Chapter 359

As soon as Dean Wei's smiling words came out, Cheng Nuo's expression couldn't help but change.

An essay that argues logically wrong?

Let yourself find the mathematical language logic errors that exist in it in half an hour?

Cheng Nuo frowned and thought about the difficulty of this test that Dean Wei had revealed.

However, it is difficult for him to come up with an accurate conclusion without reading through the entire paper.

Whether it can be completed or not, even if he is as confident as him, he has to put a big question mark!

But, at the moment, he did not "refuse" this option!

Facing Dean Wei's smiling face, Cheng Nuo nodded heavily, "Okay, you can." ”

Dean Wei squinted and pointed to a seat in the back row of the defense classroom, "You can answer the questions there first, and we will continue to interview other defense students." ”

For half an hour, of course, it was impossible for the four teachers to sit here and wait for Cheng Nuo to finish answering.

Just in time for this time, you can interview one or two defense graduates.

Dean Wei is not worried that Cheng Nuo will use his mobile phone to search for information on the Internet.

This paper was originally written by him, and because it was a fee, it was never published on any platform at all.

As for the logical error in the paper, it is even less likely to be known by abnormal means.

Everything can only rely on Cheng Nuo himself.

This can be regarded as the ultimate test of Cheng Nuo's mathematical level.

Although even if Cheng Nuo did not successfully complete the answer in the end, Dean Wei would not be able not to issue Cheng Nuo a graduation certificate, but Cheng Nuo's weight in his heart would definitely be greatly reduced.

The allocation of follow-up scientific research resources will also be readjusted.

Cheng Nuo took Dean Wei's thick paper and came to a seat in the back row of the defense room.

In the drawer hole of the seat, there is a stack of various stationery such as scratch paper and carbon pens.

It seems that this is Dean Wei's premeditated plan!

Cheng Nuo smiled bitterly, whether he knew this set before or not, he could only jump into it helplessly!

The paper is 34 pages in total, a few pages less than the one Cheng Nuo submitted.

The title of the dissertation and the thesis title are exactly the same as Cheng Nuo's, both of which prove the Bertrand hypothesis.

The only difference is that the proof method described by Cheng Nuo is a correct, reasonable and feasible proof scheme.

Dean Wei's, on the other hand, is a false proof scheme.

Hahaha!

If you think about it this way, it is indeed much better!

The haze in Cheng Nuo's heart that was calculated by Dean Wei was swept away.

He moved his fingers, rubbed his face that had been smiling until now, and lowered his head to begin to read Dean Wei's paper.

Attentively, he chewed the contents of the paper little by little.

Even the first four teachers communicated with the defense graduates, and he didn't notice it.

Although Dean Wei's dissertation and Cheng Nuo's dissertation chose the same topic, the specific steps of proof are very different.

When Cheng Nuo and the great mathematician Chershev of the last century proved Bertrand's hypothesis, they both used the method of lemma substitution and derivation.

But in this paper, Dean Wei took a different approach and adopted a completely different line of proof.

Euler Product Formula Introduction!

Cheng Nuo is named after this for the time being.

In this paper, Dean Wei introduced the concept of Euler product formula from the beginning of the proof process, and then derived the proposition through the mathematical logical relationship between Euler product formula and Bertrand's hypothesis.

What is the Euler Product Formula?

This is one of the starting points of the mathematician German's proposal for the distribution of complex numbers, which is as follows: for any complex number s, if Re(s)>1, then: Σn n-s = Πp(1-p-s)-1.

This is a rather unpopular mathematical formula, and it is almost impossible to use it in today's academic research in mathematics.

Unexpectedly, Dean Wei would have the whimsical idea to use it as another entry point to prove Bertrand's hypothesis, and he really deserved to be a great bull in the Chinese mathematics community. However, the results do not seem to be perfect.

It took more than ten minutes for Cheng Nuo to read the entire paper.

Of course, this does not refer to Cheng Nuo's reading of the full 34 pages of the document.

Like the graduation thesis submitted by Cheng Nuo, it is really genuine, only those five or six pages of content.

After reading it, Cheng Nuo also understood Dean Wei's proof ideas.

First, if f(n) is a function satisfying f(n1)f(n2) = f(n1n2) and Σn|f(n)|<∞ (n1 and n2 are both natural numbers), then we can successfully derive that Σnf(n)=Πp[1+f(p)+f(p2)+f(p3)+...].

After deriving the above series of derivation theorems, the first step of the proof is completed.

Below, since Σn|f(n)|<∞, 1+f(p)+f(p2)+f(p3)+... Absolute convergence. Consider the part of p < N in the conjoined product (finite product)......... Using the product property of f(n), we get: Πp

In the third step, since 1+f(p)+f(p2)+f(p3)+...= 1+f(p)+f(p)2+f(p)3+...=[1-f(p)]-1......

Step 4,......

............

The last step, consisting of (2n)!/(n!n!) =Πp≤2n/3 ps(p)。 Decompose the multiplication into two parts: p ≤√2n and √2n < p ≤ 2n/3...... Thus, Bertrand's hypothesis is valid.

Step by step, logical and rigorous.

The idea is strange, but it seems to be in common sense.

After reading it for the first time, Cheng Nuo did not find any flaws in the paper.

Cheng Nuo frowned slightly.

Sure enough, it's not that simple.

Cheng Nuo didn't have time to read through and check it again, he first excluded the simple part of the logical deduction in the paper and ignored it.

If that logical error really appeared in that kind of low-level logical deduction step, it would be impossible for Dean Wei to use it as the topic of Cheng Nuo's dissertation defense.

Because, that's too embarrassing.

There are five places in the paper where there is a huge amount of computation and careful derivation steps.

Cheng Nuo checked them one by one.

"First, the sum of the right end of the Euler product formula and the reasoning of the ordinary finite product, first, all the f(n) terms containing factor 2 at the right end of the equation are eliminated, and then ......"

"The second place, the distribution of prime numbers and the exact ,...... of the two steps"

............

"Fourth, the substitution of the properties of f(n), f(2)Σnf(n) = f(2)+f(4)+f(6)+..."

Suddenly, Cheng Nuo, who saw this part of the content, suddenly froze his eyes.

He stared at a line of formulas, to the left and to the right, and then a faint smile appeared on the corner of his mouth.

I've found you!

Cheng Nuo picked up the carbon pen, wrote and drew on the scratch paper for a while, and then drew a horizontal line under the formula of the paper.

The formula on the horizontal line: Πp[1-f(p)]Σnf(n)= f(1)= 1,(2n)!/(n!n!) =Πp≤√2n ps(p)，Σnf(n)=Πp[1-f(p)]-1

Here it is, yes.

There is a habitual error in the logical relationship between the third formula and the first two formulas.

These three formulas can be regarded as one of the core formulas in the whole paper proof process, and therefore, the error of the formula leads to the whole paper becoming a fee.

Cheng Nuo was in an extremely good mood at this time.

Because he not only found the logical error that Dean Wei requested, but also calculated a reasonable correction plan in his mind!

When I looked up, there was no one on the defense table in front of the four teachers.

Cheng Nuo picked up the paper and strode onto the podium.

Then, in the slightly stunned eyes of the four teachers, they smiled faintly, "Teacher, I've done it!"