia University's internal affairs?" Gong Changwei said with a smile.

"The eight Ivy League schools are one family; we are all interconnected." Shen Qi smiled as well.

"Hi, Ou Ye, hello. We've interviewed each other via video, so we're not strangers," Gong Changwei greeted Ou Ye.

Ou Ye replied politely, "Hello, Professor Gong, please give me your guidance."

Gong Changwei explained the basic academic requirements for graduate students in the Mathematics Department at Columbia Princeton University. Similar to those at regular universities, Ou Ye needs to attend classes, assist with research, and write papers. It can take one or two years, or three to five years, to obtain a master's degree in mathematics from Columbia University.

After leaving the Mathematics Department building, Ou Ye said to Shen Qi with reluctance, "Qi, you should go back to Princeton University as soon as possible. You've been neglecting your studies too much lately."

"Princeton University's doctoral students are basically left to their own devices. There's only one requirement: coffee every Wednesday," Shen Qi said. "But I still have to go back to Princeton University first. I don't have anything to hold me back from; what I'm worried about is your studies. After all, you're new here, and your studies are demanding. You need some time to calm down and get into an academic mindset."

Ou Ye nodded. "Yes, I will try my best."

"Then I'm leaving. I won't be coming back to Columbia for a month. I'll come see you after a month." Shen Qi kissed Ou Ye goodbye and then drove back to Princeton.

Princeton is a little over an hour's drive from Columbia University, which isn't too far or too close; it's fairly convenient if you have a car.

Shen Qi really had nothing to waste. He had already prepared all the necessary materials for his PhD graduation from Princeton University before Christmas, and now he was just waiting for his dissertation defense.

Although there was no strict requirement, Shen Qi still wanted to do something meaningful, so he began drafting "History of Number Theory," which was his hobby and not a necessary condition for obtaining a PhD.

Number theory studies pure numbers, and because of her pure and noble origins, she is hailed as the "Queen of Mathematics".

Number theory can be divided into two main branches. One is the study of solutions to equations, namely Diophantine equation. This branch dates back to about two thousand years ago and was founded by the great Greek mathematician Diophantus.

Fermat, Andrew Wiles, Faltings and other masters have made contributions to this field. Famous Diophantine equation include Fermat's Last Theorem, Catalan's Theorem and BSD. The first two have been proven, while BSD is extremely difficult and is one of the seven Millennium Prize Problem.

The Wash Conjecture, proved by Shen Qi, also belongs to the Diophantus series. The Wash Conjecture was renamed Wash theorem a year ago and can be directly cited.

Another branch of number theory is Analytic Number Theory, which was jointly founded by masters such as Gauss, Riemann, Euler, Dirichlet, Weyl.

Famous examples in Analytic Number Theory include Gauss's trigonometric sum theorem, Euler's pentagon theorem, the proof of Dirichlet's two prime problem, the Weyl sum formula, Goldbach Conjecture, the Riemann Hypothesis, and so on.

Most of the famous problems in Analytic Number Theory have been solved, with only Goldbach Conjecture and the Riemann Hypothesis remaining to be solved.

Shen Qi attempts to gain a deeper understanding of Diophantine equation and Analytic Number Theory from the perspective of the history of number theory.

Instead of relentlessly attacking until you're sick of it, why not find some inspiration from the great mathematicians of history?