Translator: Henyee Translations Editor: Henyee Translations
Once the inspiration came to Lu Zhou, he could not stop writing. He had even completely forgotten about eating.
Lu Zhou’s brain was filled with creative juice, and he was totally motivated as he took his pen and started to write on the paper.
[
The restriction group G is provided 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 the vertex p. Redefine C(G)=…
]
…
Time slowly passed by, but he did not stop writing.
This felt different than the last time.
Last time his inspiration was given. This time, his inspiration was created by himself.
The pen moved swiftly on the paper.
Without him realizing it, he had already written five draft papers.
Lu Zhou rubbed his stomach and leaned against his chair before he took out his phone.
He was shocked when he looked at the time.
“F*ck, it’s already five o’clock!”
He had not even eaten his breakfast yet.
Lu Zhou could not handle it anymore. He then went to the crowded cafeteria and ate some dinner. After dinner, he continued to work.
It was at six o’clock in the evening when Shi Shang returned from his class with his food. When he saw Lu Zhou writing on the desk, he asked, “Zhou, what are you doing? Master’s students have homework too?”
Lu Zhou was at a crucial point, so he did not raise his head when he replied, “Writing a thesis.”
Suddenly, Huang Guangming and Liu Rui also came back with their food.
Liu Rui placed his backpack on the table and took out his homework while Huang Guangming walked over to Lu Zhou and looked at the paper curiously.
He was muddled when he saw what Lu Zhou was writing.
“F*ck, Zhou, I don’t understand a single word you wrote.”
Out of curiosity, Shi Shang also came over.
“Guangming, we’re third-year students already, so you should at least be able to understand the symbols… F*ck, this is group theory… Advanced stuff!”
Liu Rui was writing his homework when he twirled his pen and said calmly, “It’s not that advanced, I think some fourth-year students take that. But it’s not related to us applied mathematics majors… Well, unless you transfer to theoretical physics…”
Applied mathematics and theoretical physics were similar, so it was not that unusual for people to transfer.
Most people transferred for the fat physics research budget.
“No way I would transfer,” said Huang Guangming as he shook his head and walked away.
“Of course you couldn’t transfer, you’re not like Lu Zhou,” said Shi Shang. He patted Guangming’s shoulder with a look of defeat.
Lu Zhou, “…?”
…
Rome was not built in a day. A well-established theory required inspiration and time.
Over the next few days, Lu Zhou spent all his day time at the library, and all his night time in his dorm.
Occasionally, he would have to reply to Professor Frank’s email. However, since there was no new data from CERN, he did not have to do too much work.
Lu Zhou felt fulfilled.
Although other people could not understand, he himself was happy.
The second week of September, on a sunny morning, Lu Zhou leaned against his chair in the library. He glanced at the dozens of papers in front of him and said with relief, “Finally done!”
All it took was some inspiration to solve the bottleneck. After that, he could cruise through the rest.
He was exhausted but he also had an unexplainable pleasant feeling.
It was not just because he solved another difficult mathematics conjecture, but it was also because while he was solving this problem, it deepened his understanding of group theory. This gave him new tools in his mathematics toolbox.
This was more exciting than the conjecture itself.
Hilbert once said that Fermat’s Great Theorem was a chicken that could lay golden eggs, Not because the chicken had fed a large number of mathematicians, and nor was it because the chicken had given many journals a chance to publish their sub-par papers, but because through it, many novel mathematical methods were derived.
Inspired by the Fermat problem, Kummer introduced the concept of ideal numbers and found the only decomposition theorem that decomposed the number of a circular domain into an ideal prime factor. This theorem had been promoted today by Dedekind and Kroneeck. It occupied a central position in the theory of modern numbers, and its significance had gone far beyond the scope of number theory.
Lu Zhou’s work at the Princeton conference was the same. His applied topology method solved the twin prime conjecture.
The original sieve theory was applied by Mr. Chen, and the number theory community believed that in order to solve the Goldbach’s conjecture in the form of “1+1”, they needed a new method.
It appeared now that the sieve method was more useful than they thought.
Even the professor that introduced the sieve theory in 1995 had not expected this.
This is the value of number theory.
While Lu Zhou was solving the Polignac’s conjecture, he also found a unique solution.
He named this method “Structure Research Method of the Group Theory” or “Group Structure Method” for short.
Using the group theory method, the problem of infinity was studied as a whole. The “K=1” form was extended to “k is an infinite natural number”, which thoroughly proved that “for all natural numbers k, there are infinite pairs of prime numbers (p, The proposition of p+2k)”.
The conclusion might be one only sentence, but it took up several blackboards to prove.
Lu Zhou spent an entire day organizing the proof on his computer before converting it into PDF format.
As he looked at the finished product on his screen, he nodded with satisfaction.
“This should do.”
He could still write more on his Group Structure Method.
However, Group Structure Method was not the focus of his thesis.
So far, the Polignac’s conjecture had been proved.
While it might seem that the proof was only an extension of the twin prime conjecture proof, but no one other than Lu Zhou knew of its difficulty.
Lu Zhou added a sentence to his thesis.
[… Due to structural reasons, the Group Structure Method theory will be explained in my next thesis.]
Re-format, upload.
Target, Annual Mathematics!
