In the reply, in addition to commending him and the Jinling Institute for Advanced Study for the contributions, the state also asked for his opinion on the industrialization of the carbon-based chips.
Lu Zhou didn’t have any strong opinions. The only thing that surprised him was how efficient Beijing was. They had a conference last night, and they sent him the letter the next day.
With the envelope in his hand, Lu Zhou asked, “That quick?”
Wang Peng was sitting next to Lu Zhou, and he replied, “Letters at this level are all sent by air. It takes half an hour to reach Jinling from Beijing. I received a call at four o’clock in the morning, informing me that the letter has arrived at the Jinling Ministry of State Security department.”
“That’s not what I meant… Never mind, forget about it.” Lu Zhou put away the letter and said to Wang Peng, “Take me to Jin Ling University.”
Wang Peng nodded and opened the car door for Lu Zhou.
“Okay, get in.”
…
Lu Zhou put the carbon-based chips matter aside.
After Lu Zhou arrived at Jin Ling University, he went to his office as usual and sat down at his desk.
Because he received the mission rewards yesterday, he got off work early and went to the Institute for Advanced Study. Then, he was caught up in the carbon-based chip breakthrough, so he hadn’t had a chance to continue his research.
Lu Zhou pulled out the half-written piece of draft paper from yesterday and spent 5 minutes reviewing what he had written. He then found a pen and started to quietly finish his calculations.
The hour hand on the wall went from 8 o’clock to 9 o’clock.
Suddenly, the office door was opened. Luo Wenxuan walked in excitedly with a stack of A4 papers on his hand and a smile on his face.
“A while ago, I dug up Dyson’s thesis and read it, guess what I found out?”
Lu Zhou was used to Luo Wenxuan not knocking. He looked up and jokingly replied, “Dyson? That physicist who switched to writing science fiction?”
“Incorrect, he’s not just some science fiction writer, he is one of my idols!” Luo Wenxuan waved the stack of A4 papers in his hand and said confidently, “I found something interesting in his thesis, I’m sure you will be interested as well!”
Lu Zhou was just joking about the science fiction part. He obviously knew that Dyson wasn’t just a “fiction writer”. Dyson’s “Spin wave theory” was one of the most outstanding physics results in the 1950s.
However, just like Hawking, because of Dyson’s fame in the science fiction world, his academic abilities were often overlooked. After all, in the eyes of the public, academic researchers were either genius scientists, or nerdy freaks…
Luo Wenxuan’s excitement didn’t faze Lu Zhou, Lu Zhou said, “Right now, I’m only interested in the Riemann zeta function. If you’re talking about quantum chromodynamics research… I suggest you talk to the physics department of the institute.”
“It’s not quantum chromodynamics, I am talking about the Riemann zeta function!”
“Oh really?” Lu Zhou put down his pen and looked intrigued. He said, “Tell me then, what did you find in his thesis?”
Lu Zhou didn’t believe that Dyson had studied the Riemann hypothesis before.
Even though physics and mathematics were closely related, the gap between theoretical physics and analytic number theory was too big.
Luo Wenxuan placed the stack of A4 papers on the table and spoke energetically.
“Precisely speaking, this is a diary that is apparently written by Dyson himself. An old man from the Firestone Library gave it to my friend… You know who I’m talking about, right?”
“That old guy who wears a robe and looks like a wizard?”
“That’s right, him… Of course, that’s not the point. The point is that we found this.” Luo Wenxuan grabbed his phone and showed Lu Zhou a photo. “In Dyson’s diary, we found a transcript of a conversation between him and Montgomery.”
Lu Zhou raised his eyebrows.
“And?”
Luo Wenxuan excitedly said, “They were talking about Riemann’s hypothesis. Even though Dyson isn’t a mathematician, the results were extremely shocking! Can you believe that the Riemann zeta function’s zero-point density function coincides with the pairwise correlation function of the Hermitian matrix.”
When Lu Zhou heard about the Hermitian matrix, he was intrigued.
Luo Wenxuan noticed Lu Zhou was interested, so he patted the stack of A4 papers on the table.
“Then, I found his thesis published in Physical Reviews… Are you still not interested?”
“Let me have a look.”
Lu Zhou stood up from his chair and began reading the stack of A4 papers.
When he got to the second page, he had a serious look on his face.
“I’m so surprised. I’ve never heard anyone who is researching the Riemann hypothesis talk about this thesis.”
Luo Wenxuan sat on the corner of the desk and smirked as he said, “That makes sense. Have you ever seen anyone on Mathoverflow talk about using a critical line proof? This thesis has been around for half a century, with no new developments.”
“You’re right…” Lu Zhou looked at Luo Wenxuan and asked, “Can you sit on a chair?”
“Oh, my bad.” Luo Wenxuan got off from the table and said, “I’m used to sitting on my own desk like this.”
Lu Zhou placed his focus back onto the thesis, and the more he read, the more shocked he was.
Not because of Professor Dyson’s own research results, but because of the mysterious phenomenon Dyson found.
Which was, the distribution density of the eigenvalues of an N-th order random Hermitian matrix was P (λ1, …, λN) = C exp[-Σiλi2] Πj u003e k (λj-λk). By analyzing the distribution density, using the Wigner semicircle distribution law to perform a scalar transformation of the eigenvalues, and then normalizing the average interval of eigenvalues to Δμ ~ 1, one could obtain the correlation function P2 (μ1, μ2 ) = 1- [sin (π | μ2-μ1 |) / π | μ2-μ1 |] 2.
What did this mean?
This was the non-trivial zero-point correlation function of the Riemann zeta function!
It wasn’t just similar, the functions were exactly the same!
“Very… interesting.”
Lu Zhou rubbed his chin. He was more intrigued than ever.
Actually, he wasn’t just intrigued, he was in disbelief!
Why was a purely mathematical function, such as the non-trivial zero distribution of the Riemann zeta function, related to an applied linear algebra function, used in quantum systems, disordered media, and neural networks?
Where did this mysterious relationship come from?
Lu Zhou’s eyebrows furrowed.
He had a gut feeling that this relationship was important.
But how could he apply this relationship?
Suddenly, Lu Zhou received an email notification.
While Lu Zhou looked at the computer, Luo Wenxuan asked curiously, “What now?”
“New email… I think it’s from the Annual Mathematics editorial department.” Lu Zhou clicked on the notification and began reading the email.
Luo Wenxuan paused for a second and then asked, “Approved?”
The entire office was silent now. They were all listening in on the conversation.
Especially He Changwen, who was sitting nearby.
Lu Zhou stared at the email and went silent for a while.
Then, he spoke with an uncertain tone.
“Not approved?”
The office went silent for a few seconds.
After a while, everyone looked muddled.
Luo Wenxuan: “…?”
He Changwen: “…?”
Assistants and students: “… ???”
