Confirmed by the Paper-It Was You

Before coming to the United States, Allen Muller taught at the University of Bonn in Germany, where Mary Schmidt was an undergraduate in the Mathematics Department University of Bonn was Muller's student.

After graduating from the University of Bonn, Dr. Mary Schultz -Schmidt came to the Princeton Mathematics Department to serve as Muller's teaching assistant.

Mary's surname changed from undergraduate to doctoral student.

She married a man named Schultz while she was pursuing her doctorate, so her current name is Mary Schultz -Schmidt, and she is wearing a wedding ring on her finger.

"Dr. Schultz -Schmidt, you've dyed your hair blonde?" Shen Qi asked tentatively.

"It was originally gold, but I dyed it red when I was doing my PhD in Germany," Schultz -Schmidt said.

The profile picture posted online by the German female PhD student is so heavily photoshopped that she looks exactly like Nicole Kidman, even with a halo effect. She has the face of Cate Blanchett, but the photoshopped image makes her look like Nicole Kidman.

"Your doctoral dissertation is brilliant. I've read it many times. The Evitzer proof of the Diophantine equation is a stroke of genius." Shen Qi couldn't make eye contact, so he could only confirm the dissertation.

"This is thanks to your effective algebraic approximation, Shen Qi."

Schultz -Schmidt smiled knowingly, "I cited your algorithm on page 7 of my doctoral dissertation. Strangely, you removed your paper from arVix shortly afterward, and it hasn't been formally published since. We'll be working on the same team from now on; you can call me Mary."

That's right!

The paper has been verified!

It's her!

It's because of you, German woman, that I failed to keep my promise. The paper I promised Ou Ye has not been published yet, while you're so arrogant and smug!

"It's a pleasure to meet you, Mary. Your beauty would make any other woman in the world envious." Shen Qi smiled and took the initiative to shake hands with Mary. Even if he was unhappy inside, he had to maintain his composure.

"Does that include your girlfriend?" Mary shook hands with Shen Qi. Her demeanor was mature, and her personality differed from that of the more independent Muller and Jonas.

Shen Qi continued smiling, "My girlfriend is an angel."

"Hehe." Mary and Shen Qi's first exchange ended there.

Jonas sipped his coffee, seemingly unconcerned about the subtle undercurrents and sharp exchanges between Shen Qi and Mary.

Muller seemed quite interested. "Mary, Shen Qi, do you know each other?"

"We've been friends even though we've never met." Shen Qi spoke calmly and concisely, recounting his past experiences with Mary regarding their thesis.

By seniority, Mary was Shen Qi's senior, but Shen Qi felt that this mature German senior was not cute at all; she had a strong aggressive nature.

"So there's this story between you two," Muller said. "Getting back to the point, let's begin today's meeting. Jonas, start by talking about your Doctoral Thesis."

Jonas picked up his coffee cup and said calmly, "My Doctoral Thesis will take some time to complete. Yes, I'm thinking about it."

"You've been thinking about this for two and a half years, and you haven't written a single word or published a single paper," Muller, offering only a reminder and not urging him on.

"I need some time. Yes, I need time. In mathematics, the thought process is more important than the final result." Jonas took a sip of coffee, found it a bit bitter, and added some sugar.

"Okay, Jonas, you're right. Please continue thinking." Jonas wasn't in a hurry, and neither was Muller. Professor Muller agreed with Jonas's point of view; thinking was a very important thing. Andrew Wiles, who once taught at Princeton University, thought for ten years without publishing a paper until he proved Fermat's Last Theorem.

Princeton's academic atmosphere is indeed very tolerant; the Princeton University's broad-mindedness accommodates all kinds of eccentric scientists, fanatics, and even mental patients.

In the Oscar-winning film "A Beautiful Mind," Russell Crowe successfully portrayed the brilliant mathematician Nash.

Nash, who suffered from mental illness, had a true story that took place in Princeton, and he eventually won the Nobel Prize in Economics.

Princeton University only offers arts, sciences, and engineering programs; popular fields in the US such as business administration, law, and medicine are not included in Princeton University's academic curriculum.

Since its founding in the 18th century, Princeton University has never offered programs in business, law, or medicine—disciplines that are highly sought after in the job market.

This research university prioritizes academic research and gives little consideration to utilitarian matters.

So Jonas can stay at Princeton University for as long as he wants; there's no rush.

"And Mary, what about you?" Muller then inquired about Mary's research progress.

Mary opened the folder and formally handed Muller a written report, unlike Jonas just gave a perfunctory response.

This detail reveals Mary's meticulousness and procedural nature. She said, "My project is progressing according to plan, although I've encountered some minor troubles. I should be able to make significant progress before the Christmas holidays."

Muller quickly reviewed Mary's report, which was actually an unfinished mathematical paper. "Mary, you've put in a lot of hard work these past few months, but it seems you haven't seen anything new. Forgive my bluntness, but the current arguments and proofs in this paper are clearly outdated, even somewhat tedious. Over a hundred years have passed, and all the methods have been exhausted. We must stimulate innovative thinking to have any chance of cracking RH."

"Professor, you're absolutely right." Mary was a little disappointed, but she didn't lower her proud head.

"RH?" Shen Qi, who was listening in, was inexplicably excited. There aren't many abbreviations for RH in the Mathematics Community. Mary studies number theory, and in the field of number theory, RH stands for the Riemann Hypothesis.

The Riemann Hypothesis, one of the seven Millennium Prize Problems in mathematics.

In 1858, Riemann, a professor at the University of Göttingen, proposed the famous Riemann Hypothesis in an eight-page paper on the distribution of prime numbers.

One or two hundred years have passed, and as Muller said, mathematicians have racked their brains and exhausted all the methods they could, but RH has still not been fully proven.

"Yes, just as you understand, Shen Qi, RH is the Riemann Hypothesis." Muller handed the paper to Shen Qi and said casually, "This topic is quite challenging, but also very interesting."

Shen Qi took the paper and read the abstract and introduction. He was extremely excited. Professor Muller's team was launching a fierce offensive against RH!

The core of the Riemann Hypothesis is the Riemann zeta function ζ(s) = Σn^-1 (Re(s) > 1), whose properties are a powerful tool for solving number theory problems and play a crucial role in Analytic Number Theory. It has always been a hot topic in Analytic Number Theory research.

It is well known that the distribution of prime numbers in the natural number system does not follow any pattern. However, Riemann observed that the distribution of prime numbers is closely related to the function ζ(s): all the complex zeros of the function ζ(s) lie on the vertical line σ=1/2.

If this conjecture is correct, then there will be a pattern to the distribution of prime numbers, and many problems in number theory will be easily solved.