The Military-industrial Scientific Research System of the Academic Master Chapter 760

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 next night, Chang Haonan had completed the work.

His biggest shortcoming was originally his English proficiency, but the mathematics paper actually did not 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 what I'm saying.

 After all, just because the reviewer can understand it doesn't mean that the editor can also understand it.

I really received a submission full of incomprehensible characters, and the submitter was an unfamiliar name with no achievements in the world of theoretical mathematics. There is a high probability that it will be thrown directly into the trash can.

This kind of thing is also part of academic hegemony if we talk about it above and below the line.

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

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

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

 But theoretical mathematics doesn't care much about this.

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

Of course, these are all things for later.

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

 Some Swedish journals, such as ActaMathematica, accept submissions in Swedish.

 In general, his article contains two parts.

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

 This is also what Chang Haonan, including all Chinese research institutions, lacks most today.

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.

 The conjecture about Ricci flow itself was proposed by Qiu Chengtong.

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

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

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

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

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

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

This 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 stretch accordingly.

But I never found the opportunity.

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, it is obviously not possible to play this way.

 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 mathematics, 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, “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.

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

 Some parts of this paper are just a few treasures spilling out of the cracks.

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

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

 There is nothing worth choosing about difficulty.

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

 Hence...   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 direction of attack.

 Hence, 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.

 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.

 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 too, 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 reached out 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 shown a strong ability to multi-task, and can even lead two unrelated projects at the same time.

Hence, Ding Gaoheng was a little shocked when he said the words "not easy to distract".

Chang Haonan also noticed the other party's eyes.

In order to prevent Ding Gaoheng from thinking that he was showing off his hair, he hesitated for a moment and put 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 has not yet realized the seriousness of the matter:

 “Where to invest?”

 “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 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 finally asked:

“Then...do you think the probability of winning the manuscript is...high?”

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

 Mainly, he has seen many science scholars switch majors to the engineering field, but it is indeed strange to switch from engineering to science, especially to 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 switched to theoretical physics.

When the latter was 18 years old, he was admitted to Qinghua University with a score of 100 in Literature and History, 5 points in Physics, and a total of 20 points in Mathematics and Chemistry. However, he caught up with the September 18th 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 also became a leading figure in the fields of mechanics and applied mathematics.

Although Ding Gaoheng has heard this story many times, when another similar person appears, he still feels...

  A bit outrageous.

 (End of this chapter)

Chapter end