Chapter 235: Proving The Conjecture!

Translator: Henyee Translations Editor: Henyee Translations

The sky shined bright outside the window.

Lu Zhou was sleeping on his desk. He slowly opened his eyes.

He rubbed his sore eyebrows and looked at the calendar on the corner of his table.

It’s already May...

Lu Zhou had a slight headache and he shook his head.

Since arriving at Princeton in February, he had spent almost half of his time in this tiny apartment. Other than going for grocery shopping, he basically did not leave the room.

The worse was his $5,000 USD food club membership. He had barely used it.

After receiving the mission, he had been challenging Goldbach’s conjecture for almost half a year.

Finally, there was a result.

Lu Zhou took a deep breath and stood up.

He was almost at the finish line and he did not have to rush anymore.

Lu Zhou went into the kitchen and made himself a snack. He even took out a bottle of champagne from the refrigerator and poured himself a glass.

He bought this champagne two months ago just for this moment.

historical

Lu Zhou quietly finished his food. He then went to wash his hand before he returned to his desk. He began to put an end to his work.

He started to continue where he left off.

[... Obviously, we have Px(1,1)≥P(x,x^{1/16})-(1/2)∑Px(x,p,x)-Q/2-x^(log4 )...(30)]

[From equation (30), Lemma 8, Lemma 9, Lemma 10, it can be proved that theorem 1 holds.]

The so-called theorem 1 was the mathematical expression of Goldbach’s conjecture in his thesis.

That was, given a sufficiently large even number N, there were two prime numbers P1 and P2 that satisfy N = P1 + P2.

Similar theorems were Chen’s theorem N = P1 + P2.P3, there were an entire series of theorems about P(a,b).

Of course, although he labeled this as theorem 1 in his thesis, it would not be long before the mathematics community accepted his proof. After that, it could be upgraded to “Lu Zhou’s theorem” or something like that.

However, the review process for this type of major conjecture was longer.

Perelman’s proof of the Poincaré conjecture took three years to be recognized by the mathematics community. The proof of the conjecture was filled with a lot of “mysterious terms”. Therefore, it was difficult for anyone but him to understand the thesis.

The speed at which a major conjecture was reviewed largely depended on the popularity of the conjecture.

When Lu Zhou proved the twin prime conjecture, he did not use a particularly novel theory. He only used the twin prime method mentioned in Zellberg’s 1995 thesis. Therefore, people quickly understood his proof.

However, for Polignac’s conjecture thesis, the review process took a long time.

Even though Lu Zhou used his already proven Group Structure Method, he made significant modifications and it became very different than the large sieve method. Even for a big name like Deligne, it would take a long time to review.

Lu Zhou wrote fifty pages for the Goldbach’s conjecture thesis. Half of which was to discuss the theoretical framework he built for the proof.

This part could be published as a thesis on its own.

To a large extent, his review process depended on other people’s interest in his work, and how accepting other people were.

As for how long it would take, it was out of his control.

Actually, Lu Zhou thought about what the system’s criteria were for completing the mission.

If he completed the proof, but for decades, no one accepted his work, would he be stuck on this one mission?

What he was most confused about was where the system’s large database came from. It must have come from a civilization far more advanced than humans.

Lu Zhou felt like the system would make its own judgment whether or not he proved the conjecture. The system would not rely on “humans”.

Lu Zhou’s conclusion was that the completion of his mission would depend on two factors.

The first was correctness.

The second was publishing!

Actually, there was a very simple way to verify if his proof was correct.

He did not have to publish in journals...

...

After proving Goldbach’s conjecture, Lu Zhou spent an entire three days sorting the thesis onto his computer. He converted it into PDF format and uploaded it onto arXiv.

He was almost certain that his thesis was correct because his habit was to carry out rigorous double checks on each line of conclusion. He would repeatedly scrutinize all possible errors.

As for publishing...

ArXiv did not have a peer-review process, so it was undoubtedly the fastest option!

The only drawback was that it could conflict with submission to other journals. For example, uploading the thesis before the deadline may violate some double submission rules, but Lu Zhou did not care about those things. He also believed that reputable journals would not care either.

After all, Lu Zhou was not some no-name guy. He was the winner of the Cole Prize in Number Theory. Plus his thesis was not some random work. It was the famous Goldbach’s conjecture, the eighth question of Hilbert 23, which was one of the Millennium Prize Problems!

He would spend the next two days editing and organizing his thesis. After that, he would submit it to [Annual Mathematics].

When Fermat’s last theorem was first proved, it took six peer reviewers to check the proof. Lu Zhou did not know how many reviewers he warranted, but it should be no less than four.

Lu Zhou looked at the “upload finish” message on his browser and took a deep breath.

Does this mean I’ve finished it?

After the publication of his thesis, someone in this field received an alert. Somewhere on this planet, someone was already reading his thesis.

However, Lu Zhou did not know if the system counted this as a successful submission.

Lu Zhou sat in front of the computer and took a deep breath. He then closed his eyes and whispered.

“System.”

When he opened his eyes again, he was met with a pure white view.

It had been a long time since he came here. Lu Zhou almost felt uncomfortable.

He walked to the semi-transparent information screen and clicked on the mission panel.

He was going to see if his mission was completed...

He could also verify if his thought process was correct.

Wait a minute...

Lu Zhou realized a problem.

If the system did not respond, that either meant that his guess of the system mission evaluation process was wrong or that his thesis was wrong.

The system did not give him time to think.

A notification sound rang.

Then, a line of text appeared.

[Congratulations, User, for mission completion!]