The seven-thousand-year-old math puzzle is really hard to crack.

At present, only the Poincaré conjecture has been overcome, and the Russian mathematician Perelman has thoroughly proved the Poincaré conjecture on the basis of the mathematical genius Lu Qiujian.

The Riemann hypothesis was proposed in the 19th century, spanned the entire 20th century, and is still alive and well in the 21st century.

Any mathematician who studies number theory has the desire to prove that RH will go down in history.

Just as difficult as Gochai's proof process was, RH has not been fully proven for three centuries.

Gochai's 1+1 has not been proven, but Mr. Chen Jingrun has proved 1+2, which is the closest result to Gochai.

One step completely proves that RH and Gochai are not easy things to do, and history says it all.

Mathematicians have been working on phased proofs of RH for centuries.

With regard to the representation of the Riemann zeta function ζ(s), for any complex number, if Re(s) > 1, then:

ζ（s）=Σn^-s=∏（1-p^-s）^-1

where n is a natural number and p is a prime number.

Mathematicians have tried all the means and exhausted all means, from Euler's classical formula to Bernoulli's number, and then to Ramanujan's formula in the case of positive odd numbers, and finally made important phased progress, and the special cases of k = 3, 5 and k = 4, 6, 7 have been recognized by all contemporary mathematicians.

Now, there is still a bridge between the milestones and the full proof of RH.

The key bridge between the previous and the next is the two recursive formulas of ζ (2n+1).

If the two recursive formulas of ζ (2n+1) can be proven, then Shen Qi believes that Professor Muller's team is not far from finally proving RH.

What excites Shen Qi is that the semi-finished paper in his hand is a proof of the two recursive formulas of ζ (2n+1).

The framework of the paper was set by Mill, and the specific arguments proved to be written by Mary.

It was clear that Professor Müller was in the right direction, but Mary's tactical execution had little effect.

Mary's tactical play is too old-fashioned, and RH should have been fully proven based on your calculations to prove the derivation logic, but it is not. Shen Qi returned the manuscript to Mill and said: "We need a new lemma to prove that the conclusion at k=1 is true, then the two recursive formulas of ζ (2n+1) are expected to be reasonably derived, so as to launch a general attack on the complete proof of RH." ”

"Hey, kid, I thought about it too!" Mueller's eyes lit up and he looked at Shen Qi.

"We?" Mary looked at Shen Qi questioningly, and then said as a matter of course: "Yes, we, this is a topic that Alan and I are jointly researching. ”

"Mary, I have a bold idea to invite Shen Qi to join our team and work together on the topic of ζ (2n+1). What do you think?" Mueller was very democratic, and he politely asked his student Mary.

"I think we should maintain the status quo because there's nothing wrong with the status quo. Mary gave a strange expression.

"I would love to join Prof. Müller's ζ (2n+1) research group. Shen Qi ignored Mary's questioning expression and directly expressed his determination to Mueller.

"Your main focus is mathematical physics, and your secondary direction is algebraic geometry. Shen, don't tell me you want to add another number theory direction. Mary said coldly.

"Professor Müller is my idol, he is proficient in mathematical physics, algebraic geometry, number theory, group theory and many other fields. My second assistant chooses number theory, which is not bad for me and the whole team. Shen Qi replied.

"Shen Qi, if your girlfriend agrees with you to minor in number theory, I have no problem, I told you before, why don't you choose number theory, after all, you are a student praised by Elon. "Muller intends to have Shen Qi work with Mary.

"She'll agree. Shen Qi couldn't miss the opportunity to conquer RH with the mathematics research team of the University, and Ou Ye would definitely agree and support him in doing so.

"Mary, why don't you give Shen Qi a chance, you need his help. You also admit that you have actually collaborated once when Shen Qi's algorithm was cited in your doctoral dissertation. "Shen Qi was an amazing student, he published ten mathematical papers in two years. Mary, the number of papers you and I combined during our undergraduate years is exactly half that of Shen Qi. ”

Mary was expressionless, but finally agreed to Mueller's proposal, after all, Mueller was the boss of the team.

"Then Shen Qi, from now on you are Mary's assistant, I wish you a happy cooperation. Mueller gave final instructions and adjourned.

Shen Qi has obtained a document on the ζ (2n+1) project, and he has an ambitious and mature idea, and he will use an innovative idea to complete the proof of the two recursive formulas of ζ (2n+1).

"You'd better not mess with me. Mary invited Shen Qi to the campus café for coffee, and the two spent time alone to exchange plans for the next step of the project.

"Mary, do you think I look like a mess guy?" Shen Qi asked rhetorically.

"Who knows?" said Mary, noncommittal.

"If I'm a mess guy, so are you, and your PhD thesis cited my algebraic approximation algorithm. If you had done this algebraic approximation by yourself, you might have just graduated with a Ph.D. right now, or you wouldn't be graduating until next spring. This algebraic approximation algorithm doesn't work out in a few months. Shen Qi stated the facts, and this Diophantine equation Walsh conjecture essay incident has always been a pain in his heart.

"The paper on the Diophantine equation Walsh conjecture is a thing of the past. Mary said lightly, "Tell me, how do you want to carry out the next work of the ζ (2n+1) project?"

Professor Müller's framework remains the same, and the concrete argument proves that the overturn is repeated. Shen Qi said firmly.

"Are you sure?" said Mary with a sneer.

"Pretty sure. Shen Qi nodded resolutely, "Mary, I know you're very busy, and you have to take undergraduates' tutorials and correct their homework and exam papers. If you don't mind, I'll do the new discourse on the ζ (2n+1) topic alone, and I'll finish it before Christmas, rest assured, the co-first author will have your name. ”

"Hahaha. Mary laughed, her stomach aching from laughter, as if she had heard the most ridiculous joke in the world.

"Arrogant, ignorant, incorrigible. Mary pulled a $10 bill from her beautiful lady's purse, pressed it under her coffee cup, and got up to leave.

"Coffee, I please. After a few steps, Mary turned back and said, "But there are only two co-first authors, me and Professor Müller." ”

"Then each has its own powers. Shen Qi spread his hands and said.

"Hmph. Mary left coldly, and her cooperation with Shen Qi did not look pleasant.

Shen Qi published a total of 10 papers during his time at Yan University, and it is this rich scientific research experience that makes him the only graduate student in China to enter the Department of Mathematics of General University this fall.

Shen Qi is the first author or co-first author of all ten papers.

A paper can have more than one author, and the authors below the paper name are sorted from left to right, and the first author is in the first position.

Shen Qi once marked his and Ou Ye, Sun Erxiong, and Lu Guozhen's names behind them, and the marks represented the identity of the co-first author.

Then there is the second author, the third author......

If you don't write a paper as the first author or co-first author, then you still write a ghost.

Shen Qi couldn't accept that his name was ranked after the first author, or the co-first author.

Mary didn't wait to see Shen Qi, there was no way, Shen Qi could only do it alone.