Chapter 345

Chapter 348

inspiration is always coming, and I can't prevent it!

Cheng Nuo's mouth slightly tick, turn the page back to the original page.

Since the proving process of Bertrand hypothesis given by Chebyshev is so complicated, I'd like to challenge myself to see if I can prove Bertrand hypothesis in simpler mathematical language.

By the way, to verify, this year's in-depth study, their ability to what extent.

A simple proof method of Bertrand hypothesis.

This paper title alone is enough to be called a district level paper. Of course, the premise is that Cheng Nuo can really explore that simple solution.

As Cheng Nuo had assumed before. The proving process of every conjecture or hypothesis in the mathematical field is a process from the starting point to the end point. Some routes are tortuous, others are straight.

Perhaps, Chebyshev found the more tortuous route, while Cheng Nuo needs to open up a more simple road on the basis of predecessors.

But it's simpler than proving Bertrand's hypothesis alone.

After all, it is standing on the shoulders of giants to look at the problem. With the proof scheme proposed by Chebyshev, the "pioneer", Cheng Nuo can more or less learn something from it and make a unique understanding.

Do what you want!

Cheng Nuo is not such a hesitant person. In any case, there is plenty of time for Cheng Nuo to find another paper direction after finding out that "this road is blocked".

If we want to put forward a more simple scheme, we should first understand the ideas of proof put forward by predecessors.

Instead of rushing into his own research, he bent down and read the dozen pages of Bertrand's hypothesis from beginning to end.

Two hours later, Cheng closes the book.

After a few seconds of contemplation, he took out a pile of blank draft paper from his schoolbag, picked up the black carbon pen on the desk, and concentrated on his deduction:

to prove Bertrand hypothesis, he must prove several auxiliary propositions.

Lemma 1: [lemma 1: let n be a natural number and p be a prime number, then the highest power of P that can divide n! Is: S = ∑ I ≥ 1floor (NPI) (where floor (x) is the largest integer not greater than x)]

here, we need to arrange all (n) natural numbers from 1 to N on a straight line, and stack a column of Si markers on each number. Obviously, the total number of marks is s.

The relation s = ∑ 1 ≤ I ≤ NSI means that the number of marks (i.e. SI) of each column is calculated first and then the sum is obtained. The relation thus obtained is lemma 1.

Lemma 2: [let n be a natural number and p be a prime number, then Π P ≤ np4n]

use mathematical induction. When n = 1 and N = 2, the lemma obviously holds. Suppose lemma holds for NN (n; 2), let's prove the case of n = n.

If n is even, then Π P ≤ NP = Πp ≤ n-1p, the lemma is obvious.

If n is odd, let n = 2m + 1 (m ≥ 1). It is noted that all prime numbers m + 1p ≤ 2m + 1 are factors of the combinatorial number (2m + 1)! M! (M + 1)! On the other hand, the combinatorial number (2m + 1)! M! (M + 1)! Appears twice in the binomial expansion (1 + 1) 2m + 1, so (2m + 1)! M! (M + 1)! ≤ (1 + 1) 2m + 12 = 4m.

in this way, we can

Cheng Nuo thought smoothly, almost without much effort, he used his own method to prove these two auxiliary propositions.

Of course, this is just the first step.

According to Chebyshev's idea, we need to introduce these two theorems into the proof step of Bertrand hypothesis.

Chebyshev's method is hard to gather, yes, it's hard to gather!

Through the continuous transformation between formulas, one or several necessary and sufficient conditions of Bertrand's hypothesis are transformed into lemma one or lemma two, and then the solution is simplified and integrated.

Of course, Cheng can't do that.

Because with this kind of proof scheme, let alone Cheng Nuo, even if Hilbert comes, I'm afraid the proof steps will not be much simpler than Chebyshev. Therefore, we must change our thinking.

But what kind of conversion

Er Cheng Nuo hasn't decided yet.

Seeing the sun slanting to the West and it's time to finish eating, Cheng Nuo thinks in his mind and walks to the canteen.

…………

At the same time, the United States is far away on the other side of the ocean.

The headquarters of inventiones Mathematicae magazine is located in Los Angeles, USA.

As one of the top SCI journals in mathematics, they receive tens of thousands of contributions from mathematicians from all over the country every year.

But in the end, less than 200 papers were published.Moreover, almost four fifths of the 200 academic papers are occupied by the top mathematicians in the world.

For example, Peter Scholze in the field of algebraic geometry.

Richard Hamilton in differential geometry.

Jean bourgain in the field of mathematical analysis.

Wait, wait

Therefore, when reviewing the contributions, we should not judge the contributions according to the order of authorship.

After all, the higher the academic level of authors, the more likely they are to meet the inclusion criteria. However, the number of papers in each issue of the journal is a floating number, but the fluctuation is not large.

In this way, the time of reviewing and editing can be greatly saved.

It is not an unknown person to be a peer reviewer in such a top mathematical journal.

For example, Raffi petrel, one of the reviewers of inventiones Mathematicae, is a well-known mathematician who thought he had won the ramanugold prize.

At present, in addition to being a peer editor of the journal, he is also a visiting professor at UCLA, specializing in analytic number theory.

As a mathematical bull with multiple titles, he can't stay in the office from 9 to 5 every day to review manuscripts like he goes to work.

Generally speaking, he takes one or two mornings a week to stay in his apartment to review the contributions of several top mathematicians sent by ordinary peer reviewers, as well as contributions from some less well-known mathematicians who are considered as qualified by them.

But in most cases, due to the low level of mathematics of ordinary peer reviewers, only a few of the selected e-mails meet the inclusion standards of journals.

Eight in the morning.

Professor Peters leisurely made a cup of coffee and sat on the balcony, reading the contributions displayed on his laptop and sipping leisurely and contentedly.

"It's been a bit quiet in mathematics these days." Raphael closed a paper and sighed softly.

In recent months, with the end of the battle of ABC conjecture, the whole mathematical world has fallen into a calm. Perhaps, it will be exciting again when the Philippines prize is awarded in November this year.

Slowly, it's eleven o'clock.

He has reviewed all seven papers submitted by several top mathematicians. Among them, the level of five papers is higher than the standard line. Petel marked out a few places and asked his men to contact the author for minor repairs.

I had planned to finish my work like this, but when I remember that there is a treat at noon today, I don't have to worry about making lunch.

In that case, let's read a few more.

Petel controls the mouse and clicks on the next email.

The title of the paper: "proof of weak BSD conjecture when analytic rank is 1"!

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