"The One Who Knows No End"
I really enjoyed watching this movie. It feels like watching a perfect Kung Fu performance, clean, natural and impeccable, and more importantly, it is very real and very kind. The movie is based on real people and real events, and the protagonist Srinivasa Ramanujan has a relationship with me (forgive me). I learned about this special genius in "History of Mathematics" before, and then happened to be on WeChat public. I have seen his legendary statement on the number (exaggerated a bit). I have been waiting for the most perfect interpretation. Although the story may be ordinary or even boring and boring, it must be complete and lead us to a deeper level. The movie did it, and I am deeply impressed. New ideas brought by the mathematics masters of intuitionism. The most important and remarkable thing about the movie is that it fully shows us the demeanor of two mathematicians, showing two ideas and concepts, mathematical concepts, and even some key charms of mathematics. Either point is enough to make a movie a classic. Hardy’s achievements are not the key to this film, but he discovered Ramanujan and helped Ramanujan. Ramanujan’s achievement is naturally worthy of admiration, especially the direction of Ramanujan was originally different from him. What contribution did Ramanujan make to the history of mathematics? In the film, he attracted Hardy and his friend Littlewood the most, and was also his own most important achievement. He always asked Hada to help him publish the "Prime Number Theorem": I even created a function that just represented an infinite series. The form of represents a prime number less than X. It means that as long as we provide a number, no matter how big it is, the formula he provides can calculate how many prime numbers are smaller than it. This theorem is indeed very fascinating. It may be true for relatively small numbers, but in the end Littlewood proved it to be wrong through the substitution test. This formula may be beautiful in form, so it is very attractive to mathematicians, but Ramanujan cannot provide a "proof" in the traditional sense. (Hardy: Your theory is really interesting. If you compare the approximate value of prime numbers with the number of prime numbers, what is the result? The result will keep growing, even if the value is as high as one thousand or one million. Is infinity right? How do you prove it? Ramanujan: I proved it to you, I proved it. Hardy: You didn't. No matter how correct you feel it is, in actual calculations, it is wrong, Mr. Littlewood substituted The result shows that compared with the actual number of prime numbers, using your theoretical number will be less, not more. Your theory is wrong. This is also before you can trust me and prove it. We can’t announce the reasons at will. Intuition can only help you get here.) Finally, I helped Ramanujan get the Academy of Trinity College. The qualification of the scholar is his "integer split", what does it mean specifically? The film also provides a certain description. The simple division that we can understand is this, the division of 4 is equal to 5, which means that there are five combinations of 4: 1+1+1+1, 3+1, 2+1+1, 2+2, with 4. It seems very simple. But if the number of divisions is increased to 100, there will be 204,226 different methods. The mathematician McMahon worked it out in a few weeks. Now he can use a formula to solve it, substitute any number, and get the result of the split, just like magic. Fortunately, with the help of Hada, Ramanujan finally succeeded in proving his "integer split" formula. Obviously, the prime number theorem and the division of integers attract mathematicians because they have found and deduced the laws of numbers by proposing a concise formula. The "beauty" of the question seems meaningless, but it just so happens that the "beauty" is of great significance! In the film, Ramanujan and his wife Janaki have a conversation, trying to explain to his wife what is the use of a large number of mathematical formulas he wrote, and the beauty of these formulas: they are like paintings, imagined as an invisible color Painting. It may not look good to you, but to me this is everything. There may be other people who can see and understand them. This will be very important to them. In addition to the unseen colors, I want to learn more. If you look closer, you can see each gravel, one by one. Think about it, everything has rules to follow. The colors in the light and the reflections on the water surface are shown in an incredible form in mathematics. It is really beautiful. I don't know if this is what Ramanujan said. From a literary point of view, he has not said thoroughly. What he meant is that, firstly, the beauty of mathematics is abstract, it is "paints with invisible colors"; secondly, mathematicians can see this "beauty that others can't see"; and finally, this kind of beauty lies in its display of laws and revealing secret. Thinking in terms of our "vulgar practicability" is equivalent to economists discovering a formula that can completely describe the changes in stocks and accurately grasp the changes in tomorrow's stocks. Then how would we react to such a "get rich" formula? Hungry? Maybe some people are still entangled, Ramanujan's formula can't help us make money, and it doesn't even need to buy food. In fact, it happens that these "very abstract and inaction" formulas continue to make contributions at the top level. For example, our computers cannot be built without the support of these pure formulas. The formula provided by Ramanujan is not just like this. As far as the film is concerned, he gave Hardy two books full of these formulas when he first met, and at the end of the film, he wrote another one within a year after returning to India. How many formulas should be recorded in a formula book? The secrets and functions of these formulas that have been shown and not yet shown may be far beyond imagination, as the film said: In 1976, a "missing pen" Kite. You can feel the tension on the line, and you will understand that he is aloof. "And I said: "If there is no wind, can the kite fly?" "No... I don't believe in God. I don't believe in ancient Eastern wisdom. But I do believe in you. Obviously, Hardy did not shake his beliefs, just as Ramanujan did not shake his beliefs. Understand that Hardy believes. Ramanujan believes in the "miracles" he showed. Next, we will continue to explore the mystery from the perspective of "stubborn materialism." From a superficial level, there are many similar "geniuses" in the real world. ". And Ramanujan has always shown this kind of genius: when he was an accountant, he didn't need an abacus at all, he used mental arithmetic directly. He was playing against McMahon to calculate the square root of "58639", and both of them could do it. Speaking directly, it is faster than a computer. More importantly, there is not only an inherent "arithmetic talent", Ramanujan can also directly analyze "numbers." When Hardy sent Ramanujan, When the taxi got lost, he complained that the license plate number "1729" was too stupid. The taxi Ramanujan told him immediately: No, Hardy, this number is very interesting. It can be expressed by the sum of two cubes, and there are two types Among the numbers of expression methods, 1729 is the smallest. Think about it, even if we follow the calculations, I am afraid that there is no clue. Ramanujan can analyze the numbers backwards. This ability is obviously higher. A level. Not only that, he was able to jump directly to the result. At Trinity College, Cambridge, Hardy sent him to the mathematician Howard’s class. As a result, Ramanujan was called to the podium to complete the topic Howard was explaining. He I wrote the answer directly, without any process. Howard was taken aback: But I haven’t fully proved it, so how do you know. Ramanujan said: I don’t know, just write it down. Obviously, he has a direct description. The ability of regularity. So Littlewood commented: Ramanujan's existence is no less than a miracle, his talent has exceeded my imagination, not to mention the Jacobian, he can even compare to Newton. I now begin to believe that for Ramanujan, every positive integer is a good friend of his. Since he has such a "talent", it is not surprising to find a pattern in endless numbers and describe it with a formula. To understand in this way, Ramanujan’s talent is really a miracle, regardless of whether we think that God created him, but that such a genius naturally exists, and nature created him. (As for why nature exists like this Of people, I think the biggest possibility is the "cosmic holography." Regarding all the human history as a holographic photo, each of us includes the entire universe Information, because we are relatively too small, so the information we display is always flawed. It's like there is a world in a mirror. When the mirror is broken, every fragment can show that world, but it is flawed. Of course, this view also seems to imply a theory that unifies science and religion: God is everything in the universe, we are all part of God, and each of us can record the whole, but only shows part of it). Ramanujan believes that "an equation is meaningless to me unless it expresses the will of God." Therefore, he does not care about proofs, but more care about recording the will of God, just like secretly plagiarizing the heavenly book and intending to send it. Just like going to the world to benefit mankind, the more you copy, the better. So he thought: I don't quite understand why we waste time to prove. Hardy knew the value of Ramanujan’s formulas, and he really wanted to make his books public, but as Hardy said: I’m very satisfied with them, but if I publish them in my current state, I will be sent to the lunatic asylum. As a master of mathematics, you can know the value of these formulas, but these formulas are not sufficiently proved. In other words, it is equivalent to letting a group of atheists accept the existence of God, but they can't come up with half a reason. Hardy also proved all of Ramanujan’s many drugs, only requiring him to prove one or two, which can win the affirmation of mathematicians. At that time, even if Ramanujan’s formula has not been verified, it can at least become a "conjecture". "Let future generations continue to complete. Otherwise, even if Hardy releases them, they will soon be forgotten and abandoned. Proof, how important is it? Because it is proved, that is the truth that mathematicians and atheists can accept. Even if it corresponds to a large number of verifications, and even Ramanujan completes Howard’s question in a leap, for Howard, Ramanujan’s solution may be more of a "innate insult"; but for mathematicians Said that it was just "lucky" and still could not enter the palace of truth. Therefore, the conflict between Hardy and Ramanujan and the obstacles to cooperation are all around this point. Use a common language. You don’t want us to talk in Tamil. Mathematics, like art, is a common language, but it also requires a recognized method of communication-proof, to achieve communication. Ramanujan has always insisted But it’s: I don’t want these formulas to be my funerary). However, when Ramanujan proved the "integer split" he proposed, he accomplished what mathematicians thought was "impossible." Hardy has a little basis to persuade everyone to accept Ramanujan’s special way . The following is the speech content of Hardy’s persuading the mathematics masters of Trinity College to pass Ramanujan’s academician qualifications, and we can use this to understand Ramanujan’s deeper contribution: this is our research on integer division and what we have achieved A major breakthrough. Please note that all of this comes from one person. When I first met him, the limitations of his knowledge shocked me as much as the profoundness of his wisdom. Regarding the importance of Ramanujan’s achievement and the possible impact on future mathematics, people may have different opinions in voting. But this result showed a profound ingenuity. Mr. Littlewood once said to me that "every positive integer is a good friend of Ramanujan", and I am convinced of this. He once told me: An equation is meaningless to him unless it expresses the will of God. Although I personally cannot agree with this at all, maybe he is right. Because this is what we want to prove in our pursuit of pure mathematics, we are just in the process of pursuing absolute perfection, countless explorers. We didn't invent these formulas because they existed by themselves, but we were waiting for people like Ramanujan with endless wisdom to guess and verify them. Therefore, in the end, I can’t help thinking about why we question Ramanujan, let alone question God, thank you everyone. In other words, the value of Ramanujan lies in the fact that he and Goldbach’s conjecture are the same, and this conjecture is “original”. In fact, the discovery of a conjecture itself is to propose a possibility for people to try to prove, whether the proof is successful or not, it is of extraordinary value. And Ramanujan put forward so many "conjectures" at once, which is naturally even more remarkable. Not only that, but I think the film actually illustrates another contribution, a very important contribution. In the film, in order to gain support, Hada sent Ramanujan to the Howard class, who opposed Ramanujan’s admission to the college. Later, he brought Ramanujan to the dean of the department and the pioneer of combinatorial mathematics, McMahon. Go there (Director McMahon, he is the pioneer of combinatorics in the school. He also happens to be one of your most high-profile opponents. He said that there can be no formulas for integer splits). McMahon believes that Ramanujan cannot successfully complete the "integer split", and he can succeed. The only way is to use the "stupid way": calculate with your hands, use long and painful additions, and then you will knowledge. The formula you two dreamed up is wrong, and then you can roll back to your isolated India. Then we don't have to accompany you here to guess riddles. However, when McMahon asked Ramanujan to calculate the split of 200, Ramanujan told him that the answer was 3972998000000. And this is very close to McMahon’s "hand calculation" result, with an error of less than 2% . So McMahon naturally began to understand and accept Ramanujan. Let us think carefully about the problem behind it. The success of the so-called "integer splitting" is naturally not about splitting a specific number, such as 200, because in that case, a dumb person can use a dumb method and spend time to make it. Therefore, mathematicians should study "integer splitting", in fact, they have to find the law and work out a formula, and then no matter how big the number is, it can be directly substituted into the formula to calculate the split. However, to find a pattern, everyone’s solution is to make a lot of attempts, such as splitting from 1 to 200 (McMahon asked 200, indicating that he has tried more than 200 numbers, how painful this is. The work must be error-free, and it must be persisted for a long time), and then see what is the relationship between these numbers and the numbers that have been dismantled. This is a stupid way, but it is also a "popular" way, there is no way. And Ramanujan can directly perceive the law, even express the law, and formulate the formula. He was able to calculate the result mentally, and McMahon naturally looked at him with admiration, no longer sarcasm and doubt. Therefore, Ramanujan's real contribution is to bring this "intuitionism" into the world of mathematics. Although intuition is not necessarily accurate, previous mathematics masters, especially those who have made conjectures and have originality, may also have this kind of talent to some extent. Finally, the most impressive thing about the film is that it clarifies the values of scientists. Hardy took Ramanujan, who was eager to be affirmed and published his two formulas, to the Lane Library and told him: There are many ways to gain honor in one's life. For us, being elected as an academician is one way. . But in my opinion, after our death, it is the greatest to be able to leave a legacy in the Lane Library. There are "The Letters of Paul", Milton's poems, and the "Morgan Bible", but in my opinion as a mathematician, the most important one is Newton's "Principles of Mathematics", just like Newton is the material representative of our field. . And your notes are abstract representatives, and Newton also took a long time to prove himself, so we are obliged to prove it. Once we succeed, I believe that one day, these notes will have a place here. Now you understand what our main point is. Obviously, this passage is enough to make us understand what is the name of the snail angle and what is the true value. It is to leave one's own mark in the heritage of mankind, the others are secondary. And this pen is absolutely not tolerant of falsehood, nor can it be forged with power or money. It can only rely on "proof" and must stand the test. This is the most shocking for us who are addicted to the snail horn's fame and petty profits, and for the "in vain", the life style and attitude of the pig. Human civilization is not created by those who have so much power and enjoyed so much wealth, but in the end it is just the accumulation of one elite after another. As Sima Qian said, "The ancients were rich and famous, It's unbeatable, only the very suave people call Yan. "Those people are nothing more than lightning and flint, no matter how brilliant they are, they will be forgotten, but the civilization created by the elite is accumulated bit by bit, and is continuously inherited and carried forward. The second is the wonderful secondary content. Because even the most Dispensable, Ramanujan’s love story is also vividly shown, and it can be thought-provoking. At the beginning of the film, Ramanujan is already married, but there is a "gap" in the love between him and his wife. "Gap", as my wife said, "I heard that you like numbers more than people." It is obvious that Ramanujan does. However, as a genius, he is also afraid of loneliness, or as a pious A believer does not want to hurt others, so he would say to his wife "some people, not including you." Although he also wanted to take his wife out of India and go to England. But because of his mother's selfishness, he was afraid that Ramanujan's wife would follow him. London, England, then would never go back to India, and never see his son again. At first the couple decided to go to the UK together, but when the mother said, "Do you want to go, or did she persuade you to go?" So do you want to go together? Is this all a good thing she did? She wants to occupy you alone", so that the wife dare not follow. When the wife has been waiting for the husband who arranged everything to write a letter to let herself go to London to meet, the mother wrote her daughter-in-law to her son. They all hid, causing the young couple to suspicion each other and also feel abandoned. His wife went to his brother and Ramanujan wanted to commit suicide again (more because of math work and a serious illness). People are finally reunited, and it’s only a year together. Maybe, we’ll think, if Ramanujan takes his wife to the UK, then maybe he has someone to take care of him, he won’t get sick, he can live longer, and can write more More formulas, or prove more things. But, he has written so many, proved so important things, no amount of greater value, not to mention he himself endowed the history of mathematics, endowed science History has been enlightened enough. Maybe, we still think that someone depends on each other and will not feel too lonely and humiliated. He may cooperate better with Hardy, may enter the state faster, and get it earlier. The qualifications of an academician... But in fact, just as Ramanujan believed that he was "condemned by the heavens", because he had leaked too many "secrets", he had left too much to the world. Not only showed love, but also showed Friendship. In India, Narayana, who served the Englishman Francis, also had a certain degree of mathematical literacy. He hired Ramanujan, who had no degree, to help him keep his books because he found the value of his formulas. It is precisely because of Narayana’s insight to recognize the hero, he hired Ramanujan and indulged him (with mental arithmetic), suggesting where he got the paper (the paper is not cheap here, but on the dock, you can find many sacks. Paper), to encourage him (Ramanujan tried to show his writing to almost all the people in the city, but no one understood, he was disappointed. But Naraya would encourage him and tell him Madeira The city, the name comes from "Mandarajya"-the state of ignorance. There is a big world outside, England), and through the recommendation of the boss Francis, he can write to Hardy. Because he knows the value of Ramanujan’s formula "These results are very important and should not be buried in this way, it must be made public", and he also knows the value of Ramanujan "If you are an Indian, use these mathematical formulas to reach the top , Then even the British who have conquered us must admit: our wisdom can match them." Without him, Ramanujan's achievements would not be possible. Of course, there is also the friendship between Ramanujan and Hardy. Hardy was not married. According to him, "I have never known anything about this kind of thing, but I still want to say that there is neither proof nor law governing the outcome of this kind of thing." People who don't even have love are naturally very It's hard to know how to care about friends. However, the film shows a deeper "revolutionary friendship". When we first met, it was Ramanujan who had been invited by Hardy. When Ramanujan entered the academy, Hardy happened to talk to everyone about Ramanujan's talent. But after seeing Ramanujan and getting to know each other, he coldly said to Ramanujan: I am very looking forward to starting our work, so I will be there at my office at ten o'clock tomorrow morning. Then turned around and left. I didn't even have to say greetings or help arrange food and accommodation. Ramanujan was so scared that he thought he had said something wrong and offended him. He did not ask Ramanujan about other things, whether he had any dependents, or whether he had any difficulties in life (Ramanujan is a Brahmin and vegetarian. He can't even eat potatoes made with lard. The food at the school is very rich. , But he can only go to the vegetable market every day to buy vegetables, eat clear soup and lack of water, leading to malnutrition), just forcing him to work to prove those formulas (these are obviously also the reasons why Ramanujan suffered from tuberculosis). It wasn't until Littlewood reminded him to take good care of Ramanujan, and he didn't realize his problem until Ramanujan nearly died by suicide. He said to Ramanujan: I’m sorry, I didn’t become your good friend in the traditional sense. I know you need such a friend, but I am not good at it, I have never been good at it. To me, life is... always mathematics. In fact, upon hearing this sentence, we will think of Ramanujan's wife's evaluation of him. They are originally just about mathematics and don't care about other people, so how do they know how to care about people and how to care about people? However, we have no way to criticize them. On the contrary, we lament the friendship between the two people. It is precisely because of the heroic sympathy that Ramanujan has made achievements and contributions. Therefore, the film is also teaching us how to treat such geniuses and how to understand their lives. 16.9.5
View more about The Man Who Knew Infinity reviews
