From small town scholar to chief scientist

Chapter 97 Proof of the Unification of Newton's Problems of 'Lattice Type' in 5 6 7 Dimensions

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

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

Hundreds of pages of proofs, the logic before and after,
Whether every word is redundant, whether the definition of mathematical theorem is accurate or not, must be carefully polished.

The main purpose of the dean's conversation with Zhou Yi this time is still 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 tends to go to Shuimu University is because the 18-year Fields Medal winner Bill Carr used the induction method to mutually deduce six auxiliary theorems in proving the BAB conjecture.
In Zhou Yi's proof of Kepler's conjecture, he also used mathematical induction to deduce auxiliary theorems.

It can be said that there are similarities but the same results.

Both are 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 enlightenment.

Secondly, Mr. Qiu is also in Shuimu University, and Mr. Yang is also in Shuimu University. The world's top mathematicians and physicists are all in this university.

But it's still early, even if they graduate together with senior year this year, there are still more than three months left.

It's only mid-March now.

Zhou Yi was typing on the keyboard while thinking, this paper involves too many things, not just the Kepler conjecture.

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

It would be uneconomical to release all of them at once.

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

Applied to people's livelihood, military, aerospace and other places.

However, Zhouyi has too few branches in informatics, and the level is too low, so it cannot be applied at all.

Zhou Yi stopped the keyboard at this moment, and began to think, or learn from others, and first publish a proof that the 'lattice type' Newton problem is unified to 40 in the five-dimensional space.

What is Newton's problem?

This goes back more than 300 years.

One day in 1694, when Newton and mathematician Gregory were discussing 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 be tangent to one ball at the same time.

They agreed that there is no dispute that a sphere is simultaneously tangent to 12 spheres of the same size.

Gregory is a follower of Newton's theory. He admires Newton, but he does not follow Newton blindly.

Due to his natural ability, he is very strong in geometric intuition,
In an instant, I thought that all 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 proper movement, maybe Probably put at least one more sphere tangent to the one in the center.

Still, Newton insisted that the ball was impossible to get in.

In the end, none of them could give mathematical proofs for their conclusions.

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

So the connection between Kepler's conjecture and Newton's problem is inseparable. From a macroscopic point of view, should each ball at a local position be tangent to as many balls as possible when the packing density of balls is the largest?
But Newton's problem is simpler than Kepler's conjecture.

The seemingly simple problems of elementary three-dimensional geometry made many civil science teachers think that I can do it myself.

In fact, they can't even get in.

After hundreds of years of continuous development by mathematicians, Newton's problem was transformed into a 'lattice type' Newton's problem.

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

So Zhou Yi is going to divide the paper into three parts,
In the first part, first prove that the 'lattice type' Newton's problem is unified to 40 in the five-dimensional space.

之前不少数学家证明了2、3、4、8、24维的情况，其结果分别是6、12、24、240、196560。

For the fifth dimension, it is only limited to between 40-44.

6 micro is 72, 7 dimension is 126.

None of this has been proven.

Thinking of this, Zhou Yi stopped what he was doing.

Instead, I started to create a new TeX document, and then started the work.

Zhou Yi is going to prove the proof of the three dimensions of 5, 6, and 7 dimensions in one fell swoop.

Just do it, the keyboard slapped.

It didn't stop until the night when my stomach felt hungry.

With the grid pattern of these dimensions, Zhouyi can hardly be published in a top journal.

The latter is researching and researching, can there be a few more top-level journals.

A big conjecture, just posted it directly, it's a pity, it's only reasonable to discover the greatest benefits.

As a triple crown champion, plus 2 SCI papers in District 2 as a base, and 10 SCI papers in District 4, it is reasonable to publish an article in such a top journal!

No one would question the talent of a teenage prodigy.

Zhou Yi browsed arXiv while eating, looking at some rubbings of the papers on it.

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

Scanning arXiv at mealtimes every day has become a regular thing in Zhou Yi.

Because there are too many people studying Kepler's conjecture, especially some masters, even Fields Medal winners are doing research.

Leaving aside, in China, both Professor Zong and Professor Xiang are experts in this field.

After dinner, Zhou Yi replied to Xia Xue's message, telling Xia Xue that he has been busy with liver papers recently, so he didn't go to the library.

It took five days in a row before Zhou Yi wrote this "water" essay.

Zhou Yi read it again for the last time, and after finding that there were no problems, he directly submitted to the "Annual Journal of Mathematics".

Four top journals in mathematics, "Annual of Mathematics", "Journal of Mathematics", "New Advances in Mathematics" and "Journal of Mathematics Society of Magnesium".

These four types of journals are absolutely unique in mathematics, and their authority is second to none.

However, if you look through the four major divine journals, you will find that the author's nationality is the Great Xia Kingdom, which appears less than 100 times.

This number may be more.

Fold in half is not necessarily available.

It can almost be said that if the name of an ordinary mathematics professor appears in these four major journals just as a collaborator, it is guaranteed to make people feel that life has reached a climax and that life has reached its peak.

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

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

Acta Mathematica Sinica was founded in 1882 by Mittag-Leffler Publishing House and is affiliated to the Royal Swedish Academy of Sciences. Acta Mathematica Sinica is a quarterly publication with 2 volumes per year and 2 issues in each volume, covering almost all research directions in mathematics.

The "Journal of the Mathematics Society of Magnesium" is a journal established by the Mathematics Society of Magnesium, and it is also a quarterly publication.The number of articles published in one year is 32, which is equivalent to 8 articles in each issue, which shows how difficult it is to publish!
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　PS: I washed it first and went to bed. It was put on the shelves in the early morning of today. There were many problems, but fortunately they were solved. I was exhausted, at least I kept it on the shelves.

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(End of this chapter)