Tong Gexiao was really angered by Li Yi's unreasonable request, so the fourth test paper she gave Li Yi was not a student's test paper at all, but a collection of exercises about Riemannian geometry. Pen × fun × Pavilion www. ｂｉｑｕｇｅ。 ｉｎｆｏ

Riemannian geometry is a geometry beyond Euclidean's geometric system, and the basic axioms are different from normal geometry.

Euclidean geometry tells us that there is only one straight line parallel to the known straight line, but in the world of Riemannian geometry, there will be no straight line parallel to the known straight line, i.e. any two straight lines of the same plane intersect in this geometric system.

In such a mathematical structure that is different from the real world and has twisted rules, all the problems become plausible and require a lot of brain cells.

Tong Gexiao likes Riemannian geometry very much, she is studying for a doctoral degree at Capital Normal University, and the research direction of her graduation thesis is Riemannian geometry, that is, the questions on this test paper are the research content of doctoral students majoring in mathematics.

Moreover, for Tong Gexiao, an in-service doctor, this set of Riemann geometry exercises is a bit super difficult, she doesn't know the first few questions, and she didn't come up with it for several days, so she happened to meet the rampant Li Yi, so she threw it to him.

Aren't you capable? I even dare to ask the teacher for that kind of request! Since you are so capable, you can do Riemannian geometry, and if you can even do this, the teacher will admit it!

In Tong Gexiao's view, no matter how superb Li Yi's mathematical ability is, it is impossible to master Riemannian geometry. As a high school student, being able to solve the Olympiad is already a demon among demons, and if you can solve a problem that even a doctoral student can't solve, then what can you do?

However, Li Yi surprised her again!

The math problems of Riemann geometry, in Li Yi's eyes, are actually kindergarten-level math problems, which are not much different from the previous papers.

If you think about it, kindergarten children will think that the "two plus two equals four" topic is much more difficult than "one plus one equals two", and the fingers will be more than two, but adults will not feel that there is a difference between these two topics. At Li Yi's level, there will be no difference between Riemann geometry and "one plus one equals two", both of which are the most basic things.

When the question was in hand, he wrote down the answer like a cloud, without even a pause!

Tong Gexiao opened his big eyes and watched Li Yi write down the equation quickly, and he could almost put a duck egg in his mouth!

Oh my God, the first question turned out to be like this, so ingenious, I didn't think of it!

The second question actually needs such a function transformation, which is too genius!

Question 3...... Hey, why can't I understand this step, what kind of thinking is this?

When Li Yi finished writing the entire question collection, Tong Gexiao was still staring at the third question, studying how Li Yi did it!

"This is mainly a tensor analysis method......" Li Yi saw Tong Gexiao's puzzled expression, and casually explained two sentences.

"Huh?" Tong Gexiao suddenly realized, it turned out that this question was like this!

Then her eyes when she looked at Li Yi completely changed. Who is this sacred, even Riemann geometry is so slippery? Mathematics undergraduates won't be so good!

And such a great man is actually her student, and every math score is in single digits, can you believe it?

Li Yi didn't take Tong Gexiao's surprise seriously at all, and pointed to the exercises behind him and said, "If you look at what else you don't understand, I'll tell you everything." ”

Seeing that a student was going to give him a lecture, Tong Gexiao was embarrassed to ask even if he really didn't understand. recalled what she had just said that if Li Yi could get this set of questions right, it would be up to him, and her face turned into sunset again.

"He must have been joking at that moment, he must have ......" Tong Gexiao kept comforting himself.

Li Yi seemed to have forgotten what he had just teased Tong Gexiao, and only said lightly: "Is there still a question?" ”

Tong Gexiao looked at Li Yi's pride, and for some reason anger surged up, and said loudly: "Yes! ”

She took a blank piece of paper and wrote on it. Li Yi looked sideways, good guy, Goldbach guess!

Goldbach's conjecture was a hypothesis of the eighteenth-century German mathematician Goldbach, but he could not prove it himself, so he wrote to ask the famous mathematician Euler to help prove it, but until his death, Euler could not prove it.

Today, Goldbach's conjecture has been circulating in the mathematical community for nearly 300 years, and countless mathematicians have studied it carefully, but none of them have been able to prove it.

After Tong Gexiao finished writing Goldbach's conjecture, a look of pride flashed in his eyes. Aren't you capable? I don't think you'll be deflated this time!

"If you can prove this problem, the teacher doesn't need to say that to you, even if he sells himself to you!"

"This problem is complicated, and there is not enough paper to write!" Li Yi looked at the blank paper and sighed, "I have time to write an electronic document for you!" ”

"Okay, don't pretend, the teacher knows you won't." Tong Gexiao raised his chin, and finally found a trace of self-esteem.

Li Yi said: "I really know this, but it's really cumbersome to prove, so I won't write it to you today." So, give me all the papers you have in your hand, and I can write you the solution to another problem. ”

"Another?" Tong Gexiao blinked.

"Yes, don't you like Riemannian geometry? Then I'll give you an argument, the other concept is also proposed by Riemann, the Riemann hypothesis! ”

"The Riemann hypothesis?" Tong Gexiao was so shocked that she almost jumped.

The Riemann conjecture is a conjecture about the zero-point distribution of the Riemann ζ function ζ(s), which was proposed by the mathematician Riemann in 1859.

Compared with the Fermat conjecture that was solved after more than three and a half centuries, and the Goldbach conjecture that stood still after more than two and a half centuries, the Riemann conjecture is still far from a record of only one and a half centuries, but its mathematical importance far exceeds that of these two more popular conjectures, and it is the most important and most anticipated mathematical problem in the mathematical community today.

"What, don't you want it?" Li Yi reached out and pinched Tong Gexiao's face.

Fortunately, all the students in the class were frightened by Tong Gexiao, and they bowed their heads to answer the questions and did not dare to look up. Otherwise, when they saw Li Yi pinching this Teacher Tong's face like a child, wouldn't they faint on the spot?

However, this extremely excessive move did not make Tong Gexiao react, she was already frightened stupid by Li Yi's wild words.

"It's all for you!"

Tong Gexiao stuffed the entire stack of scratch paper to Li Yi, and then opened his eyes wide, wanting to see if this guy was really going against the sky!

That's the Riemann hypothesis! One of the most important problems in mathematics could be won a Fields Medal or a Wolf Prize in mathematics if it was solved?

You must know that the Nobel Prize only has physics, chemistry, biology or medicine, literature, peace, and in 1968, the Economics Prize was added, and there is no mathematics at all.

In this context, two international mathematics awards have been established in the world: one is under the auspices of the International Union of Mathematicians. the Fields Medal, awarded at the quadrennial International Congress of Mathematicians; The other is the annual Wolf Prize in Mathematics established by the Wolf Foundation, and they are the "Nobel Prize" in mathematics.

In addition, in the early 2000s, the Scientific Advisory Board of the Clay Institute of Mathematics in the United States selected seven major problems that can guide the direction of mathematics and have an impact on the development of mathematics and promote it as the "Millennium Prize Questions" and made them public. No matter which puzzle you solve, you'll be rewarded with millions of dollars!

The Riemann hypothesis is one of the seven grand prize-winning millennium puzzles!

If Li Yi can solve the Riemann hypothesis, it will definitely cause a sensation in the world!

Seeing Li Yi pick up the pen and write down the equations on the white paper, Tong Gexiao's heart also pounded. Reason told her that it was impossible for Li Yi to accomplish such a feat, but the incredible test papers just now made her think that Li Yi could do it!

After writing a piece of scratch paper, Li Yi casually handed it to Tong Gexiao and asked her to read it slowly, and then took the next blank piece of paper and continued to write. After a while, the manuscript paper in Tong Gexiao's hand became a thick stack!

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