Chapter 226 The jewel in the crown of mathematics, Goldbach’s conjecture
As one of the top awards in mathematics, the Abel Prize naturally attracts many international scholars.
Originally, as last year's winner, Deligne was supposed to attend this award ceremony.
But because of Grothendieck's physical condition, Deligne still refused to go.
After staying at the farm for a few days, seeing that the date of the award ceremony was approaching, Wang Donglai said goodbye to Deligne.
This time, he took a plane directly from Gaul to Norway.
It has to be said that the jury of Abel, the winner, still attaches great importance to him, and there is a dedicated person to greet him at the airport.
Then a special car took Wang Donglai to a five-star hotel to stay. It can be said that he was taken care of extremely well.
After staying in the hotel, Wang Donglai did not go out again.
Because, he is busy with something.
[The End of the Mathematics Emperor] He has already thought about how to do this temporary side task.
Crack the math puzzle!
As for the difficult problem of choice, it is Goldbach’s guess who is famous for difficult problems in the world.
It just so happens that the status of this question in the academic world is quite good.
Goldbach’s conjecture has been pushed to 1+2 by Chen Jingrun. Compared with several other conjectures, the difficulty is somewhat easier.
With this thought in his mind, Wang Donglai was in the hotel, working out his calculations without sleep or food.
Goldbach’s conjecture is a conjecture mentioned by Goldbach in a letter to the famous mathematician Euler in 1972: any even number greater than 2 can be written as the sum of two prime numbers.
But Goldbach himself could not prove that this was correct, so he wrote to ask the famous mathematician Euler for help. However, Euler did not prove this problem until Euler's death.
Although this problem was not solved, Euler also gave another equivalent version, that is, any even number greater than 2 can be written as the sum of two prime numbers.
Now, because today’s mathematical community has adopted the convention of ‘1 is also a prime number’, the original conjecture has become: any certificate greater than 5 can be written as the sum of three prime numbers.
In 1966, Chen Jingrun proved that "1+2" is true, that is, "any sufficiently large even number can be expressed as the sum of two prime numbers, or the sum of a prime number and a semi-prime number."
Nowadays, the common conjecture is stated as Euler's version, which states the proposition: 'Any sufficiently large even number can be expressed as a number with no more than a prime factors and another with no more than b prime factors. The sum of the numbers is recorded as 'a+b'. Also known as "Strong Goldbach's conjecture" or "Goldbach's conjecture about even numbers".
From Goldbach's conjecture about even numbers, it can be deduced that any odd number greater than 7 can be written as the sum of three prime numbers. The latter is called "Goldbach's conjecture" or "Goldbach's conjecture about odd numbers".
If Goldbach's conjecture is true about even numbers, then Goldbach's conjecture about odd numbers will also be true.
The weak Goldbach conjecture has not yet been completely solved, but in 1937, the former Soviet mathematician Vino Grodov had proved that sufficiently large odd prime numbers can be written as the sum of three prime numbers, Also known as the "Goldbach-Vinogradov theorem" or the "three prime number theorem".
Sitting on the stool in the hotel, Wang Donglai quickly thought of the above information.
Not only Goldbach's conjecture, but also other slightly famous mathematical conjectures that have not yet been cracked and proven, he has seen.
“If you want to study Goldbach’s conjecture, there are four ways, namely, almost prime numbers, exception sets, the three prime number theorem of small variables and almost Goldbach’s problem.”
Brother Jiang After recalling the general information of Debach's conjecture, Wang Donglai began to think about which method he should use.
A nearly prime number is a positive integer with a small number of prime factors. Now assume that N is an even number. Although it cannot be proved that N is the sum of two prime numbers, it is enough to prove that it can be written as the sum of two almost prime numbers, that is, N=A+B, where A and B do not have too many prime factors. , for example, the number of prime factors does not exceed 10.
Use "a+b" to express the following proposition: Every large even number N can be expressed as A+B, where the number of prime factors of A and B does not exceed a and b respectively. Obviously, Goldbach's conjecture can be written as "1+1".
Progress in this direction has been achieved using the so-called sieving method, and the effect is extremely significant.
Beginning in 1920, Brown of Norway proved ‘9+9’.
In 1924, Germany’s Ratmacher proved ‘7+7’.
In 1932, British Esterman proved "6+6".
In 1937, Italy's Lacy successively proved "5+7", "4+9", "3+15" and "2+366".
In 1938, Sulian’s Buchshetabo proved “5+5”.
In 1940, the Soviet Union’s Buchshelter proved “4+4”.
In 1956, Wang Yuan of China proved "3+4", and later proved "3+3" and "2+3".
In 1948, Hungary's Reni proved "1+c", where c is a large natural number.
In 1962, China's Pan Chengdong and the Soviet Union's Balbaan proved "1+5", and China's Wang Yuan proved "1+4".
In 1965, Buchshtabo and Vinogradov of the Soviet Union, and Pembelli of Italy proved "1+3".
In 1966, China’s Chen Jingrun proved “1+2”.
These are the results achieved through almost prime numbers.
The exception set is to take a certain large integer x on the number axis, and then look forward from x to find those even numbers that make Goldbach's conjecture invalid, that is, the exception even numbers.
The number of all exception even numbers before x is recorded as E(x). We hope that no matter how big x is, there is only one exception even before x, and that is 2, that is, only 2 makes the conjecture wrong.
In this way, Goldbach's conjecture is equivalent to E(x) always equaling 1. Of course, it has not been proven that E(x)=1 until now; but it can be proven that E(x) is much smaller than x. The number of even numbers in front of x is probably x/2; if the ratio of E(x) to x tends to zero when All even numbers hold. This is the idea of exception collections.
Vinogradov's three prime number theorem was published in 1937.
On the approach of exception sets, just one year has passed, and four proofs have appeared at the same time, including Mr. Hua Luogeng's famous theorem.
If Goldbach's conjecture is correct for even numbers, then the conjecture for odd numbers is also correct.
We can think about this problem in reverse.
It is known that the odd number N can be expressed as the sum of three prime numbers. If we can prove that one of the three prime numbers is very small, for example, the first prime number can always be 3, then we have proved it. Goldbach's conjecture for even numbers.
This idea prompted Mr. Pan Chengdong to study the three prime number theorem with a small prime variable in 1959, when he was 25 years old. This small prime variable does not exceed N raised to the power of θ. Our goal is to prove that θ can take 0, that is, this small prime variable is bounded, thereby deducing the Goldbach conjecture of even numbers. Mr. Pan Chengdong first proved that θ can be taken as 1/4. For a long time, there was no progress in this area of work until 1995 when Professor Zhan Tao advanced Teacher Pan's theorem to 7/120. This number is already smaller, but still greater than 0.
The difficulty in proving Goldbach's conjecture is that any prime number that can be found is not true in the following formula.
2*3*5*7*. . . . . . *PN*P=PN+(2*3*5*7*...*P-1)*The difference between the even number before PN minus any prime number PN must be a composite number.
Therefore, even though he was already at a math level of LV7, Wang Donglai didn't have much progress for a while.
In any case, this mathematical problem has existed for so many years. If it could be solved so easily, it would have been solved long ago.
I dare not say that all mathematicians in the world have tried to prove Goldbach's conjecture, but more than 80% of them have tried. This data is definitely not an exaggeration.
A variety of problem-solving ideas have been tried, from sieving methods to exception sets to three prime numbers and so on.
Although every one or two years, someone will shout loudly that they have proved Goldbach's conjecture.
At the beginning, there was still some interest in the academic world, but as time went by, no one believed the words of these civilian mathematics enthusiasts anymore.
Even if anyone says that he has proved Goldbach's conjecture, he will be regarded as a joke and a clown who is sensationalizing.
The current mathematical community has reached a formula.
That is, if Goldbach's conjecture is proved, it must use a completely new mathematical method.
So, as long as a mathematician can truly solve Goldbach's conjecture, he must be a great mathematician.
What is a mathematician? Only those who have made great contributions in the field of mathematics can be called mathematicians. Ordinary people are just scholars at best.
Great mathematicians are big guys like Krethendieck.
Created new fields and made great contributions to the development of mathematics.
The simplest way to verify is whether the textbook can avoid him. If it can be avoided, it cannot be counted. If it cannot be avoided, then it is!
Judging from his previous results, Wang Donglai is not yet a great mathematician.
But if he develops a brand new mathematical method and achieves a breakthrough from zero to one, then countless scholars around the world will continue to study along Wang Donglai's ideas.
As time goes by, an academic school with Wang Donglai as the core will be formed.
It can be said that choosing Goldbach's conjecture as a breakthrough is definitely an extremely difficult choice.
……
May 15th.
The Abel Prize award ceremony officially begins.
The award ceremony is not complicated, and there are also many mathematicians who come to participate in the Abel Prize.
Because we knew that the winner this time was Chinese, the overseas main station also sent reporters and interview teams to record this exciting scene.
After receiving the trophy and bonus, Wang Donglai delivered a speech according to past practice.
It is worth mentioning that Wang Donglai brought a special set of Hanfu to receive the award this time.
Even the words of thanks are in Chinese.
Such a move is naturally to promote the image of China and its culture.
If someone else did this, they might be worried about being made difficult by the judges, or it might have any impact on their own awards.
But Wang Donglai was not worried at all.
It would be a real joke if Abel officials canceled his award because of this incident.
The fact is exactly as Wang Donglai expected.
Although Abel officially did not support Wang Donglai's approach, he still chose to compromise at Wang Donglai's insistence.
When Wang Donglai spoke, translators were specially prepared for simultaneous translation.
So.
When Wang Donglai appeared on domestic TV, many people in the country immediately became excited.
Wearing Hanfu, which is elegant and elegant and full of traditional flavor, we stepped onto the international stage and gave a speech of thanks in Mandarin.
Coupled with Wang Donglai’s handsome face, I don’t know how many people he attracted.
At this moment, he became the idol of many people.
……
After receiving the award, Wang Donglai did not stay too long.
After just one day, I took a plane back to China.
As soon as he got off the plane, Wang Donglai was surrounded by a dense crowd of long guns and short cannons.
This scene was beyond Wang Donglai’s expectation.
He didn’t expect that he would be treated like this.
Before, when he published a paper in China, many media reporters wanted to interview him, but they were all stopped by Tangdu Jiaotong University. He had never seen such a scene.
When the passengers who came out with Wang Donglai saw this scene, they thought Wang Donglai was a celebrity.
Stopped nearby and listened curiously.
"Professor Wang, why did you choose to wear Hanfu and speak Mandarin at the international award ceremony? Can you tell me what you think?"
"Professor Wang, there are online Some netizens say you are sensationalizing and trying to attract attention. What do you think of these comments? ”
"Professor Wang, can you talk in detail about how you maintain academic research and run the company?"
"..."
One by one, the microphones were handed to Wang Donglai's mouth , waiting for his answer.
"Sorry, if you want to be interviewed, you can contact Tangdu Jiaotong University. I will accept the interview through Tangdu Jiaotong University. I will not answer any questions here."
< br>Wang Donglai knew the news industry so well that he refused without any hesitation.
However, it did leave an opening for them to contact Tangdu Jiaotong University.
After finishing speaking, Wang Donglai dodged these reporters and walked outside.
As a result, within a short while, Wang Donglai was quickly chased by the two men.
"Professor Wang, please wait!"
A middle-aged man in his forties caught up with a young girl.
"Professor Wang, hello, I am Cai Kejin, the director of the "Super Academic" program on Suzhou TV Station."
Cai Kejin took the initiative to extend his hand and wanted to shake hands with Wang Donglai.
Wang Donglai shook hands and asked curiously: "Director Cai, do you have anything to do with me?"
"That's right, our program "Super Academic" originally We invite students from the top universities in the country to compete to find a super academic master. But now, we are ready to compete. For a larger spot in the program, students from various universities around the world will be invited to compete, including mathematics. In view of Professor Wang's outstanding achievements, our program would like to invite Professor Wang to our program..."
Cai Kejin introduced Wang Donglai in detail with a sincere smile on his face.
But before he finished speaking, Wang Donglai waved his hand and said: "I'm not interested, I don't want to go, don't bother me!"
Cai Kejin's face froze, and when he saw Wang Donglai was about to leave, he hurriedly Said: "Professor Wang, the ratings of our program are very low. Wrong, I hope you can think about it more.”
“If Professor Wang is dissatisfied with anything, you can raise it and our program team will try our best to satisfy you!”
Cai Kejin was very insistent. Various preferential conditions were thrown out one after another.
But Wang Donglai ignored them at all, and walked away from the two of them without stopping at all.
He really has no impression of this "Super Academic" program, and he doesn't know about the Butterfly Effect. It's still not very famous.
His time is so precious. If he wants to crack and prove Goldbach's conjecture when the global conference of mathematicians is held, he needs to go all out and not slack off at all.
With such a big thing to do, how could he participate in a TV show.
(End of this chapter)