Scholar’s Advanced Technological System

There was a well-known joke in the mathematics world which was used to ridicule physicists. It was about how physicist proved that “odd numbers are prime numbers”.

The joke was that 1 was a prime number, so 3,4,5,7, 9 was a random error, 11 was a prime number, so was 13…

Okay, enough experiments, all odd numbers were prime numbers!

Then, after several years of experiments, more numbers were tested. The physicists found “experimental errors” that exceeded the confidence threshold. The physicists then added onto the theory and redefined the definition of physics for three-digit numbers.

This sounded like the evolutionary nature of relativity where theories were constantly changed and improved on.

In reality, theoretical physics lacked the rigor and beauty of mathematics.

The 750 GeV characteristic peak was similar to “9 is a random error”, whereby if it was repeated multiple times, it was a “sign” or even “discovery”. However, if it disappeared, then it became a random error.

Unfortunately, even the upgraded Hadron Collider could only do experiments for “prime numbers under 100”. The theory was way ahead of the technology.

At the end of the meeting, Professor Frank dissolved the team.

Lu Zhou’s gains were merely two theses, co-signed with Professor Frank and his PhD students.

For him, this was definitely bad news.

However, Lu Zhou did not intend to give up.

Even though Professor Frank gave up, Lu Zhou would continue to research this project.

Mathematics was the language of God, and although Lu Zhou did not believe in God, he believed that mathematics would not deceive people.

Through his rigorous calculations, he predicted the appearance of the characteristic peak. Although he did not know why it disappeared, never for a second did he believed that it did not exist.

Otherwise, how else could anyone explain the detections from both ATLAS and CMS?

Could it just be quantum fluctuations?

The probability was too low for fluctuations to be observed by two detectors at the same time.

Lu Zhou originally planned on hanging around New York for a few more days but because of this bad news, he was no longer in the mood.

In the same afternoon, he drove back to Princeton.

It was already night time by the time he got back to his apartment. He bumped into Molina who was back from her night run. She was wearing a black sports bra and her golden hair moistened from sweat. She looked elegant and charming.

Molina glanced at Lu Zhou and noticed something. She teased him, “I can see that you’re not in a good mood.”

“Yeah.”

Molina raised her eyebrows and gloated, “Dumped?”

“I guess.”

Lu Zhou took out his keys. He then opened the door and went inside.

Molina looked at the door close. After a while, she whispered to herself, “I guess he really did get dumped…”

…

Excavating the 750 GeV characteristic peak required a Hadron Collider with a higher brightness detector and many other things…

Lu Zhou could predict the characteristic peak from calculations, but he could not prove the existence of this particle purely through theory. He could only perfect his model and then wait for CERN to verify his theory.

Unfortunately, many people had lost hope in this “750 GeV”.

Like Molina said, he was “dumped”, physics “dumped” him and left him alone.

Lu Zhou did not have any better ideas. He could only seek comfort in the arms of mathematics.

At least, improved his Group Structure Method. Perhaps this temporary depression could be turned into motivation and maybe helped him find the last piece of the conjecture.

Lu Zhou took a shower and went to bed early.

The next morning he woke up refreshed. He printed out the lecture slides and went to the mathematics building.

The mathematics building was the tallest building in all of Princeton. It represented the significance and status of mathematics at Princeton.

However, Lu Zhou was not here for an esoteric lecture. He was instead attending a number theory lecture with a bunch of undergrads.

As a winner of the Cole Prize in Number Theory, why did he have to waste time and listen to an undergrad lecture? Yesterday night in bed, he suddenly remembered a book he read in University of Jin Ling library.

That book was the autobiography of Mr. Yang Zhenduo, in which it contained a chapter about Fermi.

In the book, the author mentioned that Fermi advised him not to stay at Princeton for too long because that place was like a monastery.

Mr. Yang’s biggest impression of Fermi was that Fermi loved to communicate with students. Fermi was keen on lecturing, organized seminars, and his students won six Nobel Prizes.

More than once, he mentioned that his ideal plan was to teach physics in a small Ivy League school and to write a book that contained all of the difficulties in physics.

From Vera’s letter, Lu Zhou suddenly realized that while studying Goldbach’s conjecture, he ignored some “well-known” things.

Helfgott’s paper was very useful, but he skipped over a lot of things and was too brief. For Lu Zhou, the things that Helfgott skipped over were “obvious”, but he missed out on many “obvious” details.

Abstraction should be done, only after careful scrutiny.

Lu Zhou hoped to recapture some basic principals and concepts and to see things from a different perspective as a way of inspiration.

Lu Zhou quietly walked into the classroom as he did not want to attract anyone’s attention. He found a seat in the last row.

The lecturer was the current head of the mathematics department, Charles Fefferman, who solved calculus at 12 years old, doctorate at 20 years old, and by 22 years old, he was a professor of Chicago University. He was considered a super genius.

Charles looked at the class and stared at Lu Zhou’s face for a second. He clearly recognized Lu Zhou. However, he did not say anything. Like usual, he wrote on the whiteboard and started his lecture.

Princeton’s students were all exceptional. There were IMO competition finalists, Putnam competitors, and geniuses from all over the world attending this lecture.

Doing a lecture for these geniuses were obviously different than at a normal university.

Especially for those sloppy professors.

Charles was talking about the proof of the prime number theorem. When he wrote down the 20th line of proof, someone raised their hand.

“Professor, the value of the Φ(s) function should be 2 instead of 3!”

Obviously, someone had already studied the prime number proofs.

Charles turned around. He smiled calmly and said, “You’re right, but can you believe that even if this step is wrong, I can still prove the theorem.”

That student was stunned and whisperings were heard in the classroom.

From the whispers, Lu Zhou could feel a sense of disbelief coming from the students.

It was not just the students, but Lu Zhou himself was also in disbelief.

Lu Zhou was very rigorous toward calculations and he would never make a mistake.

However, Lu Zhou did not say anything. Instead, he patiently waited for the professor to finish the proof.

Charles did not say anything. Instead, he turned around and started to write on the whiteboard.

15 minutes went by and he finally finished his last line of calculations. Everyone in the classroom was stunned.

Especially the student that pointed out the mistake. His face was full of confusion.

That mistake was clearly there, but…

Charles solved it!

“I’ve personally researched the prime number theorem, and there’s around a dozen of them. The rigor of calculations is very important, but when we are at the frontier field, it’s more important to be logically self-consistent. This is not just for mathematics, but for all of science. As for why I could draw the same conclusion, it’s because I’ve tried numerous methods of proofs, and found out that most methods are the same…”

Charles smiled and gently wiped out the “3”. He changed it to a “2” and said, “Of course, I was only manipulating the mistake. Student Smith is correct, the calculation result should be a 3, but whether it is a 2 or 3, we still satisfy the interval defined by function ζ(x).”

It was clear he knew this theorem inside and out, like the back of his hand.

Lu Zhou even suspected that Charles purposely made a mistake to demonstrate to these rookies.

Of course, his attention was not here.

“Same result but from different calculations?”

Lu Zhou repeated this sentence and went into deep thought.

His eyes gradually lit up.

He suddenly realized something.

The puzzle he had been searching for was in his own hands…