From June 5438 to October 2004 10, a scientific news spread like wildfire in the domestic media: "1+ 1=2 was chosen as the greatest formula." It turns out that the famous British science magazine Physical World held a unique selection activity before, inviting readers from all over the world to choose their greatest and favorite formulas, theorems or laws. To the surprise of many people, the basic mathematical formula 1+ 1=2, which is known to primary school students, was not only selected, but also ranked seventh. A Canadian reader gave his reason: "This simplest formula has a wonderful aesthetic feeling." The host of this selection activity commented: "The power of the great formula not only discusses the basic characteristics of the universe and conveys symbolic information, but also tries its best to breed more scientific breakthroughs in nature."

Coincidentally, in 197 1, Nicaragua issued a set of commemorative stamps entitled "Ten Mathematical Formulas for Changing the World", and it was this "1+ 1=2" that ranked first. It seems very important! ! ! )

1+ 1=2 is so important because it is a basic formula about numbers. Without it, there would be no mathematics at all, let alone other natural sciences such as physics and chemistry.

[Edit this paragraph] The appearance of the number

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.

[Edit this paragraph] Another "1+ 1"

Mathematically, there is also a very famous "(1+ 1)", which is the famous Goldbach conjecture. Although it sounds amazing, its title is not difficult to understand. As long as you have the mathematics level in the third grade of primary school, you can understand its meaning. It turns out that this is the18th century. The German mathematician Goldbach accidentally discovered that every even number not less than 6 is the sum of two prime numbers. Such as 3+3 = 6; 1 1+ 13=24。 He tried to prove his discovery, but failed many times. 1742, Goldbach had to turn to Euler, the most authoritative Swiss mathematician in the world at that time, and put forward his own guess. Euler quickly wrote back that this conjecture must be established, but he could not prove it.

Someone immediately checked even numbers greater than 6 until it reached 330000000. The results show that Goldbach's conjecture is correct, but it can't be proved. Therefore, the conjecture that every even number not less than 6 is the sum of two prime numbers [(1+ 1)] is called "Goldbach conjecture" and becomes an elusive "pearl" in the crown of mathematics.

19 In the 1920s, Norwegian mathematician Brown proved that every even number greater than 6 can be decomposed into a product of no more than 9 prime numbers and another product of no more than 9 prime numbers, which is called "(9+9)" for short. Since then, mathematicians all over the world have adopted screening method to study Goldbach conjecture.

At the end of 1956, Chen Jingrun, who had written more than 40 papers, was transferred to the Academy of Sciences and began to concentrate on the study of number theory under the guidance of Professor Hua. 1966 In May, he rose to the sky of mathematics like a bright star and announced that he had proved it (1+2).

1973, the simplified proof of (1+2) was published, and his paper caused a sensation in mathematics. "(1+2)" refers to the internationally recognized "Chen Jingrun theorem" that even numbers can be expressed as the sum of the products of one prime number and no more than two prime numbers.

Chen Jingrun (1933.5~ 1996.3) is a modern mathematician in China. 1933 was born in Fuzhou, Fujian on May 22nd. 1953 graduated from the Mathematics Department of Xiamen University. Because of his improvement in problems, Hua attached great importance to it. He was transferred to the Institute of Mathematics of China Academy of Sciences, first as an intern researcher and assistant researcher, and then promoted to a researcher by leaps and bounds, and was elected as a member of the Department of Mathematical Physics of China Academy of Sciences.

1in late March, 1996, Chen Jingrun collapsed just a stone's throw from the glorious peak of Goldbach's conjecture, leaving endless regrets for the world.

Without "1+ 1=2", there would be no universe. But why "1+ 1=2"? Who made "1+ 1=2"? Why? Not the average person can answer!

Scientists just say it now, it's complicated!

Why is 1+ 1 equal to 2? This question seems simple but wonderful. Axiomatic methods are widely used in modern precision science, especially in mathematics and mathematical logic. What is the law of justice? From many principles of a certain science, some basic concepts and propositions are separated. These basic concepts are undefined, and all other concepts of this discipline must be directly or indirectly defined by them. These basic propositions (also called axioms) have not been proved, but all other propositions of this discipline must be directly or indirectly derived from them. The theoretical system thus formed is called axiomatic system, and the method of forming this axiomatic system is called axiomatic method. 1+ 1=2 is an axiom in mathematics and needs no proof. Because 1+ 1=2 is the basis of all mathematical theorems and cannot be proved mathematically. As for "Why is 1+ 1 equal to 2?" As a problem, we don't need to prove it mathematically. In fact, we only need to explain why 1+ 1=2 can be said to be a definition or an axiom. However, it can be proved by reduction to absurdity that if 1+ 1 is not equal to 2, mathematics is a pot of porridge, and where mathematics is used, human society will be in a mess, then 1+ 1 must be equal to 2. 1+ 1=2 seems simple, but it is of great significance to human understanding of the world. The process of human understanding of the world is like a child snowballing: first, the child must hold a handful of snow in both hands, which is equivalent to human perceptual knowledge of the world. In the second step, the child pinched the snow in his hand and turned it into a small snowball, which is equivalent to the processing of human perceptual knowledge and formed a concept. So there is 1. In the third step, children put snowballs on the ground and found that snowballs can stick to the snow on the ground, which is equivalent to human rational understanding. Snow can stick to snow, which is equivalent to 1+ 1=2. The fourth step, children roll snowballs with snow in the snow, and find that snowballs get bigger and bigger after sticking to the snow, which is equivalent to the advanced stage of human understanding of the world and can enter a virtuous circle. Equivalent to 2+ 1=3. 1, 2,3 can be arranged in the simplest order, but they can be deduced to infinity. With 1, there is only concept; with 1+ 1=2, there is mathematics; with 2+ 1=3, the infinite change of mathematics begins. The relationship between physics and 1+ 1=2 The process of human understanding of the world is a process from perceptual to rational, from known to unknown. If 1, 2, 3 is known mathematically, it can be infinite. What is 1, 2,3 in physics? I think: the basic physical concepts such as quality, length and time are equivalent to 1, which is a brick and tile that constitutes a magnificent building of physics; Newton's law of motion is equivalent to 2, which gives us real physics and scientific physical analysis methods; The relativity principle of mechanics is equivalent to 3, which makes Newton's law of motion widely used. In classical physics, everything is certain. With known conditions, we can deduce the unknown. When the theory of relativity appeared, everything changed. Now the theory of relativity has been deeply rooted in people's hearts. Even those who oppose it basically agree with its conclusion that time is variable, length is variable, mass is variable, and space-time is curved ... Classical physics believes that the speed of light is different for different observers (although Newton is an idealist). Relativity holds that the speed of light is constant for different observers (although we are materialists). We lost all the invariable things in classical physics and got the only invariable thing in relativity-the speed of light. I think it's like getting a sesame from many watermelons. This sesame is very abstract. It is in a vacuum, the fastest, so that you can't catch it or touch it at all. I think Newton's three laws of motion are true, perfect and beyond doubt. People who question Newton's law of motion keep saying that there is no absolutely static object and there is no object that is absolutely free from external force, but they forget that the physics textbook used in school is introduced at the beginning. In the introduction, it is said that all matter is in perpetual motion, and all phenomena in nature are manifestations of material motion. Motion is the existing form and inherent attribute of matter ... It is also mentioned that abstract method is based on the content and nature of the problem, grasping the main factors and putting aside the secondary, local and accidental factors, and establishing an ideal model not far from the actual situation to study. For example, "particle" and "rigid body" are ideal models of objects. When an object is regarded as a particle, mass and point are the main factors, and the shape and size of the object can be ignored as secondary factors. When an object is regarded as a rigid body-an object with constant shape and size, the shape, size and mass distribution of the object are the main factors, and the deformation of the object is the secondary factor that can be ignored. This ideal model is very necessary in physics research. When studying the law of mechanical motion, we should start with the law of particle motion and then study the law of rigid body motion. Some people are deliberately confusing people, while others are echoing others. However, those who listen should think for themselves. Newton's abstract method of analyzing problems conforms to the guiding ideology of Marxist analysis of problems, highlights the main contradictions and denies Newton's laws of motion. What can we use to analyze the relative static state, uniform linear motion and free fall motion? It seems that relativity confuses not only our basic concepts, but also our analytical methods. This is the most dangerous thing. In the long run, physics will no longer be physics, but a pot of porridge, a pot of moldy porridge! I think the correct way to develop physics is to start with the understanding of basic physical concepts such as mass, length, time, energy and speed. , and then in physics to carry out a name movement, and then discuss whether Newton's law of motion is wrong, where is wrong. Finally, the right or wrong of relativity is self-evident and easy to accept.

Goldbach's Conjecture

1742 On June 7, the German mathematician Goldbach put forward two bold conjectures in a letter to the famous mathematician Euler:

1. Any even number not less than 6 is the sum of two odd prime numbers;

2. Any odd number not less than 9 is the sum of three odd prime numbers.

This is the famous Goldbach conjecture in the history of mathematics. Obviously, the second guess is the inference of the first guess. So it is enough to prove one of the two conjectures.

On June 30th of the same year, Euler made it clear in his reply to Goldbach that he was convinced that both Goldbach's conjectures were correct theorems, but Euler could not prove them at that time. Because Euler was the greatest mathematician in Europe at that time, his confidence in Goldbach's conjecture influenced the whole mathematics field in Europe and even the world. Since then, many mathematicians are eager to try and even devote their lives to proving Goldbach's conjecture. However, until the end of 19, there was still no progress in proving Goldbach's conjecture. The proof of Goldbach's conjecture is far more difficult than people think. Some mathematicians compare Goldbach's conjecture to "the jewel in the crown of mathematics".

Let's start with 6 = 3+3, 8 = 3+5, 10 = 5+5, ...,100 = 3+97 =1+89 =17+89. In the 20th century, with the development of computer technology, mathematicians found that Goldbach conjecture still holds true for larger numbers. However, natural numbers are infinite. Who knows if a counterexample of Goldbach's conjecture will suddenly appear on a sufficiently large even number? So people gradually changed the way of exploring problems.

1900, Hilbert, the greatest mathematician in the 20th century, listed Goldbach conjecture as one of the 23 mathematical problems at the International Mathematical Congress. Since then, mathematicians in the 20th century have "joined hands" to attack the world's "Goldbach conjecture" fortress, and finally achieved brilliant results.

The main methods used by mathematicians in the 20th century to study Goldbach's conjecture are screening method, circle method, density method, triangle method and so on. The way to solve this conjecture, like "narrowing the encirclement", is gradually approaching the final result.

1920, the Norwegian mathematician Brown proved the theorem "9+9", thus delineating the "great encirclement" that attacked "Goldbach conjecture". What is this "9+9"? The so-called "9+9", translated into mathematical language, means: "Any large enough even number can be expressed as the sum of two other numbers, and each of these two numbers is the sum of nine odd prime numbers." Starting from this "9+9", mathematicians all over the world concentrated on "narrowing the encirclement", and of course the final goal was "1+ 1".

1924, the German mathematician Redmark proved the theorem "7+7". Soon, "6+6", "5+5", "4+4" and "3+3" were captured. 1957, China mathematician Wang Yuan proved "2+3". 1962, China mathematician Pan Chengdong proved "1+5", and cooperated with Wang Yuan to prove "1+4" in the same year. 1965, Soviet mathematicians proved "1+3".

1966, Chen Jingrun, a famous mathematician in China, conquered "1+2", that is, "any even number large enough can be expressed as the sum of two numbers, one of which is an odd prime number and the other is the sum of two odd prime numbers." This theorem is called "Chen Theorem" by the world mathematics circle.

Thanks to Chen Jingrun's contribution, mankind is only one step away from the final result of Goldbach's conjecture "1+ 1". But in order to achieve this last step, it may take a long exploration process.

Many mathematicians believe that to prove "1+ 1", new mathematical methods must be created, and the previous methods are probably impossible.