Reborn Tech Scholar

Chapter 48 Lectures
Chapter 48 Lectures

On September 9, the sky was clear and the sun was shining brightly.

The first-year freshmen have started classes. In the first semester, they need to take nine compulsory courses, namely mechanics, advanced mathematics, linear generation, introduction to computing, college Chinese, military theory, thinking, college English, and physical education.

Military theory, at the time of military training, has been completed, which means that 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.

Qin Yuanqing and the others took the mechanics class together. Originally, Qin Yuanqing had great expectations and felt that the mechanics class was taught by a professor who should have done a good job in his lectures.As a result, after listening for twenty minutes, Qin Yuanqing wanted to say to the professor, "Get rid of it, professor, we are not high school students, you can go deeper.

Qin Yuanqing is very disappointed, that's all. . . . . .Better to learn by yourself!
After one class in each of several courses, Qin Yuanqing began to be too lazy to listen to the class. Qin Yuanqing sat in the back seat and read by himself in each class.

In the past four days, Qin Yuanqing posted a lecture message on the bulletin board on the side of the library: "An academic lecture titled 'Twin Prime Conjecture' will be held in the XX Ladder Classroom at 9:00 tomorrow..."

Seeing the words "twin prime number conjecture", Qin Yuanqing suddenly became interested. In the past few days, he was trying his best to overcome the final level of the "twin prime number conjecture". He never expected that a mathematician would come to the school to hold an academic lecture on "twin prime number conjecture".

interesting!
Qin Yuanqing showed interest. It just happened that there was no class tomorrow morning. You can go and listen to see the other party's research level on the 'twin prime number conjecture'.

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

孪生素数即相差2的一对素数。例如3和5 ，5和7，11和13，…，10016957和10016959等等都是孪生素数。

The prime number theorem states that prime numbers tend to become rare as they approach infinity.And twin prime numbers, like prime numbers, have the same trend, and this trend is more pronounced than prime numbers.Therefore, the twin prime conjecture is counter-intuitive.

Regarding twin prime numbers, there are two main achievements in the past century. One is that in 1920, Viggo Brown of Norway, by using the famous sieve theory, proved that 2 can be expressed as two numbers with at most 9 prime factors. Poor, 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 achievement was obtained 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 that of his Goldbach conjecture.

As for the achievements of the next 40 years, they have never been separated from these two achievements.

"What about Zhang Yitang?" Looking at the name of the lecturer, Qin Yuanqing muttered to himself. After checking it again, he found that this person was quite extraordinary. From 1978 to 1982, he obtained a bachelor's degree from the Department of Mathematics of Yan University. In 1982 - In 1985, he studied for a master's degree under the tutelage of famous mathematician and Yan University Professor Pan Chengbiao. In 1992, he graduated from Purdue University in the United States with a Ph.D. degree. He is currently teaching in the Department of Mathematics at the University of New Hampshire.

His research direction is in number theory.

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

At 08:30 in the morning, the seats in the auditorium are almost full.

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

At [-]:[-], the amphitheater was full, and even the aisle was already full of people.

Listening to someone arguing about the location of the lecture, Qin Yuanqing realized that not only students from Shuimu University, but also students from Yan University and other colleges and universities came to listen to the lecture.

Shuimu's students are listening to the lectures on their own sites, but they have no place. This is so annoying. Naturally, they want to drive away students from other schools, but the students of those schools are not good at all. Why can't they come to the lectures, you guys Schools don't ban it.

School doesn't care, how old are you?

At 9:00, the entire lecture hall was quiet. A middle-aged man with glasses came to the podium, opened his laptop, and the computer was connected to the screen, while 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.

“……我们都知道，素数是只含有两个因子的自然数，你们可能上初中的时候就背过前一百位的素数表。而孪生素数，是指差值为2的素数对，即p和p+2同为素数对。例如3和5、5和7、11和13、17和19等。随着数的变大，可以观察到的孪生素数对越来越少。”

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

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

【2003663613×2195000-1和2003663613×2195000+1】张翼唐继续说道：“存在无穷多个差值为2的素数，这就是著名的孪生素数猜想。”

Qin Yuanqing saw that Zhang Yitang went from simple to deep, and gradually led to the conjecture of twin prime numbers. Even a college student who is not a mathematics major can keep up and understand what he wants to express.

Sure enough, the students, regardless of whether they were amateurs in the mathematics department or non-mathematics department, listened with great interest.

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

For example, it introduces the results obtained in the proof of the twin prime number conjecture in history. For example, in 2005, mathematician Dan Goldstone and two colleagues proposed that there are infinitely many prime numbers whose difference is less than 16 for this weak twin prime number conjecture.

In the entire classroom, most of the people were dumbfounded, but only a few 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 said with a smile.

"Yingying, don't listen to him pretending to be forceful. He's only a freshman, so how could he understand." The man sitting with the girl glared at Qin Yuanqing with hostility in his eyes.

Qin Yuanqing shrugged indifferently. He was almost finished with the proof of the "Twin Prime Conjecture". Is it necessary to lie?

At the end of the lecture, Qin Yuanqing went to the library and quietly thought about the final proof. This "Twin Prime Conjecture" is more difficult than "Zhou's Conjecture".

Opened the laptop, QQ reminded that there was a mailbox, Qin Yuan checked and opened the mailbox, it was the reply letter from "Mathematics Chronicle", to the effect that his paper has passed the review of "Mathematics Chronicle" and will be published in this issue of "Mathematics Chronicle", Qin Yuanqing took a look. This issue of "Mathematics Chronicle" was just a few days later, on September 9, the day he happened to be visiting her house with Jingtian.

It's quite a coincidence.

. . . . . .

"Mathematics is a very rigorous subject and the foundation of all subjects."

"Whether it is science or engineering, mathematics must be learned, and it must be learned very deeply."

"The results of the college entrance examination only represent the conclusion of high school, not university. University is a brand new starting point. Some students cannot immerse themselves in the glory of the past. This is very dangerous!" The math teacher said meaningfully.

The classmates turned to look at the last seat. Qin Yuanqing, who was dozing off, knew that the math teacher was talking about Qin Yuanqing.

"Big brother, wake up, wake up!" The little fat man sat in the seat in front of Qin Yuanqing and quickly pulled Qin Yuanqing's clothes.

"What's the matter? There's 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: "Student Qin Yuanqing, I know you are a CMO and IMO gold medalist. Mathematics is your strength, but that is high school. Now you enter Shuimu University. Among the undergraduates of Shuimu University, there are many CMO and IMO gold medal winners, and they don't take advanced math classes to sleep."

Qin Yuanqing was sleepy and said lazily, "Teacher, what you said is too simple, I already know it."

Qin Yuanqing saw that the teacher's face was almost gloomy and dripping with water. 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 listen to the class carefully in the future."

“这是你说的，别后悔！”高数老师直接在黑板上写下一道题：“求球面x2+y2+z2=a2（a>0）被平面z=a/4与z=a/2所夹部分的面积。”

Qin Yuanqing read this question, and secretly slandered, thinking how difficult the question would be, so it was like this.

Qin Yuanqing stood up and walked towards the blackboard. He picked up the chalk and drew an xyz coordinate axis. This ball is centered at (0, 0, 0) and has a radius of a. Then he made two planes z=a/4 and z=a/2. , through the thinking of equal proportions, the area of ​​the ball sandwiched by the two faces is obtained.

Then write the second proof idea next to it, and directly calculate the area through calculus.

The classmates watched in amazement as Qin Yuanqing wrote five calculation methods on the blackboard, which filled the entire blackboard. Except for the first one they could understand, and the last four proof methods, they were all confused.

What the hell!The boss is indeed the boss!

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

But now, it appeared on Qin Yuanqing, a freshman.

(End of this chapter)