The m conference is one of the regular academic activities of the American Society for Materials Research and the most influential conference in the field of materials science.

Its coverage covers almost all research directions in the field of materials science, and its status is probably equivalent to the "International Congress of Mathematicians" in the field of materials science. Almost all of the material scholars will show their faces at the conference.

However, unlike the "International Congress of Mathematicians" which opened in four years, m is twice a year, divided into spring and autumn. Spring is generally in Phoenix, Arizona, and it is more stable in the fall, usually in Boston, Massachusetts.

The purpose of the conference was to exchange technology, showcase results to the industry, and bridge the gap between rich companies and labs that lack money, while also providing a torn place for peers.

Yes, it is torn.

If someone throws shoes at the speaker at the meeting, it must not be strange. On the contrary, no one had quarreled at that session. Everyone calmly opened the meeting, exchanged opinions, reached a consensus, and praised the technology of the peers... It will surely make people in the industry doubt whether the sun is coming out to the west.

The more the big cow, the more it is torn.

This situation is hard to see at the International Congress of Mathematicians.

In a sense, the style of mathematics and other disciplines is really different.

As a mathematics professor, Lu Zhou has no interest in tearing.

But for him, this meeting is an opportunity.

And m suddenly sent him an invitation, presumably there are many people who are very interested in his research results.

Of course, even so, Lu Zhou did not forget his identity.

He is a professor of mathematics.

Even if he wants to see the "future era" after the tenth level, he has to look a little longer, and he can't say the mathematics that determines the upper limit of other disciplines.

On the last day of August, Lu Zhou tested two other students in the office of the Institute of Advanced Studies.

The same is the ten questions, limited to two hours.

After handing the a4 paper with the title to the two hands, Lu Zhou picked the book from his desk and flipped it through his hand.

Time passes by.

As the ringing of the mobile phone rang, Lu Zhou slammed the book in his hand and looked at the two people who had worked **** the paper.

"Time is up, let me see how you are studying this month."

Hardy put down his ballpoint pen in a headache, and Qin Yue, who also stopped the pen, was also nervous.

"Professor, the time you gave is too short," got up and handed the test paper to Lu Zhou's desk. Hardy looked bitterly. "If you give me another ten minutes, I can definitely write the next one." ”

"The length of time is not the key, and I have not asked you to make every question, let me see what you will do."

After taking the test papers of the two people, Lu Zhou said, while sweeping the subject above.

For him, these are very simple things to answer, and there will probably be a number in the heart.

Qin Yue made six questions, and the seventh question was not finished, but the idea was not a big problem.

In general, his situation is not bad, and this is also expected in Lu Zhou.

Hardy made five roads and barely reached the eligibility criteria. This is somewhat unexpected.

Lu Zhou originally thought that at least one person could not pass his test, and this person is most likely to be Hardy. Because among the three students, his character is the most impetuous.

However, it seems that the situation is more optimistic, and all three have obtained the qualification to participate in this topic.

Put a4 paper on one side, Lu Zhou cleared the scorpion and said.

“First of all, congratulations on joining my topic.”

Hearing this sentence, Hardy, who was somewhat frustrated because he only made five questions, was surprised and widened his eyes. Next to Qin Yue, it also showed a strange expression.

As if to see through what they were surprised, Lu Zhou explained in a relaxed tone: "The pass line I set is five questions, at least five can be made, indicating that you have listened to the tasks I arranged, this one and a half months. Time is at least not ruined."

"For the specific content of our topic, I will simply say it."

After drinking a cup of coffee, Lu Zhou stood up and walked over to the whiteboard in the office and picked up the marker.

Vera, who was sitting in the corner of the office and silently collecting documents from the computer, stopped working on her hands. Like the other two students, she moved to her chair and sat in front of the whiteboard, waiting for the boss to speak.

"One and a half months ago, I told you that our subject is related to the hail."

"If you have an understanding of additive number theory, I believe you probably already guessed what the topic is."

Hardy and Qin Yue nodded.

As Lu Zhou said, they have already guessed what the subject is.

As for Vera, there is no extra reaction. After all, half a month ago, she passed the assessment and even participated in the project.

After a pause, Lu Zhou continued to preach.

"The so-called hail conjecture, also known as the corner valley conjecture, or the 3n+1 problem. The proposition described is that for any given positive integer n, after fokn(n) = 1 continuous action for a limited number of times, there is no exception. Enter the number trap of {4,2,1}."

"Popularly speaking, choose an n, if n is odd, the next step is 3n+1; if n is even, then the next step becomes n/2. After a finite number of cycles, no matter how its value expands during this period, but ultimately It will surely fall to the bottom of the 1st like a hail."

Having said that, Lu Zhou paused for a moment and smiled and continued.

"Like a black hole."

Compared to Goldbach’s conjecture, Hail’s conjecture is no doubt better in the United States.

In the 1970s, almost all American college campuses saw people delving into this magical "digital game." This phenomenon, even on the North American old newspaper "Washington Post", and formed a wave in a period of time.

Of course, for ordinary people, this is a digital game, but for mathematicians, it contains deeper things.

"This is a number theory problem, and it is a classic problem in additive number theory. But in the end, it is a complex analysis problem!"

"The Corner Guess is your mission for the next three years. I don't ask you to fully prove this proposition, but you have to at least complete a paper worthy of being included in the mathematics journal in this direction..."

Lu Zhou thought about it, raised the pen, and wrote a line of calculations on the whiteboard.

[h(z3)=h(z6)+{h(z2)+λh(λz2)+λ2h(λ2z2)}/3z] (where λ=e{2πi/3})

Seeing this line of calculations, Qin Yue immediately took out the notes he took with him from his pocket, and Hardy quickly started his spirit.

As for Vera, it is as concentrated as ever.

"Although the outside world is generally pessimistic about the solution to this problem, in fact, the number theory community is not making no progress on this issue."

"In the 1990s, it was exactly 94 years. Professor Benguez and Minardus proved that the 3n+1 conjecture is equivalent to the function equation h(z3), which is the equation I wrote in the previous panel. ”

“The emergence of this equation paved the first brick that led to the summit for subsequent proof.”

Some things can't be said.

Responding to the three pairs of expectations, Lu Zhou turned and continued to write on the whiteboard.

[g(z)=z/2+(1?osπz)(z+1/2)/2+1/π(1/2?osπz)sinπz+h(z)sin2πz satisfies: n?Φ(g) . 】

[...]

Seeing these lines of calculations, Vera's eyes gradually brightened.

Qin Yue and Hardy, respectively, revealed a thoughtful and incomprehensible expression.

After stopping the pen, Lu Zhou gently placed the marker on the table next to him and smiled at his three students.

"This step is critical."

"If it can be proved that there is an integer function h(z), for each g(z) above, each branch of Φ(g) containing a positive integer has z0∈d, so that [gok(z0)] converges. To 1..."

After a moment of pause, looking at the three pairs of anticipation, Lu Zhou smiled and said in a positive tone.

"Therefore, we can prove it."

"3n+1 is established!"-

References: bergl,-eations-oned-with-the-collatz——in-math, 1994, 251-12

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