As one of the top four mathematics journals, almost any mathematics laboratory or research institute would subscribe to Annual Mathematics.
Tao Zhexuan's office was no exception.
The new Annual Mathematics was delivered to his office. He stopped what he was doing and flipped open the journal table of contents. He began to search for theses that he was interested in and marked the pages. He planned to read them when he wasn't busy.
At this moment, the pen in his hand suddenly paused and stopped behind a page number.
[Global Existence of Smooth Solutions for 3D Incompressible Navier-Stokes Equations at Certain Initial Values]
"Navier – Stokes equation?"
Tao Zhexuan looked at the title of the thesis and had a look of interest on his face.
He hadn't seen research on the Navier – Stokes equation in a while.
After all, even though the Navier – Stokes equation had a wide range of applications, for pure mathematics, it was too difficult to produce results that could be published in Annual Mathematics!
Tao Zhexuan couldn't suppress his curiosity, so he put down the pen in his hand and flipped to the page where the thesis was.
When he saw the name of the author of the thesis, he was stunned for a second. He raised his eyebrows with interest.
Lu Zhou?
He originally planned on reading through the thesis collection when he had time, but when he saw this familiar name, he couldn't wait any longer.
Professor Tao grabbed a blank piece of draft paper from the table and picked up the pen again. He had a serious look in his eyes as he carefully read the calculations on the thesis.
Time slowly passed by.
Before he knew it, it was already noon.
Professor Tao spent the entire morning reading the thesis from beginning to end.
When he put down the journal, he couldn't help but exclaim in admiration.
"Professor Lu is amazing …"
Although he only skimmed through the thesis, it didn't stop him from appreciating the content.
What impressed him the most was that Lu Zhou used mathematical methods that he had never seen before.
Of course, if he wanted to understand the beauty of this thesis, he would have to spend more time reading it.
Professor Tao was in high spirits and did not want to go to the afternoon class. He called his teaching assistant and pushed the responsibility of teaching the class to him. Then, he opened his laptop.
Just like Lu Zhou's passion for posting on Weibo, this big shot also had a famous hobby in the industry.
That was to update his blog.
He commented on hot topics, papers, and peers in the academic world.
As well as sharing his own thoughts!
【
… I think this is a very interesting discovery. What's exciting is not only the conclusion in his thesis, but also the fact that he used a very enlightening method in his argument.
Based on what I know of him, his ability to use a variety of mathematical tools is one of his strengths. He has the widest range of research fields of any scholar I have ever seen. Not only that, but his ability to understand and use mathematical tools is also rare among scholars I have seen.
Under normal circumstances, if a scholar could use a mathematical tool to the extreme and make innovations based on it, they would be worthy of the word "outstanding".
Obviously, his work was above outstanding.
He was good at choosing a new idea, injecting new content into an old method, or using it as nutrients to create an unprecedented mathematical method.
If I had to say, if he continued to perfect this mathematical method, he might be able to solve this century's problem.
Of course, we have to admit that this is extremely difficult!
】
In the field of partial differential equations, among the scholars that studied the Navier – Stokes equation, Tao was probably one of the best.
In 2014, a Kazakh mathematician, Otelbayev, claimed to have proved the existence and smoothness of the Navier – Stokes equation. This caused a lot of controversy in the international mathematics community.
Because this scholar was much better than Professor Enoch, who claimed to have proved the Riemann's conjecture the following year, he was considered a serious mathematician. From preprint to journal submission, he did not receive the cold shoulder.
However, it was not easy to review the thesis for this scholar.
Even though Perelman, who solved the Pang Jialai conjecture, was a loner, he wrote his thesis in English. However, this Mr. Otelbayev did not seem to be good at English. He wrote in Russian, and his thesis was 90 pages long. This directly drove away a lot of interested colleagues.
Tao Zhexuan, who only knew Cantonese and English, obviously did not understand Russian. However, this did not stop this genius from being nutty.
According to Professor Otelbayev's thesis, Tao Zhexuan first imitated his ideas and constructed an equation that was similar to the Navier – Stokes equation. If the conclusion of the original proof was valid, then there was no doubt that the example he constructed would also have a smooth solution.
Then, something even more nutty happened.
By setting a special initial value, he proved that the smooth solution corresponding to the initial value would lose its regularity in a limited time. This was equivalent to finding a counterexample and skipping the proof process, logically denying the correctness of this idea.
If the idea itself was wrong, then there was no question of whether it was correct or not.
This conclusion was recognized by many scholars in the field of partial differential equations, and reality proved that his conjecture was correct.
Not long after, Professor Gregory Selegin, a Russian mathematician from the University of Oxford, finally finished reviewing Otelbayev's thesis. He pointed out six errors in Otelbayev's thesis, which finally ended the debate on the thesis.
Of course, Otelbayev realized his mistakes and admitted his mistakes in the end. However, this was a story for another time.
All in all, Professor Tao had a lot of say in the Navier – Stokes equation field.
Even though he rarely posted academic content on his blog, the information he conveyed through his blog was often verified by himself.
Actually, Tao Zhexuan wasn't the only one who gave high praise to this thesis. Many big names in the field of differential equations also gave neutral opinions.
For example, Professor Fefferman, the head of the mathematics department at Princeton, had the same opinion as Tao Zhexuan. He believed that the method used by Lu Zhou in the proof process was more important than the conclusion of the thesis itself.
Regardless of whether or not he was researching the "existence and smoothness of a solution to the three-dimensional incompressible Navier-Stokes equation", the mathematical method he used would bring a lot of inspiration to his peers who were researching this proposition.
Before this, when Lu Zhou suddenly changed his research to materials science and chemistry, many scholars expressed their regret. They felt that he shouldn't have diverted his energy to other fields at such a young age. Instead, he should have focused his energy and pushed his field of expertise to a higher level.
However, after Goldbach's conjecture, Lu Zhou had been quiet for more than a year. He hadn't published a single mathematics thesis, and many people suspected that this genius was tired of mathematics.
However, it seemed like all of the rumors had been disproven.
Not only did this genius not give up on his research in mathematics.
It was more like …
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