Chapter 760 Chang’s Lemma

After the content has been sorted out, it actually does not take too long to write the entire proof process into a paper with a decent format.

Everything fell into place.

By the second night, Chang Haonan had completed the work.

His biggest weakness was originally his English proficiency, but the mathematics paper did not actually rely heavily on this.

Since even Yao Mengna can understand it, even if he writes it in Chinese, the top mathematicians responsible for reviewing the manuscript will probably not have any difficulty in understanding it.

Of course, that's just saying it.

After all, just because the reviewer understands it doesn’t mean the editor can understand it.

If you really receive a submission full of incomprehensible characters, and the submitter is an unfamiliar name who has not made any achievements in the world of theoretical mathematics, there is a high probability that it will be thrown directly into the trash can.

If this kind of thing is discussed in detail, it is also part of academic hegemony.

But we can only wait until later to slowly solve it——

If a top journal could be published by Huaxia, the manuscripts would naturally be in Chinese.

Some Swedish journals, such as Acta Mathematica, accept submissions in Swedish.

In fact, this is what Chang Haonan has been planning since he was reborn.

But I never found the opportunity.

After all, running an academic journal, especially a top journal, is not just about registering a publication.

You must have top scholars willing to submit papers to you.

This generally depends on the research institution or the editor-in-chief's own reputation in the academic world.

It is also Chang Haonan who, including all Chinese research institutions, is most lacking today.

Of course, these are things to follow.

What is before Chang Haonan is to consider where to submit this article.

Although this proof has no direct "use" to the material world.

But theoretical mathematics doesn’t really care about this.

If you are too utilitarian, those people who do pure mathematics may even look down upon you.

Overall, his article contains two parts.

In addition to the main conclusion that "for any set of high-dimensional data Stretch and expand.

The theory holds that if a metric is given on a manifold and then improved by the Ricci flow development equation, the curvature of the manifold will also stretch.

In the process of proving his main conjecture, Chang Haonan also proved that Ricci flow can be used to complete a series of topological operations to construct geometric structures and transform irregular manifolds into regular manifolds.

Prior to this, Qiu Chengtong, Li Weiguang and Richard Hamilton had conducted research in this direction for more than ten years.

In fact, Chang Haonan also made reference to the papers of these three great masters during the past month's compilation process.

And the conjecture about Rich Flow itself was proposed by Qiu Chengtong.

If this were in the engineering world, assumptions like this that cannot be falsified would have been used as tools long ago.

But in the world of theoretical mathematics, this obviously cannot be done.

Therefore, Chang Haonan's proof is equivalent to giving scholars in the field of differential geometry two tools that they have long wanted to use, but have never been able to use.

According to the conventions in the mathematical world, if nothing else happens, they will probably be pinched together and named "Chang's Lemma".

As for the use of Chang's Lemma...

Intuitively, it may be possible to prove the Poincaré conjecture.

That is to say, "Every simply connected 3-dimensional manifold is homeomorphic to the 3-dimensional sphere."

And proving the Poincaré conjecture itself...

Chang Haonan naturally tried it a few days ago.

It's just that the theoretical level provided to him by the current level 3 system is obviously not enough for him to formulate a "complete and feasible" idea.

Chang Haonan also wrote this at the end of the article:

[These two proofs have more profound significance in the field of differential geometry, but due to the length of this article, I will explain it in more detail in the future...]

If the Poincaré conjecture can be compared to a sealed treasure box filled with treasures, then the tools in Chang Haonan's hands can only pry open a gap in it.

And some parts of this paper are little treasures spilling out of the cracks.

Such a treasure is naturally enough for the theoretical mathematics community to directly consider the so-called "four major journals"——

"Annals of Mathematics", "New Advances in Mathematics", "Journal of the American Mathematical Society" and the aforementioned "Journal of Mathematics".

There is nothing worthy of choosing difficulty.

In 1999, among the four major journals, only the Annals of Mathematics accepted and published electronic versions of papers, and the differential geometry greats mentioned earlier were also closely related to this journal.

then……

Select the file and upload it!

……

For Chang Haonan, this can only be regarded as an episode on his scientific research journey.

At least for now, he is not ready to take theoretical mathematics as his main focus.

Therefore, after completing the submission, he shifted his energy to preparing for the National Day ceremony.

After all, that's all for the past few days.

Although Chang Haonan does not need to do anything, almost one-third of the aircraft participating in the ceremony are equipped with engines that he participated in or presided over the design. Zheng Liangqun has sent invitations more than once, asking him to visit Jinmen WQ District Airport. .

He had been immersed in academics before, but now that the research on manifold learning has come to an end, he has to go there anyway.

And it just so happens that we can go with Ding Gaoheng.

The distance from Beijing to Tianjin is not long, but the security along the way is also quite troublesome.

Traveling with two people can somewhat relieve some of the pressure on the security department.

"Xiao Chang, I heard from Commander Zheng that he has invited you for almost a month."

In the specially modified minibus, Ding Gaoheng sat opposite Chang Haonan and said with a smile.

"I also received it, but I can't help it. I've been studying a new topic recently, and it's hard to be distracted and interrupt my thoughts, so I've put it off until now."

Chang Haonan stretched out his hand to straighten his hair, which was slightly longer because he hadn't cut it for more than a month, and replied.

"A subject that you can't get away from?"

Ding Gaoheng glanced at Chang Haonan's thick black hair with complicated eyes, and raised his eyebrows slightly.

In the past few years, Chang Haonan has demonstrated a strong ability to multi-task, and can even lead two unrelated projects at the same time.

Therefore, Ding Gaoheng was really shocked when he said the words "not easy to distract".

Chang Haonan also noticed the other party's eyes.

In order not to make Ding Gaoheng think that he was showing off his hair, he hesitated for a moment before putting down his hand:

"Well... I originally just solved a problem of information retrieval and data dimensionality reduction, but in the process I discovered some results in theoretical mathematics, so I spent some time proving it and submitted a manuscript."

"Oh……"

At this time, Ding Gaoheng did not realize the seriousness of the matter:

"Where did you vote?"

"Annals of Mathematics."

Chang Haonan picked up the cup and took a sip of water.

"what?"

Ding Gaoheng's eyes widened.

Although he was born in the Soviet Union and cannot speak English very well, it does not mean that he knows nothing about things in the United States.

"Annals of Mathematics...the one from Princeton University?"

"Yes, a conjecture in the field of differential geometry proves that they are more professional there."

Chang Haonan nodded.

Ding Gaoheng opened his mouth, seeming to be hesitating.

But in the end he asked:

"Then...do you think the probability of winning the draft is...high?"

It's not that I don't trust Chang Haonan's ability.

The main thing is that he has seen many science students switch majors to the engineering field, but it is indeed strange to switch from engineering back to science, especially theoretical mathematics.

Although Chang Haonan has made considerable achievements in control theory before and published an influential article, it is still regarded as the highest achievement in Chinese control theory.

But although control theory also contains the word theory, it is generally regarded as an engineering subject.

Now go directly to challenge the top boss like Mathematics Annual, and everyone has to weigh the success rate in their hearts.

Compared with this behavior, Ding Gaoheng could only think of Qian Weichang who gave up history and transferred to theoretical physics.

When the latter was 18 years old, he was admitted to Qinghua University with a score of 5 in Literature and History, 20 points in Physics, and a total of points in Mathematics and Chemistry. However, he caught up with the September th Incident the following year and decided to abandon literature and pursue science, and learned to build airplanes and cannons. .

Then I got the highest score in my major when I graduated.

Later he became a leading figure in the fields of mechanics and applied mathematics.

Although Ding Gaoheng had heard this story many times, when another similar person appeared, he still felt...

Kind of outrageous.