The MRS conference was one of the regular academic activities of the American Materials Research Association. It was also the most influential conference in the field of materials science.
It covered almost all of the research directions in the field of materials science. Its status was equivalent to the "International Congress of Mathematicians" in materials science. Almost all of the big names in the materials science field would show up at the conference.
However, unlike the "International Congress of Mathematicians" that was held once every four years, MRS was held twice a year, in spring and autumn. The spring conference was usually held in Phoenix, Arizona. The fall conference was more stable, usually held in Boston, Massachusetts.
The main purpose of the conference was to exchange technology, show the results to the industry, connect rich companies with poor laboratories, and also provide a venue for people in the same industry to argue.
Yes, it was a catfight.
If someone threw a shoe at the presenter, it would not be strange. On the other hand, no one argued during that session. Everyone calmly finished the meeting, exchanged opinions, reached a consensus, and praised the technology of their peers … That would definitely make people in the industry wonder if the sun had risen from the west.
The more powerful the person, the fiercer the argument.
This kind of situation was rare at the International Congress of Mathematicians.
In some sense, mathematics was quite different from other disciplines.
As a mathematics professor, Lu Zhou was not interested in arguing.
However, for him, this conference was an opportunity.
Also, MRS suddenly sent him an invitation. Presumably, a lot of people were interested in his research results.
Of course, even so, Lu Zhou did not forget his identity.
He was a mathematics professor.
Even if he wanted to see the "future" beyond level 10, he had to look further. He could not let the upper limit of mathematics, which determined the upper limit of other disciplines.
On the last day of August, Lu Zhou was in his office at the Institute for Advanced Study. He was conducting a test with two other students.
It was the same ten questions with a time limit of two hours.
After Lu Zhou handed the A4 paper with the questions to the two students, he picked up a book from his desk and began to read.
Time quickly passed by.
Lu Zhou's phone rang, and he slammed the book in his hand. He looked at the two people writing on the paper.
"Time's up. Let me see how you've learned this month."
Hadi put down the pen in his hand with a headache. Qin Yue, who had also stopped writing, also looked nervous.
"Professor, you didn't give me enough time." Hadi got up and placed the test paper on Lu Zhou's desk. He had a bitter expression on his face as he said, "If I had ten more minutes, I would definitely be able to write the next question."
"The length of time isn't the key, and I'm not asking you to answer every question. I just want to see what you know."
Lu Zhou took the test paper from the two and said while glancing at the questions on it.
To him, these were all very simple things. With just a glance, he had a rough idea of what was going on.
Qin Yue had answered six questions. He had not finished the seventh question, but his thought process was fine.
All in all, his situation was not bad, and this was also within Lu Zhou's expectations.
Hadi was able to answer five questions, barely reaching the passing standard. This was somewhat out of Lu Zhou's expectations.
Lu Zhou originally thought that at least one person would not be able to pass his test, and that person was most likely Hadi. Because out of the three students, Lu Zhou was the most impetuous.
But now, it seemed that the situation was quite optimistic. All three of them were qualified to participate in this research project.
Lu Zhou put the A4 paper aside and cleared his throat.
"First of all, congratulations on joining my research project."
When Hadi heard this, he was a little depressed because he only managed to answer five questions. His eyes widened in surprise. Qin Yue, who was next to him, also had a surprised expression.
Lu Zhou seemed to know what they were surprised about. He said in a relaxed tone, "I set the passing standard to be five questions. If you can answer at least five questions, it means that you guys listened to my instructions and didn't waste the past month and a half.
"As for the specific content of our research project, I'll give you a simple explanation."
Lu Zhou took a sip of his coffee and stood up. He walked to the whiteboard and picked up a marker.
Vera, who was sitting in the corner of the office, quietly collecting literature on her computer, also stopped what she was doing. Like the other two students, she moved her chair and sat in front of the whiteboard, waiting for her boss to speak.
"One and a half months ago, I revealed to you that our research project is related to hail.
"If you know about additive number theory, I'm sure you can probably guess what this research project is."
Hadi and Qin Yue nodded.
Just like what Lu Zhou said, they already guessed what the research project was.
As for Vera, she didn't have much of a reaction. After all, she had already passed the test half a month ago and had already participated in the research project.
Lu Zhou paused for a second and continued.
"The so-called Hail conjecture, also known as the Collatz conjecture, or the 3n + 1 problem. The proposition described is that for any positive integer N, after a finite number of continuous actions by fokn (n) = 1, all of them will fall into the trap of {4,2,1} without exception. "
"In layman's terms, if N is an odd number, the next step is 3N + 1; if N is an even number, the next step is N/2. After a finite number of cycles, no matter how much it expands during this period, it will eventually fall to the bottom of 1 like a hail. "
Lu Zhou paused for a second and spoke with a smile.
"Just like a black hole."
Compared to Goldbach's conjecture, the Hail conjecture was undoubtedly more well-known in the United States.
In the 1970s, one could see people studying this magical "numbers game" on almost every university campus in the United States. This phenomenon was even reported in the "Washington Post" newspaper in North America, and it became a trend for a period of time.
Of course, for ordinary people, this was just a numbers game, but for mathematicians, it contained deeper meaning.
"This is a number theory problem, a classic additive number theory problem. But in the end, it's a complex analysis problem!
"The Collatz conjecture is your mission for the next three years. I don't require you to completely prove this proposition, but you have to at least complete a thesis in this direction that is worthy of being included in Annual Mathematics … "
Lu Zhou thought for a bit before he picked up a pen and wrote a line of calculations on the whiteboard.
Where λ = e ^ {2πi/3})
When Qin Yue saw this line of calculations, he immediately took out his notebook from his pocket. Hadi also quickly paid attention.
As for Vera, she was listening intently as usual.
"Although the outside world is generally pessimistic about solving this problem, in fact, the number theory community has made some progress on this problem.
"In the 1990s, to be exact, in 1994, Professor Benge and Professor Manadus proved that the 3n + 1 conjecture is equivalent to the function equation h (z ^ 3), which is the equation I wrote on the whiteboard.
"The appearance of this equation paved the first brick to the top of the mountain for subsequent proofs."
Some things couldn't be said.
Lu Zhou looked at the three pairs of eyes filled with anticipation. He then turned around and continued to write on the whiteboard.
[g (z) = z/2 + (1? cosπz)(z+1/2)/2+1/π(1/2? Cosπz) sinπz + h (z) sin2πz satisfies: N? Φ (g).]
[…]
When Vera saw these lines of calculations, her eyes gradually lit up.
Both Qin Yue and Hardy seemed to be deep in thought, as if they understood something.
After Lu Zhou stopped writing, he gently placed the marker pen on the table and smiled at his three students.
"This step is critical.
"If we can prove that there is an entire function h (z), then for g (z), for every branch D of Φ (g) that contains a positive integer, there exists z0 ∈ D, so that [gok (z0)] converges to 1 …"
Lu Zhou paused for a second and looked at the three pairs of eyes. He then smiled and spoke in a confident tone.
"Then we can prove it.
"3n + 1 is established!"
Refs, s-in-Math, 1994, 25: 1-12
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