Scholar’s Advanced Technological System

The MRS Conference is one of the regular academic activities of the American Materials Research Association and the most influential top-level meeting in the field of materials science.

Its field of coverage covers almost all the research directions of the entire material sciences, and its status is roughly equivalent to that of the "International Congress of Mathematicians” of the material sciences, where almost the entire material sciences bull will show his face.

Unlike the quadrennial International Mathematicians' Conference, however, MRS is held twice a year, in spring and autumn. Spring is generally in Phoenix, Arizona, while autumn is more stable, usually in Boston, Massachusetts.

The purpose of the meeting was primarily to exchange technology, showcase results to industry, build bridges between wealthy businesses and laboratories in need, and provide peers with a torn space.

Yeah, just rip it off.

If someone throws shoes at the reporter at the meeting, don't be surprised. Instead, no one quarreled at that session. Everyone calmly finished the meeting, exchanged views, reached consensus, and praised the technology of their peers… that would surely cast doubt on the industry whether the Sun had risen from the West.

The bigger the bull, the more powerful the tear.

This was difficult to see at the International Congress of Mathematicians.

In a way, mathematics and other disciplines are very different.

As a mathematics professor, the Ark has no interest in tearing.

For him, however, the meeting was an opportunity.

And MRS suddenly sent him an invitation, and I'm sure a lot of people are interested in his research.

Of course, even so, the ship has not forgotten its identity.

He's a math professor.

Even in order to see the "future era” after level 10, he had to look at it a little longer, and he could hardly leave behind the mathematics that determined the ceiling for other disciplines.

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

It's also ten questions, limited to two hours.

Once the A4 paper with the title was handed over to the two of them, the ark picked the book from its desk and read it in its hand.

Time goes by.

As the cell phone rang, the ark slammed closed the book in its hand and looked at the two people who were screaming on paper.

“Time's up, let me see how you guys are doing this month. ”

Hadi put down the ballpoint pen in his hand with a headache, and Qin Yue, who also stopped writing, was also nervous.

“Professor, you've given me too little time.” Get up and hand the paper over to the Ark desk. Hardy's face is bitter. “If you give me another 10 minutes, I can definitely write down the next question. ”

“The length of time is not the key, and I didn't ask you to come up with every question, just let me see what you're going to do. ”

After taking the paper of the two people, the ark said, sweeping the title.

For him, these are very simple answers, and at a glance, there's probably a number.

Qin Yue made six questions. The seventh question is not finished, but the thought is not a big problem.

Overall, he's doing quite well, and that's what the ship expects.

Hardy made five moves, barely meeting the eligibility criteria, which was a little unexpected for the Ark.

The Ark had thought that at least one person could not pass his test, and this person was most likely Hardy. Because of these three students, his personality is the most irritating.

However, it now appeared that the situation was more optimistic and that all three had been qualified to participate in the subject.

Putting the A4 paper aside, the ark cleared its voice and said.

“Congratulations on joining me. ”

When I heard that, Haddie, who was somewhat frustrated because he had made only five questions, opened his eyes to surprise. Qin Yue next to him also gave a strange look.

As if to see through what they were surprised at, the ark said in a relaxed tone: “I set the pass line to five questions, at least five, which means that you have listened to my assignment, and this month and a half has not been abandoned. ”

“Let me be brief about the specific content of our topic. ”

After a sip of coffee, the ark stood up, walked up to the whiteboard of the office and picked up the marker pen.

Vera, who was sitting in the corner of the office and silently gathering literature for the computer, also stopped working on her hands and, like two other students, sat in front of the whiteboard in her chair waiting for the boss to speak.

“A month and a half ago, I told you that our subject was about hail. ”

“If you know anything about additive mathematics, I'm sure you've guessed what the subject is. ”

Hardy and Qin Yue nodded.

As the Ark said, they have guessed what the subject is.

As for Vera, there was no redundant response. After all, half a month ago, she had passed the examination and had even been involved in the subject.

After a pause, the ark continued to preach.

“The so-called hail conjecture, also known as the Corner Valley conjecture, or the 3n +1 problem. Its descriptive nomenclature is that, for an arbitrary positive integer N, after a limited number of consecutive actions of FOKN (N) = 1, it falls into the {4, 2, 1} digital trap without exception. ”

“Commonly, choose an N, if N is an odd next step 3N +1; if N is an even number, the next step becomes N2. After a limited number of cycles, no matter how much it expands during this period, it will eventually suddenly fall to the bottom of the valley of 1, like hail. ”

Speaking of which, the ark paused for a moment and laughed and continued.

“Like a black hole. ”

Hail speculation is undoubtedly more prominent in the United States than Goldbach speculation.

In the 1970s, almost all American university campuses saw people drilling this amazing "digital game”. This phenomenon, which even appeared in the Washington Post, an old North American newspaper, has been a trend for some time.

Of course, it's a digital game for ordinary people, but for mathematicians it contains something deeper.

“It's a mathematical question, and it's a classic question in additive mathematics. But in the end, it's a question of re-analysis! ”

“The Cape Valley guess is your task for the next three years. I do not ask you to prove this proposition completely, but you must at least complete a paper in this direction worthy of inclusion in the annual journal of mathematics...”

The ark thought about it, the pen, and wrote a line of formulas on the whiteboard.

[h (z ^ 3) = h (z ^ 6) + {h (z ^ 2) + λh (λz ^ 2) + λ ^ 2h (λ ^ 2z ^ 2)} 3z] (where λ = e ^ {2πi3})

Seeing this line of formula, Qin Yue immediately took the notebook he carried from his pocket, and Hadi quickly aroused his spirit.

As for Vera, it's just like always listening to Concentrate.

“While there is widespread pessimism in the outside world about solving this problem, the fact is that the digital world is not without progress on this issue. ”

“In the 1990s, to be precise, in '94, Professor L. Berg and Professor G. Meinardus proved that 3n +1 guesses are equivalent to the function equation h (z ^ 3), the equation I used in the panel book. ”

“The emergence of this equation paved the way for the first brick to the top of the mountain for subsequent proof. ”

Some things can't be said.

Responding to those three eagerly awaited sights, the ark turned around and continued the book on the whiteboard.

[g (z) = z2 + (1 − cosπz) (z +12) 2 +1π (12 − cosπz) sinπz + h (z) sin2πz Satisfaction: N ⊂ Φ (g).

……

As she saw these lines of formula, Vera's eyes became brighter.

Qin Yue and Hadi, respectively, showed a thoughtful and seemingly incomprehensible look.

After stopping the pen, the ark gently placed the marker on the table next to it and smiled slightly at his three students.

“This step is crucial. ”

“If it can be demonstrated that there is an entire function h (z), for each of the branches D of g (z), Φ (g) above, containing a positive integer, there is z0 × D, so that [gok (z0)] converges to 1...”

Paused for a moment, looking at the three expected gazes, the ark laughed and said in a positive tone.

“So we can prove it. ”

“3n +1 established! ”