When Professor Fefferman heard this, he paused for a second.
Soon after, he adjusted his expression and spoke in a serious manner.
"Can you explain it in detail?"
"Of course." Lu Zhou picked up the chalk and said, "But I need to use the blackboard."
Once the thought process was established, the calculations were just a matter of time.
It took around half an hour for the two sides of the blackboard to be filled with chalk.
Lu Zhou took two steps back and looked at the calculations on the blackboard. He gently held the piece of chalk in his hand and spoke in a confident tone.
"In summary, using the abstract proof method, we can only conclude that there is a T1 (> 0), which makes the weak solution smooth in local time (0, T1). The value of T1 has yet to be determined. "
This conclusion was very different from the final conclusion of the Millennium Prize Problems. As for how different it was, it was like Newton's law of motion to the special theory of relativity.
The former limited the initial boundary value and was only applicable in a finite time domain. On the other hand, the Millennium Prize Problem of the Navier – Stokes equation discussed the existence and smoothness of a solution to the Navier – Stokes equation under three-dimensional conditions.
The reason why the equation they constructed exploded at an unknown specific value of t = T1 was because the specific value exceeded the interval of (0, T1).
Just like how Newton's law of motion only applied to low-speed motion, it didn't apply to high-speed motion …
After listening to Lu Zhou's explanation, Fefferman was speechless.
"… If you knew this was wrong, why didn't you tell me earlier?"
Lu Zhou coughed and said, "… I just thought about it now."
Professor Fefferman stared at the blackboard for around ten minutes. He reread the steps and sighed.
"You're right, our previous thinking process wasn't perfect …"
Many things, once pointed out, weren't as mysterious as they seemed.
Professor Fefferman paused for a second and said, "However, just like you said, if we can give a certain T1 value, we can confirm that the Navier – Stokes equation has a smooth solution in a specific time interval."
Lu Zhou was slightly stunned. He didn't expect him to be so obsessed with abstract proofs.
After pondering for a while, Lu Zhou added.
"This alone is not enough. We must use a precise method to distinguish the primitive operator B from the constructed bilinear operator B '."
Professor Fefferman sighed and said, "I know what you mean. However, compared to opening up a new line of thought, I still felt that it was more appropriate to continue on the original research results. At least in my opinion, the method of abstract proof still has potential. "
After a moment of silence, he finally made a decision.
"Since we are both suitable for independent research, let's do it separately."
Although he was also optimistic about the new idea provided by Lu Zhou, he didn't plan to give up the abstract proof method so easily.
Since that was the case, the two of them set off from two different directions at the same time.
Of all the roads, there had to be one that led to Rome.
Lu Zhou nodded and agreed with Professor Fefferman's proposal.
"That's the best choice."
Mathematical propositions could be researched in a discussion, but discussion was never the only choice.
At night, after a run, Lu Zhou returned home. He took a shower and went straight to his study room. He turned on his laptop and continued to make final changes to the "L Manifold" thesis.
The research on the L Manifold was actually quite an outstanding research result.
Just like the bilinear operator B 'constructed by Professor Fefferman. Even if it couldn't directly solve the Navier – Stokes equation, it could still be published as an independent research result.
It would be more than enough to give a report at the International Congress of Mathematicians (IMU) in August.
As for what it was used for?
Researching the solution of the Navier – Stokes equation was definitely the most important thing. Other than that, it could also be used like other differential manifolds to perform "topological surgery" on some complex nonlinear differential structures, making those complex problems look less complicated.
As for its use in other fields, that would be up to other researchers.
Perhaps one day, its research results would shine in the field of theoretical physics or engineering, but none of this was guaranteed.
Lu Zhou stared at his computer screen and went silent for a long time. In the end, he made up his mind and submitted the L Manifold thesis to Annual Mathematics.
As for the IMU conference in August …
He still decided to present the Navier – Stokes equation as a gift to the international mathematics community.
Even if this decision seemed to be full of challenges.
After all, he only had a vague understanding of the Navier – Stokes equation.
It was hard to say if any idea was correct or not.
Not long after Lu Zhou uploaded his thesis, his L Manifold thesis passed the review of the academic editors and entered the peer review stage. His thesis on the Collatz conjecture was published in the latest issue of Annual Mathematics to the international mathematics community.
Just like what Lu Zhou had expected.
As soon as this thesis was published, it caused quite a stir …
…
Kai University, Shiing-Shen Chern Mathematics Institute.
The latest issue of Annual Mathematics was spread out on the table.
Academician Zhang Wei read the thesis from beginning to end and sighed emotionally.
"No wonder he's Professor Lu. I didn't expect him to not only be good at research, but he's also good at teaching students …"
Academician Zhang knew about Qin Yue's student. He was the one who recommended Qin Yue to Princeton for a master's degree.
Honestly, when Academician Zhang encouraged Qin Yue to apply for a master's degree under Professor Lu, he didn't have high hopes.
Because at the time of the Goldbach's conjecture, there wasn't a single professor in the mathematics community who was more "popular" than Princeton Professor Lu.
After all, this was Goldbach's conjecture.
It was the crown of number theory that had stumped Gauss and Euler.
Even People magazine, which was thousands of miles away from the academic world, paid attention to the mathematics world.
Standing next to Academician Zhang was Professor Fu Lei, the director of the Shiing-Shen Chern Mathematics Institute.
Compared to Academician Zhang, this director was slightly younger. However, he was still an influential figure in the mathematics community in China.
Just like Academician Zhang, who researched differential geometry, Fu Lei's main research area was not number theory, but group theory. However, this did not prevent him from understanding the academic value of this thesis.
After a long silence, Professor Fu asked.
"Do you think this thesis … was really written by his student?"
Academician Zhang smiled. "Of course. Who would be so generous as to give their research results to their students? "
Regarding the identification of research results, this was an issue of academic ethics.
Generally speaking, if a supervisor didn't steal the research results of their students, they would be considered a decent supervisor.
As for dishonestly praising the work of a university student and giving his research results to his students …
No normal person would do such a thing.
Even though Professor Fu understood this, he still couldn't help but say, "But there's one thing I don't understand. If his students can do it, why doesn't he do it himself?"
"Don't think too much about this. For a genius like him, you can't use normal logic to guess." Academician Zhang smiled and continued, "Maybe for him, this kind of problem simply couldn't arouse his interest, so he handed it over to his students."
Superintendent Fu had a look of disbelief on his face because it sounded too unbelievable.
The Collatz conjecture was not just any conjecture.
Even though there weren't many people who actually researched it, there were many people who paid attention to it.
If he were in Lu Zhou's shoes, he would be tempted. After all, with this result, as long as Lu Zhou was old enough, he could easily become a Changjiang Scholar or even an academician.
Academician Zhang saw the disbelief on Fu Lei's face. He smiled and didn't explain anything.
After all, people like him did exist in the history of mathematics, and there were quite a few of them.
For example, Grothendieck, Hilbert …
Without exception, they were all great mathematicians that could be recorded in the history of mathematics.
Compared to these great people who created an era, Lu Zhou was still far behind, but he still had the opportunity to reach that step. After all, the talent he displayed at this age had already reached a jaw-dropping level, and he still had a very long way to go in the future …
Academician Zhang paused for a second before he spoke with a smile.
"It's normal to not be interested. I just heard that Professor Lu is researching a big project. Compared to that, the Collatz conjecture is nothing. "
"Even the Collatz conjecture can't compare?" Fu Lei frowned and said, "Maybe it's chemistry? Or something like physics? "
Academician Zhang smiled and said, "It has nothing to do with chemistry. It does have something to do with physics, but it's not a big deal."
Fu Lei couldn't help but ask, "What is it?"
"It's about the existence and smoothness of a solution to the Navier – Stokes equation." Academician Zhang looked out the window and said, "It's one of the seven Millennium Prize Problems."
Fu Lei was shocked.
After a while, he opened his mouth with difficulty.
"… He's already this strong?"
"Of course." Academician Zhang smiled and said, "Why else do you think the country would make an exception and award the first-level natural science award to a young man in his twenties?"
He had only heard about it.
Before the Science and Technology Award Conference began, the leaders of the Ministry of Science and Technology told their higher-ups that they shouldn't award the first-level natural science award so hastily.
After all, a winner in his twenties was not only full of uncertainty, but it also lowered the average age of the winner by several years.
However, everyone saw the final result. The higher-ups decided to award the first-level natural science award.
There were many rumors about the reason.
The most credible and widely circulated rumor in the academic community was that some people in the academic community told the higher-ups that the award committee should bravely break the precedent.
There was only one reason that convinced the higher-ups.
The International Mathematical Union announced that there was a 90% chance that the Fields Medal in August would be awarded to Professor Lu, who was invited to participate in the one-hour report. Not just that, but he was also favored by the Nobel Prize in Chemistry winner, Professor Ertl. If everything went according to plan, he would be nominated for this year's Nobel Prize in Chemistry.
Even though Academician Zhang didn't believe that Lu Zhou could solve the legendary Millennium Prize Problems, he couldn't help but believe that Lu Zhou could.
Because Lu Zhou's name was always accompanied by miracles.
Professor Fu went silent for a long time before he said, "… If only we could invite such a nutty person to our research institute."
Of course, he was just fantasizing.
If Professor Lu returned to China, he would definitely go to his research institute.
Just like the Shiing-Shen Chern Mathematics Research Institute or the Qiu Chengtong Mathematics Center …
After hearing the director's words, Academician Zhang laughed and said, "Don't even think about it. Our small temple definitely can't invite that god. However, we can still try to contact his students. "
Professor Fu: "What do you mean?"
Academician Zhang said in a serious tone, "I will write a letter to the higher-ups and recommend Qin Yue's name to the Thousand People Initiative …"
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