Lu Zhou thought for a while, picked up his pen, and wrote a line of calculations on the whiteboard.
"3n+1 is established!"
As the ringtone of his cell phone rang, Lu Zhou closed the book in his hand with a snap and looked at the two people who were writing furiously on the paper.
As if he saw through what they were surprised about, Lu Zhou explained in a relaxed tone: "The passing mark I set is five questions. You can answer at least five questions, which shows that you have listened to the tasks I assigned. This month and a half At least the time was not wasted."
"Although the outside world is generally pessimistic about solving this problem, in fact, the number theory community is not without progress on this problem."
But for him, this meeting was an opportunity.
[…]
The more powerful you are, the more powerful you will be.
After stopping writing, Lu Zhou gently placed the marker on the table next to him and smiled at his three students.
As for Vera, she listened attentively as always.
As for Vera, there was no unnecessary reaction. After all, she had passed the assessment half a month ago and had even participated in the project.
"In the 1990s, 1994 to be precise, Professors L. Berg and G. Meinardus proved that the 3n+1 conjecture is equivalent to the function equation h(z^3) , which is the equation I wrote above.”
Hearing this, Hardy, who was originally a little frustrated because he only answered five questions, opened his eyes wide in surprise. Qin Yue next to him also showed a surprised expression.
In the 1970s, you could see people delving into this magical "numbers game" on almost all American university campuses. This phenomenon has even appeared in the "Washington Post", a long-established North American newspaper, and formed a trend for a period of time.
After handing the A4 paper with the title to the two of them respectively, Lu Zhou picked the book from his desk, held it in his hand and started reading.
Even in order to see the "future era" after level 10, he had to take a longer view, and he could not leave behind mathematics, which determines the upper limit of the levels of other subjects.
After taking the test papers from the two of them, Lu Zhou glanced at the questions above as he spoke.
Just as Lu Zhou said, they had already guessed what the topic was.
Yes, it's a joke.
Hardy finished five tricks, barely reaching the passing standard, which was somewhat beyond Lu Zhou's expectation.
Time passed by minute by minute.
"A month and a half ago, I told you that our topic was related to hail."
"If you know something about additive number theory, I believe you have probably guessed what this topic is."
Overall, his situation was pretty good, and this was what Lu Zhou expected.
After taking a sip of coffee, Lu Zhou stood up, walked to the whiteboard in the office, and picked up a marker.
"The Kakutani conjecture is your task for the next three years. I don't ask you to completely prove this proposition, but you must at least complete a paper in this direction that is worthy of being included in the Annual Journal of Mathematics... "
But now it seems that the situation is relatively optimistic, and all three people have obtained the qualifications to participate in this topic.
Putting the A4 paper aside, Lu Zhou cleared his throat and spoke.
"Like a black hole."
After pausing for a moment, looking at the three pairs of expectant eyes, Lu Zhou smiled and said in a positive tone.
Qin Yue and Hadi showed thoughtful and half-understanding expressions respectively.
Of course, to the average person, it's a numbers game, but to a mathematician, there's something much deeper to it.
Don't be surprised if someone throws a shoe at the presenter during the meeting. On the contrary, no one quarreled at that meeting. Everyone finished the meeting calmly, exchanged opinions, reached a consensus, and praised the technology of their peers... This will definitely make people in the industry wonder whether the sun is rising in the west.
[h(z^3)=h(z^6)+{h(z^2)+λh(λz^2)+λ^2h(λ^2z^2)}/3z] (where λ=e^ {2πi/3})
Having said this, Lu Zhou paused for a moment, smiled and continued.
In a sense, the style of painting in mathematics is really different from that in other subjects.
This situation is difficult to see at the International Congress of Mathematicians.
[g(z)=z/2+(1-cosπz)(z+1/2)/2+1/π(1/2-cosπz)sinπz+h(z)sin2πz satisfies: N is included in Φ(g ).]
The MRS conference is one of the regular academic activities of the American Materials Research Society and is also the most influential top conference in the field of materials science.
"The so-called hail conjecture is also called the Kakutani conjecture, or the 3n+1 problem. The proposition it describes is that for any given positive integer N, after fokn (n) = 1 is continuously acted on for a finite number of times, it will always fall into place without exception. Fall into the number trap of {4, 2, 1}."
Hadi and Qin Yue nodded one after another.
The main purpose of the conference is to exchange technologies, showcase results to the industry, connect wealthy companies and cash-strapped laboratories, and also provide a place for peers to argue.
"From this, we can prove it."
"This is a number theory problem, and it is a classic problem in additive number theory. But in the final analysis, it is a complex analysis problem!"
Of course, even so, Lu Zhou did not forget his identity.
Responding to the three pairs of expectant eyes, Lu Zhou turned around and continued writing on the whiteboard.
Seeing this line of calculations, Qin Yue immediately took out the notes he carried with him from his pocket, and Hardy quickly cheered up.
"The length of time is not critical, and I don't ask you to solve every problem. Just let me see what you know."
There are also ten questions, and the time limit is two hours.
As a mathematics professor, Lu Zhou has no interest in fighting.
"It's time, let me see how you have learned this month."
Its coverage covers almost all research directions in the entire field of materials science, and its status is roughly equivalent to the "International Congress of Mathematicians" in the field of materials science. Almost all the experts in the field of materials science will show up at the conference.
Vera, who was sitting in the corner of the office silently collecting documents on the 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 start speaking.
For him, these are very simple things, and he can probably count them in his mind at a glance.
"Professor, the time you gave is too short," Hardy stood up and handed the test paper to Lu Zhou's desk with a bitter expression on his face, "If you give me another ten minutes, I will definitely be able to write the next question. "
"First of all, congratulations on joining my project."
He is a mathematics professor.
Qin Yue finished six questions and left the seventh question unfinished, but there was no big problem with his thinking.
Hardy put down the ballpoint pen in his hand with a headache on his face, and Qin Yue, who also stopped writing, also looked nervous.
Moreover, MRS suddenly sent him an invitation letter, so many people must be interested in his research results.
Compared with Goldbach's conjecture, the hail conjecture is undoubtedly more famous in the United States.
"In layman's terms, choose an N. If N is an odd number, the next step is 3N+1; if N is an even number, the next step becomes N/2. After a finite number of cycles, no matter how its value expands during this period, but in the end It will surely fall suddenly to the bottom of 1 like hailstones."
After a pause, Lu Zhou continued to preach.
There are some things that cannot be said.
Lu Zhou originally thought that at least one person would fail his test, and this person was most likely Hardy. Because among the three students, he has the most impetuous character.
"This step is critical."
On the last day of August, Lu Zhou tested two other students in his office at the Institute for Advanced Study.
"The emergence of this equation paved the first brick to the top of the mountain for subsequent proofs."
However, unlike the International Congress of Mathematicians, which is held every four years, MRS is held twice a year, in spring and autumn. Spring is usually in Phoenix, Arizona, and fall is more stable, usually in Boston, Massachusetts.
Seeing these lines of calculations, Vera's eyes gradually brightened.
"I'll just briefly talk about the specific content of our topic."
"If it can be proved that there is an integer function h(z), for the above g(z), for each branch D of Φ(g) containing a certain positive integer, z0∈D exists, making [gok(z0)] converge To 1…”