"The question of number theory and functional analysis can be asked now. For other areas of mathematics, I welcome you to come to me at any time after the tutorial is over. ”

Shen Qi emphasized the rules, the 2-hour tutorial time should focus on number theory and functional analysis, otherwise if you ask a sentence, he will ask about geometry, and the class order will be chaotic.

"Okay, then I don't have a problem. Applejack shook her head, he wasn't interested in number theory and functional analysis, but these two courses were compulsory for math students, and it would be nice to get credits all in all.

"Odd, I have a question, number theory. "At this time an Arab student spoke, his name was Muhammad, and according to him, his family was very wealthy when he was a child, he received a good education, but then he was poor by the war, and he dropped out of school for more than a year.

"Speak your doubts, Muhammad. Shen Qi stood in front of the blackboard and made a gesture of please.

Muhammad is a few months older than Shen Qi, and he has just joined Shen Qi's tutorial class this semester, so he doesn't worship Shen Qi as much as Applejack and the other four.

Muhammad said: "I have consulted Riemann's manuscript, and he writes in the manuscript that these properties of the ζ(s) are derived from one of its expressions, but I have not been able to reduce this expression to a form that can be published to the public. ”

"That's right, this is Riemann's original text. Shen Qi nodded, he had studied Li Man's manuscript no less than a hundred times, and he was familiar with it by heart.

"So, can you tell me what form of the unpublished expression mentioned by Riemann in the manuscript?" Muhammad asked.

"Muhammad, that's a wonderful question!" Shen Qi's eyes lit up, and then he smiled helplessly: "If I can write this legendary expression, I will be able to give a report for at least 45 minutes at this year's International Congress of Mathematicians." But unfortunately, to this day, I have not received an invitation from the IMU. ”

"It seems that the work of proving the Riemann conjecture will continue for another 100 years. Muhammad spread his hands and said that he had not received a satisfactory answer and was slightly disappointed.

Regarding the expression in Riemann's manuscript, Shen Qi really couldn't answer, and if he made up this expression, he would not be far from proving Riemann's conjecture.

Whether or not this expression, which Riemann refers to as "not reduced to the point of being published to the public", really existed, and in what form, ever existed is a mystery in the history of mathematics.

The study of Riemann's manuscript has lasted for more than a hundred years, and mathematicians believe that even if the expression is not reduced to its most perfect form, it is still important to decipher RH, after all, it represents the core idea of Riemann himself.

The god-level masters in the history of mathematics have a small problem, that is, they like to play pranks, they perfectly set the stage for the foreplay that makes people want to burn, and then there is no more.

The Fermat Terrier is "too little space in the book" and the Riemann Terrier is "not reduced to a form that can be published publicly".

These two stalks, Shen Qi has been included in his "History of Number Theory", around the Fermat terrier, he will write a whole volume of "Fermat and Fermat series of conjectures".

The material is already available, most of the important and famous Fermat series have been proven, and all that remains is to spend time combing through and writing as interesting and professional as possible about the history of number theory in Fermat's period.

Shen Qi also collected a lot of materials around the Riemann Terrier, but the most critical problem is that the Riemann conjecture has not been fully proven, and the volume of "The Riemann Conjecture and the Riemann Conjecture" cannot be completed perfectly, and may be forcibly ended in the end.

It is irresponsible to write the history of number theory without writing the Riemann conjecture and the Goldbach conjecture.

However, all the books about Li Chai and Gochai in the world are to introduce these two conjectures, so that readers know the nature of Li Chai and Gochai, and there is nothing dry.

Shen Qi wanted to write something dry, but his level was limited, and in the end, his "History of Number Theory" may have become a mere formality and became a hydrology.

After finishing the tutorial, Shen Qi went to the Flint Library to consult Riemann's manuscripts again.

The flint library alone has 70 miles of bookshelves in the main building, all of which are open.

Readers can enter the library to check the books and periodicals they need, from first-year freshmen to Nobel and Philippine Prize professors, from support staff to principals.

Copies of ordinary books and published papers can be borrowed, and rare books, ancient books, and manuscripts cannot be borrowed, but they can be read in the reading room.

The original Riemann manuscript is in German and is in the collection of Germany.

The Flintstone Library of the University of Pulpa houses manuscripts in English, translated by von Neumann himself during his tenure at the University.

Von Neumann was an all-rounder, knowing everything about mathematics, computers, nuclear weapons, and biological weapons, and he was at the top of his game.

The English version of Riemann's manuscript translated by von Neumann is only 8 pages, and Shen Qi can already memorize it backwards, so he will study it again today, carefully reading word by word, trying to figure out Riemann's mind more than a hundred years ago across time and space, hoping to find even the slightest clue.

There is only one sentence in the Riemann conjecture: "All the complex zeros of ζ(s), i.e., all zeros of ξ(s), are on the straight line σ=1/2." ”

Riemann himself did not prove this conjecture, and if he succeeded, it should now be called Riemann's theorem.

For the Riemann conjecture, Riemann gives an important prediction of the property of ζ(s), which is now known to everyone:

π^-s/2γ（s）ζ（s）=π^-（1-s）/2γ（1-s）ζ（1-s）

However, Riemann himself said: "These properties of ζ(s) are derived from one of its expressions, but I have not been able to reduce this expression to a form that can be published to the public." ”

So this expression that needs to be simplified is the key to the key, and it is the key to cracking the Riemann hypothesis.

Actually, my previous thinking was not wrong, I tried to find the two recursive expressions of ζ(s), which coincided with Riemann's derivative logic. Riemann, Riemann, what form is this undisclosed expression that you are referring to?"

Shen Qi stayed in the library for a night, and seemed to get a little inspiration.

But this inspiration is very ethereal, Shen Qi can't concretize it, and the derivation, imagination, and judgment of the 11th level of mathematics are still a little low, if only it could be upgraded to 12 levels.

Back at the accommodation apartment, Shen Qi brushed the submission system of "Mathematical Inventions".

"Collected!"

Shen Qi was pleasantly surprised, he really had his wishes come true recently, and he wanted to do whatever he wanted.

The paper "Shen's Nearness Theorem" has been officially included in Mathematical Inventions, one of the four major journals.

It must be included, Professor Witten and Director Fefferman have confirmed that there is no problem with the "Shen's proximity theorem".

The two Filipino Award winners said that there was no problem, then it must be no problem.

System: "New Achievement!Congratulations to the host for publishing a paper in Mathematical Inventions, one of the four major mathematics journals, with a basic reward of 50,000 Xueba points, multiplied by the IF value of the journal of 3.331, and then multiplied by the mathematical master talent coefficient of 2.0, the final reward amount is 333,100 Xueba points. The balance is 2021400 points, please confirm with the host. ”

"These 300,000 points are just in time. Shen Qi expressed satisfaction.

At present, "Mathematical Inventions" includes the paper "Shen's Nearness Theorem", but it has not been officially recognized by the IMU.

After a while, IMU admits the "Shen's Nearness Theorem", and there should be follow-up Xueba point income.

"Mathematics is promoted to a higher master. Shen Qi took out 1999862 points and upgraded mathematics to level 12.

Level 11 and level 12 require 2 million Xueba points, and Shen Qi has recently accumulated 138 points of math experience through the accumulation of daily experience points, so it is enough to smash 1999862 points of Xueba.

System: "Congratulations to the host for raising the mathematics level to level 12, and the host's logical deduction, observation, judgment, imagination, memory and other indicators in the field of mathematics have been significantly improved compared with the previous level. ”

Host, Shen Qi

Age, 22 years old

Mathematics level 12, 0/4 million

Physics Level 6, 1123/150,000

Sports level 5, 3019/50,000

CET-5, 987/50,000

Language level 5, 999/50,000

Politics level 5, 1360/50,000

Chemistry grade 3, 502/5000

Mob level 3, 520/5000

History Level 2, 1139/3000

Geography Level 2, 689/3000

Balance of student points: 21538 points

Level 11 is a master, level 12 is a senior master, level 13 is a top master, level 14 is almost invincible, and I am so lonely at level 15.

Shen Qi, who was successfully promoted to a senior master of mathematics, suddenly got that ethereal inspiration, which seemed to be able to be concretized: "I thought of it! I thought of it! I thought of it! Riemann in 1859, he probably wanted to deduce ...... like this."