Genius of the Rules-Style System

Chapter 434: Chapter 269: The Great Master is gone, how should I teach the class now?

"The Goldbach Conjecture really is...almost impossible to make any progress on!"

"Maybe there’s a chance if it’s Zhao Yi working on it, but expecting a breakthrough in a short time is also...very difficult!"

"We should still remind Zhao Yi, he’s still too young for research!"

A few professors from the School of Sciences were discussing, and they all knew that Zhao Yi had been immersed in the proof of Goldbach Conjecture, carefully studying the materials for several days in a row, and every time they saw him, he seemed to be working hard.

Many people were worried, but they couldn’t stop Zhao Yi from seriously researching and studying.

The last sentence was said by Zhou Li, who felt that Zhao Yi was still too young. "Back when I was young, I just started teaching after studying abroad and wanted to make achievements in research. I spent almost all my time in research, except for teaching."

"But how did it turn out? My achievements only came after ten years. It’s easy to get stuck in a dead end when thinking about a problem for a long time!"

Zhou Li sighed, "Especially the Goldbach Conjecture. It’s so difficult. There has been no progress for decades. Chen Jingrun’s work had almost completed the proof."

"But everyone must have gone through this phase. Probably when he has experienced it, he’ll know."

"Zhao Yi’s journey this year has been smooth, and encountering obstacles is normal. It’s helpful for his growth."

Zhou Li’s words received a lot of support.

Everyone thought it made sense.

No one can have smooth sailing in their research, and to make a breakthrough in top-notch research, occasional moments of inspiration are possible, but no one can have them every day. It’s normal to have no achievements for several years or even decades, and success in exploring high-end mathematics cannot be achieved through just putting your head down and doing research.

Zhao Yi is still young.

He must go through the same path as his predecessors to gain more experience and deeper insights into research work.

The group decided not to disturb Zhao Yi and not intentionally remind him of anything. Just let nature take its course.

Wednesday.

There was another calculus class for biology students. Hu Zhibin arrived at the classroom on time and found a surprise--

Zhao Yi wasn’t there!

"Where’s Zhao Yi? Why isn’t he here for class?" Hu Zhibin asked with a frown. He asked Fan Lei, knowing that Fan Lei and Zhao Yi were always together and seemed to be good friends.

Fan Lei replied, "I don’t know, he stayed at the teachers’ dormitory last night, and I didn’t see him at the cafeteria this morning."

"Didn’t you call him?"

"No."

Fan Lei shook his head, "He’s been doing research lately, something about prime numbers. He told us not to disturb him if it wasn’t necessary."

"Oh." freeωebnovēl.c૦m

Hu Zhibin seemed dissatisfied, like any other student who didn’t attend class, but he felt exceptionally relaxed inside.

If there were a bottle of beer in front of him, he’d want to chug it down in celebration.

"Great!"

"Zhao Yi isn’t here! This feeling...Yes, this feeling!"

"I can teach freely, say whatever I want..."

Hu Zhibin felt light all over, with no pressure at all.

While explaining series problems, he even talked about extracurricular knowledge and popularized a high-end conclusion among students--

The sum of all natural numbers is ’-1/12’.

"This is a classic proof in series calculations."

"But the interesting thing is that the conclusion of the sum of natural numbers is correct when calculated using pure series methods, but the process is wrong."

"The mathematician who first proved that the sum of all natural numbers is ’-1/12’ was Euler, but his proof was considered absurd at the time, incomprehensible, and not recognized."

"Later, there was an Indian named Ramanujan who did not receive orthodox higher education, but he was obsessed with mathematics. He used a series method to prove Euler’s conclusion."

"The proof is like this..."

Hu Zhibin did the calculations on the blackboard, and the process was indeed somewhat simple.

First, introduce a series S, S = 1-1+1-1+1-1+1..., then convert 1-S = S, resulting in S = 1/2.

Next, introduce a series M, M = 1-2+3-4+5-6+7..., through staggered substitution, calculating that 2M = S and M = 1/4.

Finally, introduce the sum of all natural numbers, N, and use N-M’s staggered calculation to ultimately derive N = -1/12.

"As you all can see, the proof process seems to have no problems, but in fact, it is wrong from the beginning of calculating the value of S."

"S is a divergent series. In infinite series, only absolutely convergent series can rearrange their terms without changing the convergence value, which means that the sum order of non-absolutely convergent infinite series cannot be arbitrarily changed."

"And that is the Riemann Series Theorem, also known as the Riemann Rearrangement Theorem."

Hu Zhibin’s casual lecture was indeed interesting, attracting even some students who were sleeping. It was the first time they discovered that Hu, their calculus teacher, could be so interesting when talking about mathematics, instead of always rigidly teaching from the textbook and doing practice problems.

Zhao Yi was also attracted.

Zhao Yi was familiar with the proof that the sum of all natural numbers is -1/12, but he knew Riemann’s proof method, not Ramanujan’s wrong proof.

About the sum of all natural numbers, Euler had proposed the result of -1/12 early on, but more than fifty years later, Riemann used strict complex analysis to prove its rationality.

However, the result was still hard for people to accept.

In exploring the unknown field of mathematics, many mathematicians are devoted to researching mathematical theories to expand people’s cognitive range. For example, the conclusion of the sum of all natural numbers seems impossible, but the proof theory is self-conclusive.