Scholar’s Advanced Technological System

For the Ark, classes with undergraduates are also a recap of knowledge points.

As usual, these things are obvious to him, and basically they will not be considered. And it was only then that he could temporarily let go of the study itself and think about why what was obvious was obvious.

“… As many know, the Lehman conjecture is one of the most important and difficult conjectures in numerical analysis, and it is an assumption about the zero-point distribution of the Lehman zeta function. But few people know why Lehman's speculation was raised. ”

“In fact, before the Lehman speculation, there was a larger proposition that countless scholars had studied for centuries, namely, the laws of distribution of prime numbers. ”

As he said, the ark wrote down a few numbers on the blackboard and looked back at the students in the classroom to continue.

“Through the most basic arithmetic theorem, even junior high students know that each positive integer can represent the product of the prime factor, which is unique if the order in which the prime factors are arranged is not taken into account, and thus the prime number becomes the basic element that makes up the positive integer. ”

“The pattern of prime numbers, however, is not as shallow and understandable as its definition. It can even be said that the entire discipline of analytical mathematics, one of the most basic tasks, is the pattern of distribution of research prime numbers. ”

Looking at the students in the classroom gradually entering the state, the Ark knew that it was almost halfway through this lesson.

Lehman guesses that although it is a complicated problem, trying to understand that it is actually not as difficult as one would imagine, the real difficulty is how to solve it...

After a pause, the ark continued.

“In analytical mathematics, one typically studies function π (x) and uses it to represent the number of primes that do not exceed x. The law of distribution of study prime numbers is the basic task of the analysis of mathematics, while the nature of study π (x) is central to the analysis of mathematics. ”

“With regard to π (x), Gaussian and Lejende both did a lot of numerical calculations, and the assumption that π (x) ~ xlnx, when x tends to be infinite, was later proven, that is, the prime number theorem as we understand it. ”

“Euclidean had to prove the infinity of primitive numbers by elementary means, while Euler introduced a product formula that offered the possibility to analyse the question of primitive numbers, yet until the 1950s no suitable method was found to prove Gaussian speculation, until a German mathematician published a paper entitled" No more than one primitive number for a given value ", which opened a new path to the study of π (x). ”

“A lot of people have probably guessed who this bull is, and yes, he's the Lehman I'm going to talk about, and the Lehman zeta function he introduced in this paper affects the next century and a half. ”

Said the landing boat turned to the blackboard and wrote down a line of formulas on it.

[zeta (s) = Σ1n ^ s]

Looking around at the silent classroom of a raven, the ark continued.

“That's the thing... it doesn't look so hard, does it? ”

Students: "…”

MMP!

Where is it not difficult?!

“In his paper, Lehman further speculated on his proposed function, arguing that zeta (s) were all non-obvious zeros in the critical straight line. His gaze proved to be quite visionary, with all the non-obvious zeros obtained after extensive calculations being on the critical straight line. Regrettably, however, while we know its probability is correct, there is no way to prove it is. ”

“As a result, we often get a very beautiful result under Lehman's speculation, but if we cannot prove that Lehman's speculation is valid, we cannot prove that our result is correct. ”

“And vice versa, if we can prove that Lehman's assumptions are correct, then thousands of mathematical assumptions that exist assuming Lehman's assumptions are established will be honored as theorems! ”

“If anyone can prove Lehman's speculation, he will undoubtedly be the greatest mathematician of this century… I can be very responsible for saying this, even if this century is just beginning. ”

“Professor,” a student couldn't help but raise his hand and, after getting the hint of the ark nodding, stood up and asked excitedly, "What if it proved Lehman's guess, compared to yours? ”

“This is not a very good comparison, after all, my achievements are not just in mathematics,” looked at the student who asked the question, and Ark laughed and gave an uncertain statement, "but if someone could really prove this assumption, then his achievements in mathematics would undoubtedly be at the top of this era. ”

Next, the Ark continued to talk about the progress of research on Lehman speculation and some of its equivalents. Although it's all boring and tasteless, perhaps because of a change in the way they teach, students are obviously listening much more seriously than they did in the previous lesson.

Satisfied that he had gradually recovered some of his condition, the ark nodded proudly in his heart.

Time goes by and soon it's time to go out of class.

After a glance at the wall clock, the ark dropped the chalk on the multimedia table.

“This is the end of the lesson, and just now I had a few new ideas… So, off with the lesson. ”

The classroom sounded a sparse rally to pack the textbook, and the ark clamped the curriculum under his elbow, nodded to the students who had seen him leave, and turned to walk outside the classroom.

Going outside the classroom, the ark was preparing to go back to the office and record the inspiration generated during the class just now. Suddenly, it was stopped by Dean Qin, who didn't know where to drill from.

“An excellent mathematics lesson!” With a smile on his face, Dean Qin said in an emotional tone, "Even if I heard it, it would be greatly beneficial. ”

The ark laughed with embarrassment.

“I'm so flattered. I'm ashamed to say that I haven't given undergraduate classes in a while. ”

Dean Qin said comprehensively: “Everything has a sequence, the national interests are at stake, and it is of course more important to your research than to teach the students. By the way, are you busy lately? ”

Ark: “Not so busy, what's wrong? ”

“Here's the thing, I want to ask you something,” Dean Qin coughed softly, "you've heard of the Olympic Mathematics Competition? ”

Ark: “I heard about it, but I heard about it. Is there a problem? ”

Of course he heard about the IMO competition, although he never had the chance to participate.

Every year the IMO Grand Prix gold medals are won by fairy-like players.

For example, the man he knew, Schultz, described by Faltines as one of the world's three most promising young scholars, had won three IMO gold medals in a row.

When asked why he took the gold medal, he signed up for two more sessions. According to him, it was because he thought it was fun...

Dean Qin smiled and said, "Well, didn't you have a national high school math league last month? The first of the provinces have been selected, and by the national finals of the winter camp next January, approximately 30 students will have to be admitted to the national training team. It's November and it's almost time to prepare for the exam. ”

The ark stunned for a moment and laughed: "... you didn't ask me to be the proponent? ”

Dean Qin: “I'm not in charge of this matter. It's kind of an invitation from the Chinese Mathematics Institute. They want you to be the proponent of the last overwhelming issue. ”

Ark: “Is it appropriate for me to be the proponent? ”

Dean Qin smiled and said: “What's wrong with this? The last question in the national finals in previous years was also put forward by the academics. You are not only an academician, but also a Fields Prize winner. If you are not suitable, who else can be? ”

Ark: “Well, that's just the last question. ”

“Well, please do this,” suddenly remembered something, President Qin hastened to add another sentence, "By the way, don't make it too difficult, if no one can do it, it makes no sense. ”

“Don't worry, I won't be too hard," he said, pulling out a draft paper from the teaching plan that was tucked under his elbow, tearing the corner down and writing it on it.

Looking at the Ark, he took out the draft paper and wrote it down. President Qin stunned for a moment and couldn't help but cry.

“You're not going to ask questions here, are you? ”

Ark: “What else? ”

Dean Qin Khan said: “This is the national finals, you have to think about it. ”

“Already considered,” wrote the title on the paper, the ark stacked the draft paper and gently stuffed it in the hands of President Qin, “hand it over to the Chinese Mathematical Society for me, it should be fine on this topic. ”

Staring at the back of the ark's departure, President Qin moved his gaze to the draft paper in his hand and silently opened his eyes.

“... the Lehman zeta function? ”

Mumbled in his mouth, President Qin touched his chin and thought to himself.

“Can this kind of question contestant do it? ”

At this moment, however, he suddenly seemed to think of something, his eyes slightly lit.

“Hiss... wait, this seems like an interesting question...”

Mysteriously looking around, President Qin carefully stacked the note in his pocket and turned around to quickly walk in the direction of the office.