From small town academic to chief scientist

Chapter 97 Proof of the unity of ‘lattice type’ Newton’s problem in 5 6 7 dimensional space

After continuing to talk for a while, Zhou Yi returned to the dormitory.

The proof process of Kepler's conjecture has not been finished yet.

Hundreds of pages of proofs and logical logic,

Whether every word is redundant, whether the definition and description of mathematical theorems are accurate or not, must be carefully polished.

The main purpose of the dean's conversation with Zhou Yi this time was the question of where to go to graduate school.

Having a good mentor can reduce many detours in your future academic career.

In fact, the reason why Zhou Yi prefers to go to Shuimu University is because Bill Carr, the 2018 Fields Medal winner, used the induction method to interpolate six auxiliary theorems in proving the BAB conjecture.

Zhou Yi also used the mutual inference auxiliary theorem of mathematical induction in the proof of Kepler's conjecture.

It can be said that they have different approaches but similar effects.

They are all in the direction of algebraic geometry, and the collision of common language and thinking must be extremely high.

When the time comes to study some number theory conjectures, there may be key enlightenments.

Secondly, Mr. Qiu is also at Shuimu University, and Mr. Yang is also at Shuimu University. The top mathematicians and physicists in the world are all in this university, so why bother looking for something far away?

But it is indeed still early. Even if I graduate with my senior year this year, it will still be more than three months away.

It’s only mid-March.

Zhou Yi was typing on the keyboard and thinking. This paper involves too many things, not just Kepler's conjecture.

A problem that Newton mentioned at the beginning can also be solved.

It would be uneconomical to release them all at once.

Moreover, the birth of this paper will definitely cause a revolution in discrete geometry. By then, I am afraid that the entire communication will usher in a huge development.

It is applied to many places such as people's livelihood, military, aerospace and so on.

However, there are too few branches of information science in Zhouyi and the level is too low to be applied at all.

Zhou Yi stopped the keyboard at this moment and began to think. Why don't he learn from others and first provide a proof that the 'lattice-type' Newton's problem is unified to 40 in the five-dimensional space.

What is Newton's problem?

This goes back more than three hundred years.

One day in 1694, when Newton and the mathematician Gregory were discussing issues related to the planets in the solar system at Trinity College, Cambridge University, the topic turned to the question of how many balls of the same size can a ball be tangent to at the same time.

They jointly believed that there was no dispute that a ball was tangent to 12 balls of the same size at the same time.

Gregory was a follower of Newtonian theory. He respected Newton but did not blindly follow him.

Because of his natural ability, he is very strong in geometric intuition.

In an instant, I thought that the balls centered on the twelve vertices of the icosahedron can be tangent to a ball at the center of the icosahedron at the same time, and there are still many gaps between these balls. After appropriate movement, maybe Probably put in at least one more ball to be tangent to the center ball.

However, Newton insisted that the ball could not be put in.

In the end, they were unable to provide mathematical proofs of their respective conclusions.

This problem, which seems much simpler than Kepler's conjecture, has actually become a long-term unsolved mathematical problem, known as Newton's problem.

Therefore, the connection between Kepler's conjecture and Newton's problem is inseparable. From a macro perspective, when the packing density of balls is maximum, should each ball in its local position be tangent to as many balls as possible?

But Newton's problem is simpler than Kepler's conjecture.

The seemingly simple elementary solid geometry problems make many civil science teachers think that I can do it.

In fact, they can't even get in.

After hundreds of years of continuous development by mathematicians, Newton's problems were transformed into 'lattice-type' Newton's problems.

In this process, a new branch of mathematics was developed, geometric number theory, also called the geometry of numbers.

So the Book of Changes prepared to publish the paper in three parts,

In the first part, we first prove that the ‘lattice type’ Newton problem is unified to 40 in the five-dimensional space.

Many mathematicians have proved the situation of 2, 3, 4, 8, and 24 dimensions before, and the results are 6, 12, 24, 240, and 196560 respectively.

As for the fifth dimension, it is only limited to 40-44.

6 micro is 72, 7 dimensions is 126.

None of this has been proven yet.

Zhou Yi stopped what he was doing when he thought of this.

Instead, start a new TeX document and start this work.

Zhouyi is ready to prove the proof of the 5, 6 and 7 dimensions in one fell swoop.

Just do it, the keyboard snaps.

I didn't stop until I felt hungry at night.

The grid patterns in these dimensions could not be published in a top journal in Zhouyi.

I will be studying later to see if I can publish a few more articles in top journals.

It is a pity that a big conjecture was made directly like this. It is only reasonable to explore the greatest benefits.

With his status as a triple crown winner, plus 2 SCI papers in area 2 as a foundation, and 10 SCI papers in area 4, it is reasonable to publish an article in such a top journal!

No one would question the talent of a young prodigy.

Zhou Yi was browsing arXiv while eating, looking at some paper rubbings on it.

Fortunately, none of them had the same ideas as the paper he was about to write, otherwise Zhou Yi would have wanted to publish it right away.

Browsing arXiv every day during meal time has become a regular thing in Zhouyi.

Because there are too many people studying Kepler’s conjectures, especially some masters and even Fields Medal winners.

Not to mention far away, at home, Professor Zong and Professor Xiang are both experts in this field.

After dinner, Zhou Yi replied to Xia Xue's message and told Xia Xue that he had been busy with his thesis recently, so he didn't go to the library.

It took five days in a row for Zhou Yi to write this "water" article.

Zhou Yi read it one last time and found that there were no problems, so he directly submitted it to the "Annals of Mathematics".

The four top journals in mathematics are "Annals of Mathematics", "Journal of Mathematics", "New Advances in Mathematics" and "Journal of the Chinese Mathematical Society".

These four types of journals are absolutely unique in mathematics, and their authority is unparalleled.

However, if you look through the four major divine journals, you will find that the nationality of the author is Bactria appears less than 100 times.

This number may be too high.

It’s not necessarily possible to fold it in half.

It can almost be said that if you are lucky enough to have the name of an ordinary mathematics professor appear in these four major journals just as a collaborator, it will definitely make people feel that life has reached a climax and that life has reached its peak.

The "Annals of Mathematics" contributed by Zhou Yi was first published by Harvard University. In 1911, it was transferred to Princeton University, the world center of mathematics. It is now jointly published by Princeton University and the Institute for Advanced Study.

"New Advances in Mathematics" is published by the famous SpringerVerlag company and is another authoritative journal. The impact factor is slightly lower than that of Annals of Mathematics.

"Acta Mathematica" was founded in 1882 by Mittag-Leffler Publishing House and is affiliated with the Royal Swedish Academy of Sciences. "Acta Mathematica" is a quarterly journal. It publishes 2 volumes every year, each volume has 2 issues, and its content covers almost all research directions in mathematics.

The "Journal of the Chinese Mathematical Society" is a journal founded by the Chinese Mathematical Society and is also a quarterly magazine. The number of articles published in a year is 32, which is equivalent to 8 articles in each issue. This shows how difficult it is to publish!

PS: No more, not even a drop. Please subscribe! ! ! (By the way, are there any monthly passes today? You know what I mean, please, please give me a monthly pass!!!)

PS: I washed it and went to bed first. It was originally put on the shelves in the early morning today. There were a lot of problems, but luckily they were solved. I was exhausted, but at least I kept it on the shelves.

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