Open Classification: Mathematical Numbers
The great formula that all primary school students know.
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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.
The emergence of numbers
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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.
Another "1+ 1"
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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 unattainable "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+ 1) 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.
1+ 1 = 2 This is an eternal truth, and there is nothing to say.
1+ 1 = 2. If it is equal to 1 or 0, it is wrong.
Students in China, who are not busy with their studies, are busy calculating problems that are thousands of times more difficult than 1+ 1 = 2. Many people think that as long as math and physics are good, this student is excellent, regardless of this.
How bad is a student's musical beauty and physical beauty. This is the so-called all-round development and quality education.
Students are repeatedly trained by teachers in front of the receiver;
1+ 1=2
1+2=3
……
They have lost their interest in learning since childhood. Why not let them think more and be innovative? Is this boring indoctrination good for them?
I appreciate American education very much, and I especially envy American children. They can use the classroom as a teahouse. Even the students in grade five or six can't read a few words, and they have to use a wrench to work out the math problems in grade one or two in China. They talk about inventions and do experiments all day. When American students come home, they can scribble on the wall, but their parents are happy to see them and invite their relatives and friends to visit. If they were in China, their parents would be very angry.
American students are free and have time and space to create. They are always confident and lively. Vivid discussion and in-depth exploration in the classroom have cultivated their innovative thinking ability. In China, in class, you can only hear endless explanations and severe reprimands from teachers. Look at the students sitting up straight and listening. There was a dead silence, but everyone agreed: "The teacher is more serious and the students are more attentive."
The students in China worked hard, but they didn't produce Nobel Prize winners. American students are free and loose, but they have produced many Nobel Prize winners. Why?
Because American students think that 1+ 1 cannot be equal to 2.
Instructor: Zhang
Comments: This article has fluent sentences, many quotations and rigorous structure. Explain the problem clearly with comparative writing. Formulas are titles, endings, etc. , innovative, novel and unique. However, the content is not deep enough.