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868 Mystery of the Quantum World

The controversy regarding Lu Zhou’s Quasi Riemann hypothesis proof finally came to an end. After the editorial department of Annual Mathematics received Lu Zhou’s “Hyperelliptic curve analysis” thesis, they immediately sent him an email.

In that email, the editorial department of Annual Mathematics first informed him that his thesis was in the peer review stage. Also, the Annual Mathematics would publish a special edition, solely for his thirty-page Quasi Riemann hypothesis proof and other mathematical tools used in the proof, such as the hyperelliptic curve analysis.

Generally speaking, one would have to publish a major mathematical proposition breakthrough for one of the big journals, such as Annual Mathematics, to publish a special issue.

The Quasi Riemann hypothesis was undoubtedly worthy of this honor.

Because the hyperelliptic curve analysis method was extensively used in the Quasi Riemann hypothesis proof, the editorial department decided to publish these two theses together at once.

Lu Zhou didn’t really care about the publishing plans, whether or not they were published together didn’t affect him at all.

The discussions surrounding the Quasi Riemann hypothesis would slowly die down by the beginning of next year, and maybe by then, the mathematical community would have a rough understanding of the tools he used to prove the Quasi Riemann hypothesis.

However, for Lu Zhou, this proposition was over; it was in the past.

Not to mention that after he submitted his thesis to arXiv, more than half of the mathematics community had downloaded and read his thesis. That was all he wanted.

What he needed to do now was to expand his Quasi Riemann hypothesis results to the real Riemann hypothesis...

It was worth mentioning that, during the three days after his thesis was uploaded, many people had made breakthroughs in regard to the value of ε.

That number went from infinitesimal to having a finite value.

According to the data on arXiv and Mathoverflow, the value of epsilon was being updated every day, and it slowly approached 1/2.

So far, this number had been updated to one over 60 million.

While the mathematics community was going crazy over the epsilon value, something hilarious happened.

Everyone knew that theses were time-sensitive projects.

Whoever completed their research first would get all of the credits. However, due to the academic process of a journal, the review cycle often took a long time. Therefore, many people had the habit of uploading preprints.

But uploading a preprint didn’t solve all problems. For example, if your preprint expanded epsilon to be 0.01, and someone else later expanded it to 0.1 before your thesis was accepted into a journal, then your research would become unworthy of publication.

This was a good thing for the mathematics world, but for PhDs trying to graduate, it was a disaster.

Therefore, after uploading their results on arXiv, some people tried their best to get their theses into publication. They even chose to publish in journals that had a worse reputation but a faster review process.

Unfortunately, most of these theses referenced the hyperelliptic curve analysis method, which was proposed by Lu Zhou. But that thesis itself hadn’t even passed peer review yet.

What?

You’re referencing Lu Zhou’s preprint thesis on arXiv?

Most journals and reviewers were very stubborn, and they often rejected people who cited preprints that hadn’t been peer-reviewed. However, if they didn’t cite the arXiv preprints, they might be flagged for plagiarism.

This was a ridiculous situation.

Everyone knew Lu Zhou’s thesis was correct, but they couldn’t use his tools.

Most people had no way of submitting their theses, and they could only upload them as preprints. They paid close attention to the latest Annual Mathematics publication, hoping to publish their own thesis once Lu Zhou’s thesis passed the review.

This was probably the first time where the speed of scientific research theses was faster than the journal review speed...

...

On the other hand, after bidding farewell to his old friends, Lu Zhou sat in Wang Peng’s SUV and went back to his Zhongshan International mansion.

It was as if someone threw a nuclear bomb in the mathematics community. There were countless scholars in all fields trying to further increase the value of epsilon. However, Lu Zhou wasn’t interested in the value of epsilon.

If epsilon couldn’t be increased to 1/2, then the result would be the same as the twin prime conjecture. No matter how clever someone used the hyperelliptic curve on the complex plane, it would only approach 1/2, but it would never reach it.

During this time, he occasionally checked arXiv to see if anyone used his hyperelliptic curve analysis method to create some groundbreaking results. The rest of his time was spent using Jin Ling University’s resources to find any literature on the Riemann hypothesis.

His research was in a bottleneck, and oftentimes, it was beneficial for him to read as many sources as he could, or talk with other scholars, in hopes of being inspired.

This was why Professor Faltings’ notebook was so valuable...

Lu Zhou went into his house and sat in his study room. He immediately took out that notebook and placed it on the table.

Like Tao Zhexuan had said, the notebook contained many interesting ideas.

One of them had been tested by Professor Faltings himself to be unfeasible. Some of the other ideas might be feasible, but Faltings didn’t have the time to try them.

If anyone else had this notebook, it would look like nonsense to them.

But this was exactly what Lu Zhou needed the most!

Lu Zhou read through the notes, and his eyes gradually became more and more exhilarated. However, after flipping a page, he suddenly froze.

Unlike the previous fragmented notes, the words on this page were neatly written. Also, it was written in German.

Lu Zhou didn’t know German, but thankfully he had Xiao Ai.

With Xiao Ai’s help, he easily translated the notes.

Unexpectedly, this page wasn’t about a mathematical concept, it was instead a...

Diary?

[When I studied Professor Hilbert’s theses, I found an interesting proposition in his work. Let the non-trivial zeros of the Riemann zeta function be written as ρ = 1/2 + it, then the t corresponds to the eigenvalues of a certain Hermitian operator. If this proposition holds, then the Riemann operator should be a special random Hermitian matrix.

[During afternoon tea, I spoke with Professor Klitzing from the Max Planck Institute of Physics. We were both amazed by our findings.

[Surprisingly, a pure mathematical function like the Riemann zeta function actually has a connection with quantum mechanics! Afterward, I talked with Edward Witten through email, but unfortunately, nothing came of it.

[If only I took some quantum mechanics classes... It would be too late for me to start learning physics now...]

Lu Zhou’s finger gently swiped over the texts. He put down the notebook and had a look of revelation.

So it’s not just Professor Montgomery and Professor Dyson...

Professor Faltings, who is all the way in Germany, also noticed the relationship between the Riemann zeta function and quantum dynamics. He even talked about it with Professor Klitzing and Witten.

Unfortunately, even though they also found this connection, they weren’t able to solve the puzzle.

What does this mean?

If the non-trivial zero points of the zeta function correspond to the energy level of a certain quantum mechanical system, such as the energy spectrum of a quantum mechanical system, if we say the Hamiltonian of this system is the Riemann’s operator, and if Riemann’s hypothesis holds... What does that mean for the quantum system?

In contrast, if we can find a Hamiltonian operator whose total eigenvalues correspond to the non-trivial zeros of the Riemann zeta function, does that mean we can find the proof of the Riemann hypothesis from a science perspective?

Lu Zhou looked more and more intrigued.

Even though he preferred to reveal the physics side of the Riemann hypothesis through pure mathematics, this didn’t stop him from being shocked at this unknown mystery.

These two concepts, half a century apart, somehow were connected together.

Back in the 19th century, the concept of quantum mechanics didn’t even exist...

Suddenly, Lu Zhou’s phone on the corner of the table began to ring, and this interrupted Lu Zhou’s train of thoughts.

Lu Zhou picked up his phone and connected the call.

He was about to say hello, but the other end of the phone spoke first.

The man on the phone coughed and spoke somewhat awkwardly.

“Um, Academician Lu, do you still remember me?”

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