Rebirth of science and technology academic master

Chapter 48 Lecture

On September 21st, the sky was clear and the sun was shining brightly.

Freshmen have started taking classes. In this first semester, they need to take nine compulsory courses: mechanics, advanced mathematics, linear algebra, introduction to computing, college Chinese, military theory, ideological cultivation, college English, and physical education.

Military theory has been completed during military training, which means there are still nine courses left in the first semester.

In addition, there are several elective courses, but the elective courses have not officially started yet.

Qin Yuanqing and several other classes took mechanics classes together. Qin Yuanqing originally had great expectations and felt that the person teaching the mechanics class was a professor and he should give good lectures. After listening for more than twenty minutes, Qin Yuanqing wanted to say to the professor, Get out of here, professor, we are not high school students, you can go deeper.

Qin Yuanqing was very disappointed, that's all. . . . . . It’s better to teach yourself!

After taking several classes each, Qin Yuanqing began to be too lazy to listen to the class. Every time he went to class, Qin Yuanqing sat in the back seat and read by himself.

Four days later, Qin Yuanqing posted a lecture information on the bulletin board on the side of the library: An academic lecture titled 'Twin Prime Conjecture' will be held at XX Lecture Hall tomorrow at 9:00...

Seeing the words Twin Prime Number Conjecture, Qin Yuanqing immediately became interested. In the past few days, he had been working hard to overcome the final hurdle of the Twin Prime Number Conjecture. Unexpectedly, a mathematician was coming to the school to give an academic lecture on the 'Twin Prime Number Conjecture'.

interesting!

Qin Yuanqing showed interest. It happened that there was no class tomorrow morning, so he could go and listen to see the other party's research level on the 'Twin Prime Conjecture'.

The twin prime conjecture is a famous unsolved conjecture in number theory. This conjecture was formally proposed by Hilbert in the 8th question of the report of the International Congress of Mathematicians in 1900. It can be described as the existence of infinite twin prime numbers.

Twin primes are a pair of primes that differ by 2. For example, 3 and 5, 5 and 7, 11 and 13,..., 10016957 and 10016959, etc. are all twin prime numbers.

The prime number theorem explains the tendency of prime numbers to become rarer as they approach infinity. Twin prime numbers, like prime numbers, also have the same trend, and this trend is more obvious than prime numbers. Therefore, the twin prime conjecture is counterintuitive.

Regarding twin prime numbers, there are two most important achievements in the past century. One is in 1920. Viggo Brown of Norway used the famous sieve theory to prove that 2 can be expressed as two numbers with up to 9 prime factors. Worse, this conclusion is already somewhat similar to the twin prime conjecture. As long as the number with at most 9 prime factors in this proof is improved to the number with at most 1 prime factor, the twin prime conjecture can be proved.

The second major result was achieved in 1966 by Chinese mathematician Chen Jingrun using the sieve method, which proved that there are infinitely many prime numbers p, so that p+2 is either a prime number or the product of two prime numbers. This result is very similar to his result on Goldbach's conjecture.

As for the achievements of the next forty years, they have not been separated from these two achievements.

Zhang Yitang? Looking at the name of the lecturer, Qin Yuanqing muttered to himself. After checking again, he found that this person was quite extraordinary. He obtained a bachelor's degree from the Mathematics Department of Yanda University from 1978 to 1982, and in 1982 -In 1985, he studied for a master's degree under the tutelage of the famous mathematician Professor Pan Chengbiao of Yantai University. He graduated from Purdue University in the United States in 1992 and received a doctorate. He currently teaches in the Department of Mathematics at the University of New Hampshire.

This person's research direction lies in number theory.

Qin Yuanqing continued to conquer the Twin Prime Conjecture. He had a feeling that he was not far away from completely proving the Twin Prime Conjecture, and he could achieve it with more work.

At 8:30 in the morning, the seats in the lecture theater were almost full.

Qin Yuanqing found a seat in the last row and sat down, then immersed himself in reading. He was reading a professional mathematics book borrowed from the library.

By 8:50, the lecture theater was packed, and even the aisles were filled with people.

Listening to some people arguing over the seats, Qin Yuanqing realized that it was not only students from Shuimu University who came here to listen to the lectures, but also students from Yan University and other universities came to listen to the lectures.

The students of Shuimu were attending lectures on their own territory, but there was no place for them. This was so irritating that they naturally wanted to drive away the students from other schools, but the students from those schools were not good at all. Why couldn't they come to attend the lectures? You guys The school didn't ban it either.

The school doesn't care who you are.

At 9:00 on time, the entire lecture theater fell silent. A middle-aged man wearing glasses came to the podium and opened his laptop. The computer was connected to the screen, and the host introduced the middle-aged man's identity and status. .

Everyone listening to the lecture listened quietly, opened their notebooks, and started taking notes.

...We all know that prime numbers are natural numbers with only two factors. You may have memorized the first hundred prime number tables when you were in junior high school. Twin prime numbers refer to pairs of prime numbers with a difference of 2, that is, p and p+2 are both pairs of prime numbers. For example, 3 and 5, 5 and 7, 11 and 13, 17 and 19, etc. As the number becomes larger, fewer and fewer pairs of twin prime numbers can be observed.

There are 8 pairs of twin prime numbers within 100, and in the range from 501 to 600, there are only 2 pairs. As the prime number increases, the next prime number should be farther and farther away from the previous prime number, but it is as famous as Goldbach's conjecture and An important conjecture asserts that there are infinite pairs of prime numbers that only differ by 2, such as 3 and 5, 5 and 7, and even this...

Having said this, Professor Ren wrote a line of numbers on the blackboard.

[2003663613×2195000-1 and 2003663613×2195000+1] Zhang Yitang continued: “There are infinitely many prime numbers with a difference of 2. This is the famous twin prime number conjecture.”

Qin Yuanqing saw that Zhang Yitang was gradually leading to the twin prime number conjecture from the basic to the advanced. Even college students who were not majoring in mathematics could follow and understand what he wanted to express.

Sure enough, the students, whether they were amateurs from the mathematics department or non-mathematics departments, listened carefully with interest.

But soon, the content of the lecture began to deepen.

For example, it introduces the results achieved in proving the twin prime conjecture in history. For example, in 2005, mathematician Dan Goldstone and two colleagues proposed the weak twin prime conjecture that there are infinite pairs of prime numbers whose difference is less than 16.

Most of the people in the entire classroom looked confused, and only some people could keep up.

Junior, do you understand? A student with glasses next to Qin Yuanqing asked in a low voice.

It's very simple! Qin Yuanqing smiled.

Yingying, don't listen to his pretense. He is only a freshman, how can he understand. The man sitting with the girl glared at Qin Yuanqing with hostility in his eyes.

Qin Yuanqing shrugged indifferently. He had almost completed the proof of the Twin Prime Conjecture. Is there any need to lie?

After the lecture, Qin Yuanqing went to the library and quietly thought about the final proof. This Twin Prime Conjecture was more difficult than the Zhou Conjecture.

Opening his laptop, QQ reminded him that there was an email. Qin Yuan checked the email and opened it. It was the reply from Chronicle of Mathematics. The main idea was that his paper had passed the review of Chronicle of Mathematics and would be published in this issue of Chronicle of Mathematics. Qin Yuanqing took a look and found that this issue of Mathematical Chronicle was not just a few days later, on September 30, the day he and Jingtian happened to be visiting her home.

What a coincidence.

. . . . . .

Mathematics is a very rigorous subject and the basis for all subjects.

Whether it is science or engineering, mathematics must be learned, and it must be learned in depth.

The college entrance examination results only represent the conclusion of high school, not college. College is a new starting point. Some students cannot be immersed in the glory of the past. This is very dangerous! the math teacher said meaningfully.

The students all turned to look at Qin Yuanqing, who was dozing off in the last seat, and they all knew that the math teacher was talking about Qin Yuanqing.

Boss, wake up, wake up! The little fat man sat on the seat in front of Qin Yuanqing and quickly reached out and pulled Qin Yuanqing's clothes.

What happened? There was an earthquake? Qin Yuanqing was startled and blurted out.

Then the whole classroom burst into laughter, and the math teacher looked at Qin Yuanqing with a livid face, and said with hatred: Qin Yuanqing, I know you are a CMO and IMO gold medalist, and mathematics is your strength, but that was in high school. . Now you enter Shuimu University. Among the undergraduates of Shuimu University, there are many CMO and IMO gold medalists, and they will not sleep in advanced mathematics classes.

Qin Yuanqing's eyes were sleepy and he said lazily: Teacher, what you said is too simple. I have already mastered it.

Qin Yuanqing saw that the Gaoshu teacher's face was almost gloomy. Qin Yuanqing spread his hands and said: If the teacher doesn't believe it, you can ask a question and I will solve it. If I can't solve it, I will just listen to the class carefully in the future.

This is what you said, don't regret it! The senior mathematics teacher wrote a question directly on the blackboard: Find the sphere x2+y2+z2=a2 (a\u0026amp;gt;0) divided by the plane z=a/4 and z= The area of ​​the part enclosed by a/2.”

Qin Yuanqing read this question and secretly cursed. He thought it would be a difficult question, but it turned out to be like this.

Qin Yuanqing stood up and walked to the blackboard, picked up the chalk and drew an xyz coordinate axis. The center of this ball is (0, 0, 0) and the radius is a. Then he made two surfaces: z=a/4 and z=a/2. , through the thinking of equal proportions, the area of ​​the ball sandwiched by two surfaces is obtained.

Then he wrote a second proof idea next to it, to find the area directly through calculus.

The students watched in astonishment as Qin Yuanqing wrote five calculation methods on the blackboard, occupying the entire blackboard. Except for the first one, which they could understand, they were confused by the next four proof methods.

Damn it! The boss is indeed a boss!

The advanced mathematics teachers were also speechless. Among Qin Yuanqing's five proof methods, the last three are only exposed to graduate students and even doctoral students.

But now, it appears in Qin Yuanqing, a freshman.