Chapter 760 Chang's Lemma

With the content already sorted out, it doesn't take too long to write the entire proof process into a paper with a decent format.

Everything came naturally.

By the evening of the second day, Chang Haonan had completed the work.

His biggest shortcoming was his English level, but mathematical papers don't really rely on this.

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

Of course, that's just saying.

After all, the fact that the reviewer can understand it doesn't mean that the editor can understand it.

If you really receive a submission full of incomprehensible characters, and the submitter is a strange name who has no achievements in the theoretical mathematics community, it will most likely be thrown directly into the trash.

If this kind of thing is exaggerated, it is also part of academic hegemony.

But it can only be solved slowly in the future-

If Huaxia can publish a top journal, the manuscripts can naturally include Chinese.

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

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

But he never found the opportunity.

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

You also need top scholars willing to submit to you.

And this generally depends on the research institution or the editor's reputation in the academic community.

It is also what Chang Haonan, including all Chinese research institutions, lacks the most now.

Of course, these are all later stories.

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

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

But theoretical mathematics doesn't care much about this.

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

In general, his article contains two parts.

In addition to the main conclusion that "for any set of high-dimensional data X, there must be a mapping relationship that maps X to a set of data Y in a local simple Euclidean space", Chang Haonan also extended and expanded the Ricci flow to a certain extent.

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

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

Before this, Qiu Chengtong, Li Weiguang and Richard Hamilton had been conducting research in this direction for more than ten years.

In fact, Chang Haonan also referred to the papers of these three great gods in the previous month of sorting.

And the conjecture about Ricci flow itself was proposed by Qiu Chengtong.

If this were in the engineering world, such a hypothesis that could not be falsified would have been used as a tool long ago.

But in the theoretical mathematics world, it is obviously not possible to play like this.

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 of the mathematical community, if nothing unexpected happens, they will probably be put together and named "Chang's Lemma".

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

Intuitively speaking, it may promote the proof of the Poincaré conjecture.

That is, "every simply connected 3D manifold is homeomorphic to a 3D sphere".

And proving the Poincaré conjecture itself...

Chang Haonan naturally tried it a few days ago.

However, with the theoretical level provided by the current level 3 system, it is obviously not enough for him to conceive a "complete and feasible" idea.

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

[These two proofs have a deeper meaning in the field of differential geometry, but due to the length of this article, I will explain it in more detail later...]

If the Poincaré conjecture is likened to a treasure chest full of treasures but sealed, then the tool in Chang Haonan's hand can only pry it open a gap.

Some parts of this paper are just some treasures that have spilled out from the cracks.

For the theoretical mathematics community, such treasures are naturally enough to directly consider the so-called "four great journals" -

"Annals of Mathematics", "New Advances in Mathematics", "Journal of the American Mathematical Society" and the above-mentioned "Acta Mathematica Sinica".

There is nothing to be troubled by.

In 1999, only Annals of Mathematics accepted and published electronic papers among the four great journals, and the differential geometry masters mentioned above also had close relations with this journal.

So...

Select the file and upload it!

...

For Chang Haonan, this can only be regarded as a small episode in his scientific research journey.

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

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

After all, it only takes a few days.

Although Chang Haonan does not need to do anything, almost one-third of the planes participating in the ceremony are equipped with engines that he participated in or presided over the design. Zheng Liangqun has invited him more than once to visit and inspect the airport in WQ District, Tianjin.

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

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

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

Two people traveling together 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 received it, but I can't help it. I've been working on a new project recently, and I can't let it distract me, so I've delayed it until now."

Chang Haonan reached out to tidy up his slightly long hair because he hadn't cut it for more than a month and answered.

"The project that keeps you busy?"

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

In the past few years, Chang Haonan has shown a strong ability to do two things at the same time, and can even lead two unrelated projects at the same time.

Therefore, when he said the four words "can't let you be distracted", Ding Gaoheng was indeed a little shocked.

Chang Haonan also noticed the other party's eyes.

In order to prevent Ding Gaoheng from thinking that he was showing off his hair volume, he hesitated for a moment and then put his hand down:

"Well... I was just solving a problem of information retrieval and data dimensionality reduction, but in the process I found some theoretical mathematical results, so I spent some time proving them and submitted a manuscript."

"Oh..."

At this time, Ding Gaoheng had not realized the seriousness of the matter:

"Where did you submit it?"

"Annals of Mathematics."

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

"Ah?"

Ding Gaoheng's eyes widened.

Although he was born in the Soviet Union and could not speak English fluently, it did not mean that he knew nothing about things in the United States.

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

"Yes, it's a conjecture proof in the field of differential geometry, and they are more professional there."

Chang Haonan nodded.

Ding Gaoheng opened his mouth, as if he was hesitating about something.

But in the end he asked:

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

It's not that he didn't trust Chang Haonan's ability.

The main thing is that he has seen many science scholars cross the discipline to the engineering field, but it is rare for them to go back from engineering to science, especially to theoretical mathematics.

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

But control theory, although it also has the word "theory", is generally regarded as an engineering field.

Now directly challenging the top boss like the Annals of Mathematics, anyone would have to weigh the success rate in their mind.

The only person who can compare with this behavior is Qian Weichang, who gave up history to study theoretical physics.

At the age of 18, the latter was admitted to Qinghua with an amazing score of 100 in literature and history, 5 points in physics, and 20 points in mathematics and chemistry. However, the following year, he encountered the September 18th Incident. After thinking hard, he decided to give up literature and study science, and learn to build airplanes and cannons.

Then he got the highest score in his major when he graduated.

Later, he became a master 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 that it was...

a bit outrageous.