Zeng Guofan is one of the most influential figures in the history of China, but his talent was not high since he was a child. One day when I was studying at home, I repeated an article many times and was still reading it aloud because he hadn't memorized it yet. At this time, a thief came to his house and lurked under his eaves, hoping to get some benefits after the scholar went to bed. But wait and wait, just don't see him sleeping, or read the article over and over again. The thief was furious and jumped out and said, "What books do you read at this level?" Then recite the article and leave!
The story of Zhang Guanghou, a famous mathematician in China, who studied hard when he was young will inspire everyone. When Zhang Guanghou was in primary school, he didn't get into junior high school because of his poor arithmetic performance, but he didn't lose heart. He believes that as long as he studies hard, he can overcome the defects in knowledge and make his study better. So he carefully examined his learning problems, especially the reasons for his poor math. After several months of hard training, his academic performance has obviously improved, and he was admitted to middle school with excellent results. In middle school, he studied harder. After graduating from middle school, he was admitted to the university with excellent results. Finally, he studied mathematics hard and became an internationally recognized great mathematician. Zhang Guanghou failed in arithmetic in primary school, but later he became a famous mathematician, which vividly illustrates a truth-diligence can make up for it.
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The Secret of Learning: How many mysteries are hidden in a story? ? 20 17-02-03 ? Hu yanluan ...? Source? Reading 1620? Turn to 8 1 hide in my library and share on WeChat: Why are people obsessed with stories? This question puzzles me. I once listened to a friend's book. Whenever Journey to the West is shown on TV, he watches it once. The TV play was badly replayed, but he hasn't watched enough. ? For a long time, I was addicted to theories and opinions. Because of its strong theoretical generalization ability, it has a superior geographical position and is magnificent. Later, it turned out that the facts were more important. Stories can contain many things, including theories. Facts speak plainer than words. It is easy to make up a theory and put forward an idea, but a true story, or a beautiful story, is by no means that simple. Later, I found a story that can be remembered for a long time, and each memory has different feelings and inspirations. Later, I was convinced that there was an infinite mystery behind every truth! For example, the following story: Xiao Ping Bangyan is the first mathematician in Asia to win the Fields Prize. Xiao Ping Bangyan often says that he has no talent, but since middle school, he has been the kind of person who does things meticulously and wholeheartedly. He recalled that when he first studied algebra written by Vander Waals, he hardly understood it. Then start copying books until you understand them. ? The story is over. It's that short. There don't seem to be many twists and turns. However, this story has always remained in my memory. When I first saw this story, I immediately associated it with "diligence can make up for it", "persistence is the most important thing" and "smart people will work hard" Of course, "copying books is a good idea." Of all the feelings about this story, "copying books is a good way" occupies an overwhelming position. Because, I think, many people have had the experience of copying books. For example, Montessori, the greatest educator in the 20th century, translated the masterpieces of two anthropologists and made remarkable achievements in the creation of Children. After the translation, she copied it herself. In China, many monks and Taoists also copy scriptures. There are often people with superior wisdom in this group. After a while, I found that this story has a new connotation. This comes from the feeling of daily study: many important books seem to be very laborious. Xiao Ping Bangyan's story inspired me. If I find it difficult to study, it is not a problem at all. Because, if reading is simple and effortless, it is reading newspapers, not studying. Even Hirayama, who is so awesome, is not born with talent. Reading math is as easy as reading a novel. Later, I learned the concept of deliberate practice and that human activities are in three aspects. Comfort zone, study zone, panic zone. If you stay in the comfort zone, you can learn nothing. For example, college students can learn nothing from the arithmetic of addition, subtraction, multiplication and division of natural numbers. It is also difficult to learn anything when you are active in the panic zone. For example, high school students are asked to do differential equations. You can only learn things in the study area. At this time, the current task is more difficult than your own ability, and your level has also improved in the process of striving to achieve your goals. ? So, if you are doing something difficult, you are probably in the study area. After doing this, your ability will grow. The Power of Friends Circle Later, I shared the story of Xiao Ping Bangyan with some friends I had talked about on various occasions. Everyone's opinions are varied. A friend of mine is very good at math, and almost all college math exams get full marks. After listening to Xiao Ping Bangyan's story, he said, "I often copy books and concepts." This sentence is plain, but it inspires me. The cornerstone of any knowledge is the basic concept. Many people have unclear ideas, or their knowledge is full of loopholes and their views are unclear, all because of unclear concepts. Once the concept is clear, thinking will have vitality. Just like this friend, he discovered this mystery as early as in college. Another friend said: "Copying books is like copying the answers to questions that you can't do. In the process of copying, you can deepen your logical memory." Indeed, in the process of solving problems, we often glance at it and think that I can solve this problem. Actually, I can't solve it either. Even after seeing the answer and the problem-solving process, I feel suddenly enlightened. The problem is that even if you suddenly realize it, you may not be able to master it. As this friend said, copying down the answers to the questions that you can't do (including the problem-solving process) can deepen your logical memory. I did the same in high school. Another friend said, "Calm down and take it step by step." I also agree with him. The action of copying books can level anxiety and anxiety and make steady progress step by step. Once people's thirst for knowledge is ignited, or the external pressure is great, the desire to "eat a fat man in one bite" is very strong, and they always want to learn more at one breath. I always feel that the progress is not satisfactory at this time. If you can calm down and take it step by step, it will be efficient. How are experts tempered? ? For a period of time, I have been paying attention to the topic of "how experts are tempered". I got three inspirations from the story of Xiao Ping Bangyan. Can you copy mathematicians by copying books? If copying books can copy mathematicians, wouldn't the streets be full of mathematicians? Think of what Wheeler said: "No questions, no answers". I think Ping Bangyan must have copied the book with questions. Copying a book, thinking about problems, and even guessing what the follow-up content of the book is, copying and answering. Compare what you think with what is written in the book until you understand it. When he was confused, he found the answers to all the questions in his mind. Some of them are from books, such as the answers given in books, and some are independently deduced by him according to the tips in books, so he naturally understands. ? Experts in any field of knowledge must have solid basic skills. The question is, what is this basic skill? Actually, it is a kind of thinking structure. For different knowledge fields, the corresponding thinking structure is different. Perhaps it was Hirahira who wanted to know the basic structure of algebra when he was copying a book. At least, I want to know the thinking structure of Vander Waals algebra. Learning any knowledge, mastering any knowledge, must be slow first and then fast. If he can only understand mathematics by copying books, then he can't become an international mathematician. Because there are too many works on mathematics, even the classic works are numerous. If he copies so slowly, when will he copy? In the process of copying, he is first familiar with that kind of thinking skill, which is slow. Once this thinking skill is mastered, any branch of mathematics has the same structure and uses almost similar thinking skills. So practice makes perfect, not just solving problems, but an extension of thinking. The extension of thinking is invention and creation. Therefore, there is no sharp boundary from learning to invention and innovation, but a continuous process. The year before last, I was concerned about the relationship between talent and learning. Got three more inspirations:? First, there is no absolute understanding and ignorance. The key is how much I know today, how much I know today and what I know today. What questions are thought of today and what answers are found are the key. Including when we were doing a topic, I made a mistake If I make a mistake, what do I get? I did the right thing. How much did I get? One is one, two is two, three is three. Did we do it? It is essential to do so. There is no absolute understanding and ignorance about anything. Find ways to leap from ignorance to understanding, even copying books. Take a step forward, even if it is a word. ? Second, don't worry about whether you have talent or not, unless you try. Even in the early days when he began to learn mathematics, he still encountered great difficulties. When we encounter difficulties in our study, when we have a headache, when we can't understand, when the problem can't be worked out, we often doubt ourselves. Is it true that I can't do math? I don't have mathematical thinking? Or is it that someone really has no talent? Probably, it has nothing to do with talent. For example, cognitive neuroscience research shows that we are born with mathematical thinking, which is imprinted in our neural structure. Of course, neuroscience research also shows that each of us is a supercomputer. Today, the most advanced artificial intelligence still needs to spend a lot of energy to simulate the functions of image recognition and emotion recognition that ordinary people have. With the development of life science and technology, we can't make a complete cell with inorganic substances, but there are 100 trillion cells in our ordinary people's bodies. Therefore, when we have self-doubt, especially when we doubt our learning ability, we should stop obsessing about the problem of talent unless we work hard. Since world-class mathematicians have made such efforts, we have to ask ourselves: Have you made efforts comparable to them? Second, "if there is a miracle in the world, it is just synonymous with hard work." We can solve a problem, a moderately difficult problem, which only comes from those basic knowledge points and those basic thinking operations. The more difficult topic is the same. We solved a very difficult problem. One day, I was proud of myself and thought it was a miracle. It's just what we tried to accumulate before, that is, their integrals accumulated bit by bit, first differentiated and then integrated. The same is true of other things. We can deal with more and more difficult things in life, make better works, write better articles, make better projects and open up more promising projects. These are all accumulated bit by bit. They are accumulated in the process of constantly facing discomfort, constantly facing challenges and constantly making various efforts in the field of learning. There was a TED talk "How do I hold my breath 17 minutes". Magic David? Brian described his experience of holding his breath underwater17.5 minutes, including how he trained himself step by step and what failed and successful attempts he made. I have watched this video dozens of times. Because this magic was once published as an experimental study in the New England Journal of Medicine, one of the four major international medical journals. What's more, this speech is very shocking. In the first half of the speech, david brian told many humorous stories and tried all kinds of interesting things in the process of holding his breath. At the end of the speech, he said: As a magician, I try to show something-something that seems impossible. ? I think magic, whether holding your breath underwater or playing a deck of cards, is very simple. Just practicing, training, and ... (almost sobbing, holding back tears, going on)? It's practice, training and trying. Endure those painful moments and do your best. This is what magic means to me. Thank you. By the end of the speech, Brian had lost control of his emotions. I think he originally wanted to make this speech in a relaxed and humorous style, and at the same time bring surprises and laughter to the audience. However, when he talked about his training process, he was moved himself. Many people dream or fantasize that miracles happen to them, including me. I also asked many questions about miracles. Now, I ask: have you reached the limit of your efforts for those really important things? ? How do you know that you have reached the limit? ? What prevented you from doing this? ? Last night, friends got together and had a good chat until 1 p.m. A past event can be interpreted from infinite angles. There are laughter, people's right and wrong about the world, society and human nature, and various understandings of fate. A small party can last at least a month. Everything that happens in life hides endless mysteries.