The story of love and death in mathematics

The story of love and death in mathematics

Xiaogang

I had no sleep at night and suddenly thought that I was already halfway through my life journey (according to the average age of Chinese people) ), I feel very scared when I think about it carefully. Life is a journey with no return. From the starting point to the end, people experience and calculate their own growth, struggle, love, health, time, relationships, contributions... If you build a model for love and life and death, write a mathematical expression , is it possible to automatically describe all the love stories in the world and give them a reasonable explanation? Although there are too many variables, the uncertain results are the reality of this world and the true meaning of beauty. Who said mathematics will definitely have accurate answers!

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The epitaph of Diophantus reads: "Passenger! Diophantus is buried here. Please calculate the following numbers to know how many cold and heat he experienced in his life. One-sixth of his life was a happy childhood, and one-twelfth was a carefree youth. Five years later, his son was born. The son died four years before his father, and lived only half the age of his father. How pitiful the old man was when he lost his son in his old age. Please calculate how long Diophantus lived before he met the god of death. ?"

The great British mathematician De Moivre died in 1754. His death was a miracle. Shortly before his death, he claimed that he would sleep 15 minutes more every day than the previous day. The day he sleeps for 24 hours is the end of his life. We can adapt this story into an arithmetic sequence: De Moivre's sleep time was 8 hours on September 24 of that year. When did he die? It seems that life and death can be calculated.

Everyone is bound to die, no matter what kind of person they are, great or small. Life is not a straight line that can extend infinitely to both ends, nor is a ray that can extend the length of life infinitely. Life is just a line segment with a starting point and an end point, and it is a single line and irreversible. So as we rush to the destination, should we go slower and slower, listen carefully to the sound of flowers blooming, feel the splendor of life, and appreciate the beautiful scenery along the way? Just like when we study mathematics, shouldn't we also slowly understand the thinking in the process of reaching the conclusion? Isn’t this process of exploration a beautiful scenery? Why rush to a conclusion? We must learn to slow down and wait patiently, waiting for knowledge to grow naturally and bloom fragrant flowers.

I walked through the south of the Yangtze River, and the faces waiting for the seasons are like the blooming and falling of lotus flowers. The small windows in your heart are tightly closed, my dada. The horseshoe is a beautiful mistake. I am not a returnee, but a passerby. "Mistake" by Taiwanese poet Zheng Chouyu. You see, what a beautiful poem this is. All mistakes are beautiful. The protagonist is lonely in the closed window waiting for the return of his beloved, and then he hears the sound of Dada's horse hooves and thinks it is the return of his lover. But the result was obviously disappointing. This was just a stranger passing by, so it was a beautiful mistake. What a heart-warming poem! Waiting is beautiful, even if you get disappointment in the end, the process is thrilling and full of expectations.

For children, doesn’t the beauty of mathematics lie in their mistakes in the process of seeking knowledge? They will inevitably make mistakes in the process of exploring new knowledge, guessing and thinking, and this is the mark of their growth! As long as we squat down a little, we will realize how cute and innocent these mistakes are! These mistakes are the precious wealth they gain and enjoy throughout their lives. The process of thinking after mistakes and discovering the truth of mathematics is the most beautiful and shocking. We should calm down, just like waiting for the return of our sweetheart. The little interlude in the middle, that dada's horseshoe is not the result I want, but it is still so wonderful, making people full of expectations, joy and then loss, the cycle goes back and forth, full of yearning. .

Mistakes can sometimes be cruelly beautiful. In the 5th century BC, the Pythagoreans believed that numbers were the most noble and mysterious, and the numbers they talked about were integers. "Number is everything", which means that various relationships in the universe can be expressed by integers or the ratio of integers. However, Hippasus discovered that the diagonal (root 2) of a square with side length 1 cannot be expressed by the ratio of integers. This violated the creed of this school, so a rule was established: no one is allowed to reveal the secret of the existence of the root number 2 (that is, irrational number). Hippasus discovered that the ratio of the right side to the hypotenuse of an isosceles right triangle is not a rational number. This is a counterexample to the Pythagorean school at that time that "all quantities can be expressed by rational numbers". The naive Hippasus inadvertently told others about his discovery and was killed (according to legend, the Pythagoreans were at sea at the time, but they threw Hippasus into the sea because of this discovery). But the root number 2 soon caused a revolution in mathematical thinking. This incident is called the "first mathematical crisis" in the history of science, and it also made mathematics a great step forward. History has proven that everyone makes mistakes, even great mathematicians. However, the consequences of this mistake seem to be cruel.

Mathematics is beautiful, beautiful in its depth, beautiful in its appearance, beautiful in its connotation, beautiful in its perfection, and beautiful in its imperfections.

And this is just like love. The reason why love is eternal and so beautiful lies in the difficulty of pursuing it, the joy of getting it, and the melancholy of not getting it.

Liu Hui was the first mathematician in the history of mathematics to establish a reliable theory and use the secant method to calculate the circumference of pi. This is the famous Hui rate. Like Archimedes, Liu Hui devoted himself to area. Study with volume formula. In his research on the volume of the ball, he first pointed out that the volume formula of the ball in "Nine Chapters of Arithmetic" was incorrect, so he re-study the volume of the ball. In his research, he has used the " Cavalieri's Principle", but unfortunately he did not summarize it into a general form. How to find the volume of the combined square lid, he ultimately failed to solve it. I think he is sad. I have spent my whole life asking for everything but to no avail. This is like love, which is so dazzling when you can't get it, and makes you want to cry when your heart breaks.

? Red crisp hands, yellow vine wine, the city is full of spring scenery and willows on the palace walls. The east wind brings little joy and a cup of sadness. After a few years of separation, I made a mistake! "The Hairpin-headed Phoenix" by Lu You. In that year, Lu You used a hairpin-headed phoenix as a betrothal gift to marry Tang Wan home. It was a hairpin, and the head of the hairpin was a small phoenix, which held the love of a lifetime. They hugged each other day and night, talked about poetry and poetry every day, and rubbed their hair against each other. They didn’t know what time it was. Who would be willing to neglect such a caring wife just to pursue fame and fortune? Unexpectedly, her mother was annoyed. Firstly, Tang Wan was unable to have children, and secondly, Lu You was obsessed with the love between her children, which seemed to delay his fame. So he went to a divination and found that the horoscopes did not match, so he immediately forced his son to write a letter of divorce. Tang Wan later died of grief and depression. Lu You was not a weak and cowardly man. "Thirty thousand miles east of the river flows into the sea, and five thousand miles of mountains reach the sky." Listening to the sound of wind and rain, the iron horse and the ice river come to sleep," but in front of his mother and the woman he loved most, he acted like a coward. He lost her in the end, but his longing for her and the sadness of not being able to get her were still poignant throughout his life. This is also very similar to Liu Hui's pursuit of the size of the ball, isn't it?

What Liu Hui did not get was captured by Zu Chongzhi and his son Zu Xun. The father and son fell in love with mathematics throughout their lives. They finally went further based on Liu Hui's research results and finally derived the volume of the ball. What a joy this is! Just like lovers who have been pursuing each other for many years finally hold hands and achieve success, it should be the same feeling as Du Fu's "overjoyed with endless poems and books". ball! The most beautiful guy in three-dimensional figures finally has his own perfect volume formula. Zu Xun finally arrived at the conclusion by using the two principles of complementarity of entry and exit and the principle that power potentials are the same but accumulations are not different. It is so happy that the pursuit after all the hard work has finally come to fruition. Zurich's principle is called Cavalieri's principle in Western literature, and it had an important influence on the later establishment of calculus. The beauty of mathematics, in addition to the final result, the key lies in the mental process produced in the process of pursuing the result, that kind of hazy beauty that is looming, one step away but cannot be touched. When Zu Chongzhi and his son came to the final conclusion, I think they must have been extremely calm in their ecstasy! Because after so much searching, the results are no longer so important.

Li Bai wrote in "Changgan Xing": When my concubine's hair first touches her forehead, there is a drama in front of the door. Lang came riding a bamboo horse and went around the bed to make green plums. Living together in Changqianli, the two children have no doubts about it. At the age of fourteen, she is a gentleman's wife, and she has not yet shown her shame. He lowered his head towards the dark wall and called out a thousand times. It's not far to meet each other, until the wind blows in the sand. Childhood sweethearts are the beautiful love that many people dream of! But even if the childhood sweetheart suddenly changes identities one day, it still takes time to adapt. It takes time for a person to accept another person. To love someone, you must protect someone. You must learn to wait, and wait for the day when she will open her arms to accept you. I. The same should be said for mathematics. We cannot be eager for quick success, but must learn to meditate, be good at waiting, and wait patiently. One day we will see the brilliance of blooming, just like this beautiful love.

After the world’s mathematicians waited for 200 years, Chinese mathematician Chen Jingrun conquered (1+2) in the world-famous mathematical problem "Goldbach's conjecture" and created the number theory crown of distance. The pearl on the top (1+1) is just one step away from brilliance. He proved that "every big even number is the sum of a prime number and the product of no more than two prime numbers", making him a world leader in the study of Goldbach's conjecture. This result is internationally known as "Chen's theorem" and has been widely cited. His achievements in studying Goldbach's conjecture and other number theory problems are still far ahead in the world. Chen Jingrun planted the seeds of conquest in his heart from the first time he heard about this conjecture. With his love for this queen of mathematics, he pursued it hard and guarded it all the time, and finally won the favor of the beauty. What a wonderful ending.

"If life is just like the first time we met, why is the autumn wind sad to draw a fan?" It is about Ban Jieyu, the imperial concubine of the Han Dynasty, a famous elegant and virtuous woman in history. When she first entered the palace, she was deeply favored by the emperor. Later, because Feiyan entered the palace, she lost love and became lonely, so she wrote "Song of the Fan". "Banggu" writes: The relationship between life and death is broad, and it is said by Zicheng. Hold your hand and grow old together. I am so rich, but I can't live without you. Yu Xunxi, I don’t believe you. Now please forgive me for not being able to keep my promise. This is a hopeless love story, a vow between husband and wife. However, everything can only become a luxury hope. There have been too many tragedies in this world, so small that even There are no names. The same is true in mathematics. Not every mathematical conjecture can have a happy ending.

For example, the Riemann Hypothesis is a conjecture about the zero-point distribution of the Riemann zeta function ζ(s), which was proposed by the mathematician Riemann in 1859. Hilbert proposed 23 mathematical problems that mathematicians should work hard to solve in the 20th century at the Second International Congress of Mathematicians, which are considered to be the commanding heights of 20th century mathematics, including the Riemann hypothesis. The Riemann Hypothesis is also included in the world's seven major mathematical problems currently offered by the Clay Mathematics Institute. The Riemann Hypothesis is the most important mathematical problem in mathematics today. There is an elusive goddess in everyone's heart, and many people are obsessed with it and are crazy about it. This is the Riemann Hypothesis.

Sima Xiangru conquered Zhuo Wenjun with a song "Phoenix Seeking the Phoenix". Sima Xiangru came from a poor family, and Wenjun left behind his daughter to work as a wine seller. For love, he did not hesitate to marry his father, who was the prime minister. The breakup became a good story. Later, Sima Xiangru was appreciated and reused by the emperor, became an official, and prospered. When Zhuo Wenjun wanted to marry a concubine, he wrote: I heard that you had two opinions, so I came to make a decision. I wish to win the heart of one person and stay together forever. She was not a woman who could only hold back and cry. She used the rare beauty of a woman's determination to call back Sima Xiangru, and from then on they grew old together and never left each other again. What a touching love story, so beautiful that it makes you want to cry. How many mathematicians and mathematics have been together forever! Thales, Pythagoras, Napier, Gauss, Veda, Al-Khwarizmi, Descartes, Archimedes, Newton, Leibniz, Zu Chongzhi, Yang Hui, Liu Hui, Xu Guangqi... countless people Stick to your love and focus on your research throughout your life. That's why there are so many achievements in mathematics, the perfect symmetry in architecture, the beautiful proofs in the Elements of Geometry, and the gorgeous spatial graphics, all of which are poignant and beautiful.

Yu Xuanji's "It's easy to find priceless treasures, but it's rare to find a lover." Pair. Li Jilan's "The sea of ​​​​humanity is deep, not even half as long as lovesickness. The sea still has an end, but lovesickness is endless." Each of them is a flower that bloomed grandly in the Tang Dynasty, growing wildly in that free environment. But their love is unsatisfactory, and it is this sadness that makes their temperament admired by more men and makes their poetry more free. Zhu Shuzhen said, "On the top of a willow tree in the moonlight, we make an appointment after dusk." "The charming and foolish person is not afraid of others' guessing, and sleeps in the arms of others with her clothes on. When they are most separated, she comes back and lazes by the window sill." Describes the innocence and innocence of a girl in love. It's so romantic that one can't help but feel pity for it. Falling in love with her should be the happiest thing in the world! Good things always go well with gentlemen. This is true for human love, and so is mathematics. Newton's binomial theorem, Yang Hui's polynomial multiplication, Gauss's summation of arithmetic sequences, using similar triangles to find the height of a pyramid, and Ella. Tosthenes sought the length of the equator... On the road to mathematical knowledge, people continue to surpass and enjoy the charming scenery they enjoy while climbing to the peak of mathematics!

In memory of his late wife Wang Fu, Su Shi wrote "Jiangchengzi Jihai Remembers a Dream", which made readers sad and those who heard it shed tears. "Ten years of life and death are boundless. I don't think about it. I can't forget it. I am alone in a tomb thousands of miles away, and there is no place to talk about desolation. Even if I meet each other, I don't know each other, my face is covered with dust, and my temples are like frost. At night, I have a dream and suddenly return to my hometown. Small window. I am dressing up. Looking at each other. Speechless, only a thousand lines of tears. It is expected that the heart will be broken every year, and the moonlit night will be short. "A few years later, she married Wang Runzhi, Wang's cousin, and she treated their children as if they were her own. Wang Runzhi must have known that Su Shi wrote "Jiangchengzi", but she was neither jealous nor complaining. One person guards for another person because she has a place in her heart that no one can replace. Reading "Jiang Chengzi" will break Su Shi's heart. In the fourth year of Xining reign of Emperor Shenzong of the Song Dynasty, Su Dongpo was demoted to Hangzhou Tongpan for opposing Wang Anshi's new law. One day, he and several literary friends traveled to the West Lake. The simple dress is elegant, elegant, and charming, with a unique charm, like the fragrance of orchids in the empty valley, which penetrates into Su Dongpo's heart, which has been dimmed by the changes in the world. Su Dongpo was suddenly inspired and wrote down a line describing the West Lake that has been passed down through the ages: The water is shining brightly and the sky is clear, and the mountains are empty and rainy, which is also strange. If you want to compare the West Lake to the West, it is always better to put on light makeup and heavy makeup. Chaoyun was twelve years old at the time. Although he was young, he was smart and alert. Because he greatly admired Mr. Dongpo's talent and was well treated by Su Shi and his wife, he was very grateful for his fate with the Su family and decided to follow Mr. Dongpo throughout his life. The relationship between Chaoyun and Su Shi is very strange. She lived with Su Shi for more than 20 years, and especially accompanied Su Shi through the two difficult years when he was demoted to Huangzhou and Huizhou. However, she never had the name of Su Shi's wife or wife. She was only named after she arrived in Huangzhou. The maid was changed to a concubine, and the two of them were in trouble and love. After Chaoyun's death, Su Shi buried her in the West Lake in Huizhou, and built a "Liu Ru Pavilion" beside her tomb to accompany her beauty forever. As a man, you should be like Su Dongpo. I like his sincerity and respect for his family. Such a man deserves respect. Such a beautiful love will still make people cry after reading it thousands of years later.

These poignant loves are very much like people’s love for mathematics. Learning mathematics is like pursuing your loved one. No matter what the result is, you should remain firm and persistent. This unique love is really touching. The beauty of mathematics is also the beauty of love. How many mathematicians have fallen into the gentle embrace of mathematics, intoxicated by the charm of mathematics, unable to extricate themselves, fascinated by it, and even dedicated their lives to it. The charm of mathematics is so moving and breathtaking.

Perfect numbers, triangle numbers, quadrilateral numbers, polygon numbers, symmetry of graphics, symmetry of operations, proof of Fermat’s last theorem, pi hidden in the pyramid, circles and spheres, Thales’ semicircle , the square root number 2 that destroyed Pythagoras’ belief, the Hippocratic crescent, Zeno’s paradox, the three major geometric problems of ancient Greece, Heron’s formula, the method of exhaustion, Descartes’ analytic geometry, the golden section, vectors, Entropy and mathematics...these pearls that once shone brightly in mathematics are so dazzling, charming, and fascinating. People's pursuit of mathematics has not been smooth sailing. There have been failures and mistakes, and it has gone through thousands of years. Some of them still have no results, but these will not stop people's pursuit of beauty, just like those hopeless loves, unavailable but fascinating, sad but extremely beautiful.

Archimedes actually used the lever principle to derive the formula for the volume of the ball and to find the formula for the surface area of ​​the ball. This is so unique and alternative, full of surprises. Buffon used statistical principles to calculate pi through the Buffon needle test, which is also full of imagination, romantic and beautiful. Liu Hui used his original method of dividing the ball into square covers to calculate the volume of the ball. He spent his whole life unable to do so, but it was a pity that it was full of flawed beauty. If I had known the calculus theory of Newton and Leibniz earlier, I believe that obtaining the spherical volume formula would have been simpler and smoother! The beauty of mathematics is unparalleled, even more so than love, and its beauty is always wonderful. Poincare conjecture, Birch conjecture, Riemann conjecture, Hodge conjecture, quantum Yang-Mills theory... These beautiful conjectures are not like those sad loves, full of temptation and unstoppable, close in front of you but unable to pick them up. So painful, happy and beautiful at the same time. Incompleteness is also a kind of heartbreaking beauty. Mathematics and love are the same, beautiful and full of expectations.

We live in a three-dimensional world, and the length of our lives is limited and non-recyclable, which is far inferior to the infinity of mathematics. In the limited knowledge we know, we should slowly slow down and move toward the end quietly and gently. Why be so anxious? From the day we were born, the outcome has been determined, and everyone is pointing to the same destination. How about we go for a walk holding a snail from now on! Waiting for the beauty of flowers to bloom, waiting for the excitement of mistakes.

There is no need to rush to the finish line in such a hurry, no need to fight so hard, and no need to worry about gains and losses. You cannot turn back on this train. If you miss it, you will miss it forever. If you regret it, let it be regretful! Unless you can prove the existence of the fourth dimension and find a way back from it, you only live and die once. Even if you use infinite mathematics to calculate, you cannot calculate your unknown afterlife.