"Martha's theorem--a mystery that puzzles the wise man of the world for 358 years" excerpt

• The word philosopher (philosopher) was created by Pythagoras. At a Olympia games, Pythagoras depicted himself as a philosopher to Flieuse: "Prince Leon, life is like these open competitions." Among the crowds gathered here, some are tempted by rewards, others are driven by the desire for fame and glory, and by ambition, but a few of them come here to observe and understand what is happening here.
• The same is true of life. Some people are swayed by their love of wealth, while others follow blindly by their passion for power and domination, but the best of them are dedicated to discovering the meaning and purpose of life itself. He tried to reveal the mysteries of nature. This is the man I call a philosopher. Although no one is wise in every way, he can love knowledge as the key to uncover the mysteries of nature.
• Finding a mathematical proof is the search for a sense that is more indisputable than the knowledge accumulated in any other training. In the case of the scientific theory of physics, it is considered very likely to be based only on the evidence obtained. The so-called scientific proof relies on observation and understanding, both of which are error-prone and merely provide concepts that approximate truth. "Although this is a bit of a paradox, all precise science is governed by the notion of approximation," said Russell. ”
• About Father Menison (Father Marin Mersenne): Although this person does not contribute much to number theory, he plays a far-reaching role in the exchange of mathematical researchers. Because the mathematicians of Paris 19th century ago were secretive about their findings and discoveries in order to show that they were making a contribution in one respect. But the priest encouraged the mathematicians to exchange ideas and promote their work.
• The development of any discipline relies on its ability to communicate and express ideas, and the latter by virtue of a sufficiently detailed and flexible language.
• Wiles is a simple and ambitious child, he saw a chance of success, a generation of mathematicians in the face of this opportunity has failed. It seemed like a reckless dream to others, but the young Andrew thought of him--a 20th century middle school student--who knew mathematics as much as the 17th century genius Pierre de Fermat, perhaps because his innocence would have made him happen to find a more sophisticated scholar who hadn't noticed.
• Creating mathematics is a journey full of pain and mystery. Usually the goal is clear, but the road is hidden in the fog. Mathematicians balked, fearing that every step could lead the argument to a completely wrong direction. In addition, there is concern that there is no road at all. Mathematicians may believe that a proposition is right, and it takes years to prove that it is true, but it is actually totally wrong. So, in effect, the mathematician has just been trying to prove the impossible.
• Infinite degradation Method: if the proving equation \ (x^4 + y^4 = z^4\) does not have an integer solution, Fermat assumes that there is a solution, and then proves that there will be a smaller solution that must exist, and then it goes on and on, producing a smaller solution. This is an infinite echelon, but the actual x, Y, z must be integers, so there has to be a minimal solution that creates a contradiction.
• During the invasion of the Roman army, Archimedes was concentrating on a geometrical figure in the sand so as to inadvertently answer a Roman soldier's questioning. As a result he was stabbed to death by a spear. Germain concludes that mathematics must be the most fascinating subject in the world if a person is so obsessed with a geometrical problem that results in his death.
• About invariants in mathematics: Lloyd's Digital mobile game (a bit like the Huarong Road) shows that the random number of the final digit is even if the slider is moved anyway. This is the invariant under various moving operations. Therefore, if the number of the wrong ordinal is odd, regardless of moving, it is not possible to get the first order of the correct sequence of errors. Invariants provide an important strategy for mathematicians when proving that it is impossible to turn an object into another object.
• Mathematics has its application in science and technology, but it is not the driving force of mathematicians. What motivates mathematicians is the joy of finding them. ... The desire to answer a mathematical question is mostly out of curiosity, and the payoff is the sheer and immense satisfaction of solving the problem.
• The problem with research fees may be that you may be wasting years and nothing. As long as you are studying a problem and can generate a mathematical interest in the study, it is worthwhile to study it-even if you do not eventually solve it. Judging whether a mathematical problem is good, the standard is to see if it can produce new mathematics, not the problem itself.
• John Coates's responsibility was to find something new to love for Andrew, something that would at least make him interested in studying for the next three years. "I think what a graduate tutor can do for a student is trying to push him into a fruitful direction. Of course, there is no guarantee that it must be a fruitful research direction, but perhaps one thing older mathematicians can do in the process is to use his practical knowledge, his intuition about what is good, and then how much the student can do in this direction is his own business. ”
• When they met in 1954, Valley Mountain and Chi village were just beginning to work in mathematics. The customary practice at the time (which is still the case) was to put young researchers under the leadership of a professor, who was responsible for directing young men to the first-out, but Valley Mountain and Chi Village rejected the apprentice approach. ... According to Chi village, professors are "exhausted and no longer ideal". By comparison, the war-tempered students became more fascinated and eager to learn, and they soon realized that the only way forward for them was to teach themselves . The students organize regular workshops and participate in seminars that enable them to understand each other and communicate the latest technology and breakthroughs. Although Valley Mountain often looks listless in other ways, his participation in the seminar has been a huge motivator. He will inspire senior students to explore uncharted territory, and for younger students he plays a role as father.
• Wiles clearly knew that he had to devote himself to the problem in order to find a way to prove it. But unlike Hilbert, he is prepared to take the risk. He read all the latest magazines and practiced the latest techniques until they became his second instinct . In order to gather the necessary weapons for future battles, Wiles spent 18 months familiarizing himself with all the mathematics that had previously been applied to elliptic equations or modulo forms, and derived from them.
• You will often write down some words to clarify your thoughts, but not necessarily. Especially when you really get into a dead end, when there is a real problem that requires you to conquer, that kind of disciplined mathematical thinking is useless to you. The idea of a new kind of thinking has to go through a long period of extremely focused thinking about that problem, without any distraction. There seems to be a relaxation period, during which the subconscious appears, occupying your mind. It was during this period that some new insights emerged.
• Wiles explained that part of the reason he decided to work secretly was that he wanted his work undisturbed. "I realized that anything related to the Flt theorem would be of interest to too many people. It's impossible for you to focus on yourself for years, unless you're distracted by others, and that's not possible because there are too many bystanders. ”
• Wiles borrowed the experience of passing through a dark, unexplored building to describe how he felt when he was doing his math research. "Imagine entering the first room of the building, which was dark and dark. You stumble between furniture, but gradually you figure out where each piece of furniture is. Finally, after 6 months or more time, you find the light switch and turn on the light. Suddenly the whole room is full of light, and you can see exactly where you are. Then you went into the next room and groped for 6 months in the dark. Therefore, every such breakthrough, though sometimes just for a moment, sometimes takes a day or two, but they are actually the end result of stumbling in the dark for many months before, without which they are impossible. ”
• If you don't know what the math is for, you can't understand it. Even if you know what it's for, it's hard to understand.
• The last step of Flt theorem proof: One morning in late May, Nyda went out with the children, and I sat at my desk thinking about the remainder of the elliptic equation. I took a casual look at a paper by Barry Mechul, which caught my attention in one sentence. It mentions a 19th century structure, and I suddenly realized that I should be able to use this structure to make the Kovalikin-Fletcher method also suitable for this last family of elliptic equations. I have been working until the afternoon, forgetting to go to lunch. At about three or four o'clock in the afternoon, I was really sure that this would solve the last remaining problem. When I was at the tea break, I went downstairs, and Nyda was amazed at how late I came. And I told her--I've solved the Flt theorem.
• Less than 6 months after Wiles's speech at Newton's Institute, his testimony has been flawed. Years of secret calculus brought him pleasure, passion and hope to be replaced by annoyance and disappointment. He recalled that his childhood dream had become a nightmare: "In the first 7 years of my research on the subject, I enjoyed the covert battles." No matter how difficult it was, no matter how insurmountable it seemed, I was inseparable from my beloved question. It is my childhood love, I can never put it down, I do not want to leave it for a moment. Then I talked openly about it and there was a certain sense of loss in talking about it. This is a very complex feeling.
• Wiles to Peter Sagnak that the situation was desperate and he was ready to admit defeat. Sagnak hinted to him that part of the difficulty came from the lack of a person he could rely on for a daily discussion, a man who could not discuss his ideas with him, or a person who could encourage him to take advantage of some of the lateral approaches.
• Suddenly, completely unexpected, I had an incredible discovery. I realize that although the Kolivakin-Fletcher method is not fully workable now, I only need it to make the Eva Shava theory that I used to be effective. I realized that there was enough in the Kovalikin-Fletcher approach to succeed in the way I worked on this issue in my previous 3 years of work. So the right answer to this question seems to be in the ruins of Kolivakin-Fletcher. ”
• Eva Shava theory alone is not enough to solve the problem, relying on the Kolivakin-Fletcher method is not enough to solve the problem, they together can perfectly complement each other.

"Martha's theorem--a mystery that puzzles the wise man of the world for 358 years" excerpt