As soon as he was inspired, he could not stop writing. He did not even feel hungry anymore.
Lu Zhou's body was filled with energy. He held the pen and began to write down lines of calculations on the paper.
[Let the finite group G and | G | = p1α1p2α2 … · · piαi, where pi is a prime number and αi is a positive integer. Let p ∈ π (G), define deg (p) = | {q ∈ π (G) | p ~ q) |
The number of times deg (p) is called the vertex p. Then define C (G) = …
…
】
Time passed second by second, but the flow of ideas didn't stop for even a moment.
This feeling was different from last time.
The inspiration last time was borrowed, but this time, he was inspired by himself.
The pen began to move on the paper.
Without him realizing it, he had already written five pages of draft paper.
Lu Zhou organized his thoughts and rubbed his stomach. He leaned back in his chair and took out his phone.
He thought that he did not have to wait for long, but when he looked at the time, he was shocked.
"F * ck me, it's already five o 'clock?!"
Humans were made of iron and food was steel. He would be starving if he did not eat, not to mention he did not even have breakfast.
In the end, Lu Zhou could not stand it anymore. Before the cafeteria was occupied by his juniors in green military uniforms, he quickly went to the cafeteria for dinner. He then came back and continued to work hard.
It was half past six.
Shi Shang came back from class and walked in with a lunch box. When he saw Lu Zhou writing on the table, he curiously asked.
"Zhou, what are you doing? Graduate students have homework? "
Lu Zhou did not even look up as he casually replied.
"Writing a thesis."
At this time, Huang Guangming and Liu Rui also came in with lunch boxes.
Liu Rui threw his bag on the table and took out his homework. Huang Guangming curiously walked behind Lu Zhou and looked at the paper.
He did not care about what he saw.
After looking at it, he was dumbfounded.
"F * ck me, Zhou, I don't understand a single word you wrote."
Hearing Little Cheap's voice, Shi Shang stopped eating and walked over curiously.
"You're exaggerating, Little Bitch. We're not freshmen anymore, we're already juniors. Even if you don't understand the process, you should be able to understand the symbols … Holy shit, I'm not mistaken, this is a group theory … It's beyond the syllabus!"
Liu Rui, who was doing his homework, spun the pen in his hand. He was getting calmer and calmer as he said, "It's not really out of the syllabus. In the elective courses, there is Li Qun and Li Algebra … However, it has nothing to do with applied mathematics unless you want to switch to theoretical physics."
Changing from a science subject to a science subject would be too much of a hassle.
There was nothing much to say if they were interested. If they were not really interested, everyone would just focus on engineering, which had a bright future.
"I can't afford to offend him." Huang Guangming shook his head and retreated.
"We can't afford to offend him. Otherwise, you'll be the one making big news." Patting Little Scum's shoulder and sighing, Shi Shang retreated with an expression as if he had given up.
Lu Zhou: "…?"
…
Rome was not built in a day. Perfecting a theory not only required a burst of inspiration, but it also required the accumulation of time.
For the next few days, Lu Zhou spent the day in the library. At night, he would return to his dorm and continue his research.
Occasionally, he would take the time to reply to Professor Frank's emails. Although there was no new data from CERN, perfecting the theory still required calculations.
Every day, Lu Zhou lived a fulfilling life.
Although it was incomprehensible to others, he was enjoying it.
On the second week of September, on a sunny morning, Lu Zhou was sitting in the library. He stretched his back and looked at the dozen pages of paper in front of him.
"Finally f * cking done!"
When one's sensitivity was exhausted, all of the work was to pave the way for the moment of inspiration. When he really figured out the solution to this problem, the exit of the maze seemed to be right in front of him.
Everything fell into place.
At this moment, Lu Zhou's mood was indescribably happy.
Not only because he solved another mathematics problem, but because he had a deeper understanding of group theory while solving this mathematics problem, and he developed a new set of mathematics methods.
This discovery was even more exciting than solving the mathematical conjecture itself.
Hilbert once said that Fermat's last theorem was a hen that laid golden eggs. It was not because this hen fed a large number of mathematicians, nor was it because this hen provided opportunities for many journals to publish fake papers. It was because many novel mathematical methods were derived from the research of number theory.
For example, inspired by Fermat's last theorem, Kummer introduced the concept of ideal numbers and discovered the unique decomposition theorem of a cyclic field into ideal prime factors. This theorem had been extended to any algebraic field by Didekind and Cronnek. It occupied a central position in modern number theory, and its significance went far beyond the scope of number theory and went deep into the field of algebraic function theory.
Lu Zhou's work at the Princeton conference was the same. He used topology to supplement sieve theory and cleverly solved the twin prime conjecture.
The original sieve theory had been used to the extreme by Mr. Chen. The number theory community generally believed that in order to solve the "1 + 1" form of Goldbach's conjecture, a new method must be found.
But now it seemed that there was a turning point. The sieve theory was still worth exploring.
This was something that even Professor Zehr Beck, who first introduced topology principles into sieve theory in 1995, did not expect.
This was the value of number theory.
When Lu Zhou solved Polignac's conjecture, he also completed this work and found a unique solution for this conjecture.
This new method was named "Overall Structure Research Method of Group Theory", or "Group Structure Method" for short.
Using the method of group theory, he studied the problem of infinity as a whole and extended the "K = 1" form to "k is an infinite natural number". This completely proved the proposition that "for all natural numbers k, there are infinitely many prime pairs (p, p + 2k)".
It might only take one or two sentences to describe, but if he wanted to explain the solution in detail, he would need a few large blackboards.
It took Lu Zhou an entire day to organize the entire process on his computer and convert it into pdf format.
Lu Zhou looked at the finished product on the screen and checked it twice. He then nodded with satisfaction.
"That's it for now."
There was actually a lot more to write about the detailed theory of the Group Structure Method. If he were to summarize all of it, it would be longer than his proof process itself.
However, that part was not the focus of this thesis.
So far, the Polignac's conjecture had been proven.
Although it seemed like it was just an extension of the twin prime conjecture to the form of infinitely spaced prime pairs, only Lu Zhou knew how difficult it was.
Lu Zhou thought for a bit and added a line at the end of the thesis.
[… Due to space reasons, I will explain the detailed theory of the "Group Structure Method" in my next thesis.]
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