1+ 1 Is it really equal to 1?

In Xu Chi's reportage, China people know the conjectures of Chen Jingrun and Goldbach.

So, what is Goldbach conjecture?

Goldbach is a German middle school teacher and a famous mathematician. He was born in 1690, and was elected as an academician of Russian Academy of Sciences in 1725. 1742, Goldbach found in teaching that every even number not less than 6 is the sum of two prime numbers (numbers that can only be divisible by themselves). For example, 6 = 3+3, 12 = 5+7 and so on. 1742 on June 7, Goldbach wrote to the great mathematician Euler at that time, and put forward the following conjecture:

(a) Any > even number =6 can be expressed as the sum of two odd prime numbers.

(b) Any odd number > 9 can be expressed as the sum of three odd prime numbers.

This is the famous Goldbach conjecture. In his reply to him on June 30th, Euler said that he thought this conjecture was correct, but he could not prove it. Describing such a simple problem, even a top mathematician like Euler can't prove it. This conjecture has attracted the attention of many mathematicians. Since Goldbach put forward this conjecture, many mathematicians have been trying to conquer it, but they have not succeeded. Of course, some people have done some specific verification work, such as: 6 = 3+3, 8 = 3+5, 10 = 5+5 = 3+7, 12 = 5+7,14 = 7+7 = 3+/kloc. Someone checked the even numbers within 33× 108 and above 6 one by one, and Goldbach conjecture (a) was established. But strict mathematical proof requires the efforts of mathematicians.

Since then, this famous mathematical problem has attracted the attention of thousands of mathematicians all over the world. 200 years have passed and no one has proved it. Goldbach conjecture has therefore become an unattainable "pearl" in the crown of mathematics. People's enthusiasm for Goldbach conjecture lasted for more than 200 years. Many mathematicians in the world try their best, but they still can't figure it out.

It was not until the 1920s that people began to approach it. 1920, the Norwegian mathematician Brown proved by an ancient screening method, and reached a conclusion that every even number with a large ratio can be expressed as (99). This method of narrowing the encirclement is very effective, so scientists gradually reduce the prime factor in each number from (99) until each number is a prime number, thus proving Goldbach's conjecture.

At present, the best result is proved by China mathematician Chen Jingrun in 1966, which is called Chen Theorem: "Any large enough even number is the sum of a prime number and a natural number, while the latter is only the product of two prime numbers." This result is often called a big even number and can be expressed as "1+2".

Before Chen Jingrun, the progress of even numbers can be expressed as the sum of the products of S prime numbers and T prime numbers (referred to as the "s+t" problem) as follows:

1920, Norway Brown proved "9+9".

1924, Latmach of Germany proved "7+7".

1932, Esterman of England proved "6+6".

1937, Lacey in Italy successively proved "5+7", "4+9", "3+ 15" and "2+366".

1938, Bukit Tiber of the Soviet Union proved "5+5".

1940, Bukit Tiber of the Soviet Union proved "4+4".

1948, Rini of Hungary proved "1+c", where c is a large natural number.

1956, Wang Yuan of China proved "3+4".

1957, China and Wang Yuan successively proved "3+3" and "2+3".

1962, Pan Chengdong of China and Barba of the Soviet Union proved "1+5", and Wang Yuan of China proved "1+4".

1965, Buchwitz Taber and vinogradov Jr. of the Soviet Union and Pemberley of Italy proved "1+3".

1966, China Chen Jingrun proved "1+2".

It took 46 years from Brown's proof of 1920 of "9+9" to Chen Jingrun's capture of 1966 of "+2". Since the birth of Chen Theorem for 30 years, it is futile for people to further study Goldbach conjecture.

The idea of Brownian screening method is as follows: any even number (natural number) can be written as 2n, where n is a natural number, and 2n can be expressed as the sum of a pair of natural numbers in n different forms: 2n =1+(2n-1) = 2+(2n-2) = 3+(2n-3) = 2i and 2i. 3j and (2n-3j), j = 2, 3, ...; And so on), if it can be proved that at least one pair of natural numbers is not filtered out, such as p 1 and p2, then both p 1 and p2 are prime numbers, that is, n=p 1+p2, then Goldbach's conjecture is proved. The description in the previous part is a natural idea. The key is to prove that' at least one pair of natural numbers has not been filtered out'. No one in the world can prove this part yet. If it can be proved, this conjecture will be solved.

However, because the big even number n (not less than 6) is equal to the sum of odd numbers of its corresponding odd number series (starting with 3 and ending with n-3). Therefore, according to the sum of odd numbers, prime+prime (1+ kloc-0/) or prime+composite (1+2) (including composite+prime 2+ 1 or composite+composite 2+2) (Note:/kloc) That is, the occurrence "category combination" of 1+ 1 or 1+2 can be derived as 1+ 1 and 1+2. Because 1+2 and 2+2 and 1+2 do not contain1+. So 1+ 1 does not cover all possible "category combinations", that is, its existence is alternating. So far, if the existence of 1+2 and 1+2 can be excluded, it is proved that 1+ 1 But the fact is that 1+2 and 2+2, and 1+2 (or at least one of them) are some laws revealed by Chen's theorem (any large enough even number can be expressed as the sum of two prime numbers, or the sum of the products of one prime number and two prime numbers), such as the existence of 1+2 and the coexistence of 6542. Therefore, 1+2 and 2+2, and 1+2 (or at least one) "category combination" patterns are certain, objective and inevitable. So 1+ 1 is impossible. This fully shows that the Brownian sieve method cannot prove "1+ 1". Actually:

One. What Chen Jingrun proved was not Goldbach's conjecture.

Chen Jingrun and Shao Pinzong's Goldbach Conjecture, on page 1 18 (Liaoning Education Press), wrote that the result of Chen Jingrun's theorem "1+ 1" generally means that for any even number n, an odd prime number P', p "or p/can always be found.

N=P'+P" (A)

N=P 1+P2*P3 (B)

Of course, it is not excluded that both (a) and (b) are true, such as 62=43+ 19, 62=7+5X 1 1. "

As we all know, Goldbach's conjecture holds for even numbers (a) greater than 4, and for even numbers (b) 10+2.

These are two different propositions. Chen Jingrun confused two unrelated propositions and changed his concept (proposition) when he announced the prize. Chen Jingrun did not prove 1+2, because 1+2 is much more difficult than 1+ 1.

Two. Chen Jingrun used the wrong form of reasoning.

Chen adopts the "positive formula" of compatible substitution reasoning: either A is B or A, so either A or B is combined. This is a wrong form of reasoning, ambiguous, far-fetched, meaningless and uncertain, just like the fortune teller said, "Mrs. Li gave birth, or gave birth to a boy, or gave birth to a girl, or both boys and girls gave birth to multiple births." Anyway, it's right. This judgment is called falsifiability in epistemology, and falsifiability is the boundary between science and pseudoscience. There is only one correct form of consistent substitution reasoning. Negative affirmation: either A is B or A is B, so there are two rules in B. Consistent substitution reasoning: 1, and denying one part of the substitute limb means affirming the other part; 2. Affirm some verbal limbs but don't deny others. It can be seen that the recognition of Chen Jingrun shows that China's mathematical society is chaotic and lacks basic logic training.

Three. Chen Jingrun used many wrong concepts.

Chen used two vague concepts in his thesis, namely "big enough" and "almost prime number". The characteristics of scientific concepts are: accuracy, specificity, stability, systematicness and testability. "Almost prime number" means that the number of pixels is very large. Is it like a child's game? And "big enough" means 10 to the power of 500,000, which is an unverifiable number.

Four. Chen Jingrun's conclusion is not a theorem.

The characteristics of Chen's conclusion are (some, some), that is, some N is (a) and some N is (b), so it can't be regarded as a theorem, because all strict scientific theorems and laws are expressed in the form of full-name (all, everything, all, each) propositions, which state the unchangeable relationship between all elements of a given class and apply to infinite classes. And Chen Jingrun's conclusion is not even a concept.

Five. Chen Jingrun's works seriously violate the cognitive law.

Before finding the general formula of prime numbers, Coriolis conjecture can't be solved, just as turning a circle into a square depends on whether the transcendence of pi is clear or not, and the stipulation of matter determines the stipulation of quantity. (Wang Xiaoming 1999, No.3 "The Legend of China"

Because the distribution of prime numbers itself changes in disorder, there is no simple proportional relationship between the change of prime number pairs and the increase of even numbers, and the value of prime number pairs rises and falls when even numbers increase. Can the change of prime pairs be related to the change of even numbers through mathematical relations? Can't! There is no quantitative law to follow in the relationship between even values and their prime pair values. For more than 200 years, people's efforts have proved this point, and finally they choose to give up and find another way. So there are people who prove Goldbach's conjecture in other ways. Their efforts have only made progress in some fields of mathematics, and have no effect on Goldbach's conjecture.

Goldbach conjecture is essentially the relationship between an even number and its prime number pair, and the mathematical expression expressing the relationship between even number and its prime number pair does not exist. It can be proved in practice, but the contradiction between individual even numbers and all even numbers cannot be solved logically. How do individuals equal the average? Individuals and the general are the same in nature, but opposite in quantity. Contradictions will always exist. Goldbach conjecture is a mathematical conclusion that can never be proved theoretically and logically.

"In contemporary languages, Goldbach conjecture has two contents, the first part is called odd conjecture, and the second part is called even conjecture. Odd number conjecture points out that any odd number greater than or equal to 7 is the sum of three prime numbers. Even conjecture means that even numbers greater than or equal to 4 must be the sum of two prime numbers. " (Quoted from Goldbach conjecture and Pan Chengdong)

I don't want to say more about the difficulty of Goldbach's conjecture. I want to talk about why modern mathematicians are not interested in Goldbach conjecture, and why many so-called folk mathematicians in China are interested in Goldbach conjecture.

In fact, in 1900, the great mathematician Hilbert made a report at the World Congress of Mathematicians and raised 23 challenging questions. Goldbach conjecture is a sub-topic of the eighth question, including Riemann conjecture and twin prime conjecture. In modern mathematics, it is generally believed that the most valuable is the generalized Riemann conjecture. If Riemann conjecture holds, many questions will be answered, while Goldbach conjecture and twin prime conjecture are relatively isolated. If we simply solve these two problems, it is of little significance to solve other problems. So mathematicians tend to find some new theories or tools to solve Goldbach's conjecture "by the way" while solving other more valuable problems.

For example, a very meaningful question is: the formula of prime numbers. If this problem is solved, it should be said that the problem of prime numbers is not a problem.

Why are folk mathematicians so obsessed with Kochi conjecture and not concerned about more meaningful issues such as Riemann conjecture?

An important reason is that Riemann conjecture is difficult for people who have never studied mathematics to understand its meaning. Goldbach guessed that primary school students could watch it.

It is generally believed in mathematics that these two problems are equally difficult.

Folk mathematicians mostly use elementary mathematics to solve Goldbach conjecture. Generally speaking, elementary mathematics cannot solve Goldbach's conjecture. To say the least, even if an awesome person solved Goldbach's conjecture in the framework of elementary mathematics that day, what's the point? I'm afraid this solution is almost as meaningful as doing a math exercise.

At that time, brother Bai Dili challenged the mathematical world and put forward the problem of the fastest descent line. Newton solved the steepest descent line equation with extraordinary calculus skills, John Parker tried to solve the steepest descent line equation skillfully with optical methods, and Jacob Parker tried to solve this problem in a more troublesome way. Although Jacob's method is the most complicated, he developed a general method to solve this kind of problems-variational method. Now, Jacob's method is the most meaningful and valuable.

Similarly, Hilbert once claimed to have solved Fermat's last theorem, but he did not announce his own method. Someone asked him why, and he replied, "This is a chicken that lays golden eggs. Why should I kill it? " Indeed, in the process of solving Fermat's last theorem, many useful mathematical tools have been further developed, such as elliptic curves and modular forms.

Therefore, modern mathematics circles are trying to study new tools and methods, expecting Goldbach's conjecture to give birth to more theories and tools.

1+ 1=? Life formula

1+ 1=? Isn't it equal to two? Yes, that's true. But these two should not be underestimated. 2 can be decomposed into 1+ 1, 0. 1+ 1.9, 0.5+1...1,and its components are: 0.5+0.5, 0./. For example, 1+ 1=2 is 0.5+0.5+ 1=2.

0.5+0.5= natural+acquired; 1= sweat. This is a very easy-to-understand formula. Of course, from another perspective, smart people will know that there is no absolute thing. The answer can't be only 1, which means the same thing.

As early as the age of ignorance, people gradually formed a sense of numbers in activities such as storing and distributing prey. When a primitive man faces three sheep, three apples or three arrows together, he will vaguely realize that there is a kind of * * *. You can imagine how surprised he will be at this time. However, it took a very long time from this primitive feeling to the formation of the abstract concept of "number"

It is generally believed that the formation of the concept of natural numbers may be as old as the use of fire, with a history of at least 300 thousand years. Now, we can't prove when human beings invented addition, because there was not enough detailed literature at that time (maybe words were just born). But the appearance of addition is undoubtedly to perform operations when exchanging goods or prisoners of war. As for multiplication and division, it must be based on addition and subtraction. And the score should be the need to divide the object.

It should be said that when a primitive man first realized 1+ 1=2, and then realized that two numbers were added to get another definite number, this moment was a great moment of human civilization, because he discovered a very important property-additivity. This property and its extension are the whole foundation of mathematics. It even tells us why mathematics is widely used and its limitations.

People now know that there are three different things in the world. One is the quantity that completely satisfies additivity. Such as mass, the total mass of gas in a container is always equal to the sum of the masses of each gas molecule. For these quantities, 1+ 1=2 is completely true. The second category is the quantity that only partially satisfies additivity. For example, temperature, if the gases in two containers are combined, the temperature of the combined gases is the weighted average of the respective temperatures of the original gases (this is a generalized "addition"). But there is a problem here: the amount of temperature is not completely additive, because a single molecule has no temperature.

There are still some things in the world that completely reject additivity, such as neurons in the life world. We can divide the molecules in the container into two containers, so that the gas in each container still has macroscopic quantities-temperature, pressure, etc. But we can't do this to neurons. Each of us will feel happy and painful. Biology tells us that these feelings are produced by neurons. However, we can't say how much happiness or pain a neuron will produce. Not only does not every neuron have this property, but we can't split the brain into two and make every hemisphere feel happy or miserable. Neurons are not molecules-molecules can be separated or recombined at any time, and neurons have coordination. Once separated, life is over, and it is impossible to reunite (you can experiment by yourself-. -).

Although mathematics has developed for 5000 years, it is still mainly based on additivity. When we encounter these problems that do not satisfy additivity, we often find it difficult to deal with them by mathematics. This reflects the limitations of mathematics.