The story of mathematicians 100 words
1, Chen Jingrun doesn't like playing parks, strolling the streets and studying. When I study, I often forget to eat and sleep.
One day, Chen Jingrun touched his head during lunch. Oh, his hair is too long. He should get a haircut quickly, or people will think he is a girl when they see him. So he left work and ran to the barber shop.
2. The story of mathematicians
Galois was born in a town not far from Paris. His father is the headmaster of the school and has served as mayor for many years. The influence of family makes Galois always brave and fearless. 1823, 12-year-old galois left his parents to study in Paris. Not content with boring classroom indoctrination, he went to find the most difficult mathematics original research by himself. Some teachers also helped him a lot. What did the teachers say about him? Only suitable for working in the frontier field of mathematics? .
After finishing the first grade of junior high school, Hua dropped out of school because of his poor family, so he had to stand in front of the counter for his parents, but he still insisted on teaching himself mathematics. Through his unremitting efforts, his paper "Why can't the solution of Su Jiaju's algebraic quintic equation be established" was discovered by Professor Xiong Qinglai, head of the Department of Mathematics of Tsinghua University, and invited him to Tsinghua University; Hua was hired as a university teacher, which is unprecedented in the history of Tsinghua University.
Mathematical famous sayings
1, infinity! No other problem has touched the human mind so deeply. -D. Hilbert
We can expect that with the development of education and entertainment, more people will like music and painting. However, few people can really appreciate mathematics. -Bell
Genius is not enough, cleverness is unreliable, and it is unimaginable to pick up great scientific inventions conveniently. -Hua
Another reason why mathematics is highly respected is that it is mathematics that provides an unquestionable and reliable guarantee for accurate natural science. Without mathematics, they can't reach such a level of reliability. -Einstein
5. Mathematics is the queen of science and number theory is the queen of mathematics. Gauss
6. The motive force of mathematical invention is not reasoning, but imagination. -De Morgan
In the field of mathematics, the art of asking questions is more important than the art of answering questions. cornel
9. Mathematics, queen of science; Number theory, the queen of mathematics. Gauss
10, the number is not intuitive when it is invisible, and it is difficult to be nuanced when it is small. Numbers and shapes are interdependent. How can we divide them into two sides? -Hua
1 1, number theory is the oldest branch of human knowledge, but some of his deepest secrets are closely related to his most ordinary truth. A professional who is good at creating with a certain material: goldsmith | wordsmith.
12, God created integers, and the rest are artificial. -Kroneck
13, if anyone does not know that the diagonal side of a square is an incommensurable quantity, then he is not worthy of this title. -Plato
Mathematical paradox problem
1=2? The most classic in history Proof?
Let a = b, then a? B = a^2. subtract B 2 from both sides of the equal sign to get a? B-b^2 = a^2-b^2. Note that this equation can put forward a B on the left and a square difference on the right, so there is a B? (a-b) = (A+B) (A-B). If (A-B) is omitted, there is b = a+b However, a = b, so b = b+b, that is, b = 2b. If b is omitted, 1 = 2 is obtained.
This is probably the most classic fallacy ever. Jiang Fengnan wrote in his short science fiction novel Divide by Zero:
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There is a well-known one? Proof? It is proved that one equals two. It starts with some definitions:? Let a =1; Let b = 1. ? End with a conclusion? a = 2a，？ That is, one equals two. Hidden in the middle and inconspicuous is a division divided by zero. At this point, the proof has left the edge and made all the rules invalid. Allowing division by zero can not only prove that one and two are equal, but also prove that any two numbers are equal? Reality or imagination, rationality or irrationality? Are equal.
The problem of this proof must be clear to everyone: both sides of the equal sign cannot be divisible by a-b at the same time, because we assume that a = b, that is, a-b equals 0.
The power of infinite series
When I was in primary school, this question puzzled me for a long time: What is the following formula?
1 + (- 1) + 1 + (- 1) + 1 + (- 1) + ?
On the one hand:
1 + (- 1) + 1 + (- 1) + 1 + (- 1) + ?
= [ 1 + (- 1)] + [ 1 + (- 1)] + [ 1 + (- 1)] + ?
= 0 + 0 + 0 + ?
= 0
On the other hand:
1 + (- 1) + 1 + (- 1) + 1 + (- 1) + ?
= 1 + [(- 1) + 1] + [(- 1) + 1] + [(- 1) + ?
= 1 + 0 + 0 + 0 + ?
= 1
Doesn't this mean 0 = 1
Later, I learned that this formula can also be equal to 1/2. How about s =1+(-1)+1+(-1)+? , so there is S = 1-S, and the solution is S = 1/2.
After studying calculus, I finally understand that this infinite series is divergent, so it doesn't matter? And then what? . What is the result of adding infinite numbers? This needs to be defined
I recommend it carefully.