drowning

At the beginning of winter, all the students of No. [-] Middle School shrank their necks and put on all kinds of padded jackets in their school uniforms. Xu Yanxin was no exception. He was naturally afraid of the cold and was wrapped into a ball with three layers inside and outside There is no trace of the thinness of the past.And Jiangyu doesn’t want temperature but style, so he wears light clothes. The sweater still has a V-neck, revealing a small piece of chest, as if he never gets cold.

They have been in a cold war for 77 days. It started inexplicably, but it didn't look like it was over. At first Xu Yanxin was thinking about how to bow his head, but these days were also crushed by thick books. Turning his head, he was waiting, like waiting for a long prelude to a piano piece, always waiting.

There are very few people in the corridor, and most of the students are crowded in the class to keep warm with the carbon dioxide exhaled by each other.

Xu Yanxin pressed the thermos between her elbows and waist, like a penguin with limited mobility.However, before he took a few steps, he saw the broad shoulders, and the thin sweater on his body covered the smooth and fine skin.The boy only held the rim of the water glass with two fingers, hanging down his legs. His fingers were lazy and warm, and they didn't show the stiffness of being dried in the winter, but the stretched veins on the back of his hands were exceptionally strong.

Xu Yanxin was reciting words while staring at the back collar of his pleated sweater.Maybe he stared at it for too long, Jiang Yu hooked his back collar with his other broad hand as if he had sensed it, and turned the collar inside out.

When receiving the water, the thermos cup wanted to fight against him, so it slumped in his arms. He was thin-skinned, and refused to keep the students behind him waiting, so he walked out of the line, blushing, and turned his back to the crowd while warming. He screwed the lid next to the water tank until his hands were red.The weight in his arms suddenly lightened, and the person who had just left turned back, put his water glass on the water tank, held his orange water glass, stretched his wrist slightly, and opened it.

Xu Yanxin was a little at a loss, and was about to strike up a conversation or just say thank you, but Jiang Yu didn't give him a chance to struggle, and walked away on his own, leaving him only the back of his head.It took 2 minutes, and he happened to recite the queer.

When Lin He was giving him extra lessons, he couldn't help thinking of Jiang Yu's fingers, which were too aesthetically pleasing.

"According to the examination papers of the Zhixin Cup in the past few years, it is very likely that the n-variable inequality will be tested. You can look at this question, the original question from the Soviet summer camp in 1961." Lin He's emotionless mechanical voice pulled him back to the examination paper, he After being stunned for two seconds, he concentrated his mind and looked at the question.Mathematics is like a mess of wool. If you want to solve a problem, you can't be disturbed by other things. Only by pulling out the source thread can all problems be solved.

"Any idea?"

Xu Yanxin tapped the lower volume with a pencil, and said uncertainly: "Usually when encountering this kind of problem, Cauchy's inversion is the basic spirit. Generally speaking, the multiplier relationship between molecules and basic inequalities after scaling, and what is introduced is reduced. The degree of the term is the difference between the degree of the denominator and the degree of the numerator of the original formula, but this question is a bit strange, and Cauchy’s inversion is probably not possible.”

Lin He raised his glasses and said with approval: "Polya once said that there is no perfect solution to math problems, and there will always be something worth exploring."

"If Cauchy's negation fails, use the properties of linear functions to adjust the variable to the boundary." He said.

After getting Lin He's affirmation, Xu Yanxin calculated according to his own thinking.

Functions often have rotation symmetry, and then use the internal logic between numbers to form a ring. This kind of routine is very common in algebra problems.It took Xu Yanxin a total of 11 minutes and 49 seconds from having an idea to solving the problem.Lin He looked at the numbers on the chronograph and said, "Within 15 minutes, just as Mr. Xu said, you do have a talent for learning mathematics. But—"

Lin He's eyes were fixed on him, and through the mirror frame, he always showed a kind of indifference. From childhood to adulthood, all the teachers could not help but show a little appreciation when they met him, but Lin He was always examining him, looking at him, even He was quick to answer questions without even a shred of praise from him.At first he thought it was Lin He's strictness, but now that he thought about it, he was afraid that he had slandered him.

Lin He leaned against the back of the chair, crossed his hands, and said to him: "Eight weeks ago, since you answered the phone call, you have been absent in the tutoring process since then, and you can't even do the most basic calculations well. , Just now, I have been looking at that record player from the corner of my eye."

"Sorry, I……"

"You don't need to apologize to me. For me, it's very easy to make up for you. Whether it's problem-solving skills or math talent, you are the best among your peers. Zhixin Cup is not a problem for you at all. It's just a decoration on your resume. But there's more to math than talent and skill."

Xu Yanxin was stunned, waiting for his next words.But Lin He said: "You have to think for yourself. I was just entrusted by Professor Xu to tutor you in the mathematics competition. My goal is to let you win the first place in the Zhixin Cup. As for your attitude towards mathematics, whether you want to engage in scientific research, It's your own business. But I think, if Mr. Xu finds out that you just use mathematics as a shortcut to higher education, he will suffer even more than now."

After Lin He left, Xu Yanxin was still sitting at the table stupidly, with thousands of examination papers in front of him.

His fate with mathematics can be traced back to a very young age, when he was still a little bean, four or five years old.At that time, Xu Ruqing had no respect for him.He didn't know how respected the old man who always had a naughty temper was, and he didn't know how many awards he had won for his research. He only knew that he was a grandfather, a grandfather who liked to test him.

Every new year, he looks forward to the old man's exam questions more than receiving red envelopes.That year, he just entered kindergarten, learning to sing nursery rhymes, and learning addition and subtraction within 10.And Xu Ruqing smiled wickedly, with wrinkles on his face, and was much older than his peers. When sending out red envelopes, he handed him two red envelopes and said, "Here are two red envelopes. It is known that one of the red envelopes is the other red envelope." Twice as much, Xinxin will pick one first."

The grandma next to her giggled: "Where does Xinxin know what double is called, let the baby come over to eat Jiuniang Yuanzi soon."

"I know! 2 is twice as much as 1." He said defiantly.

The whole family couldn't help laughing when they heard this, only Xu Ruqing seriously praised him for being smart and asked him to open the red envelope.

He opened one of the red envelopes angrily, and inside were five pieces of Grandpa Mao. He pouted and complained to Xu Zhao that there were fewer than last year. Hearing this, Xu Ruqing also smiled and nodded his head, and then leisurely Said: "Now Xinxin has a chance to give up this opened red envelope and take another unopened red envelope, do you want to change it?"

Grandma said angrily, "You know how to bully children when you're retired."

At that time, Xu Yanxin snapped her fingers, and the other red envelope could be 250 or 1000. If she got 250, she would lose 250. If she got 1000, she could earn 500. Of course, she had to change it.

Xu Ruqing handed him another red envelope, which contained two red-haired grandpas and one green-haired grandpa. The 250 red envelope has a chance to be exchanged, will it still be exchanged? Then this question has nothing to do with how much money is in the red envelope, Xinxin will exchange the red envelope anyway? Because for Xinxin, the expected value is 0.5*( 1000+250)=625."

He was so confused that he couldn't even break it with his fingers.Grandma saw his stupid brain smoking, so she smiled and smoothed things over, and said to go eat Yuanzi quickly. Everyone didn't take this issue seriously, as if it was just a joke Xu Ruqing used to tease him, but Xu Yanxin was eager He really wanted to know the answer, but Xu Ruqing refused to tell him no matter what.

Nine years later, in the early morning of the day before the senior high school entrance examination, after reading countless mathematics books, he finally solved it. He couldn't help but call the old man in the middle of the night. The old man first scolded him for disturbing the old man's rest, and then asked him: " Figured it out?"

"This is a typical box paradox problem. The paradox is that this problem does not have a finite expected value at all. The expected value of this game is not convergent, it is infinite, and the amount in the red envelope is an unknown distribution, and there is no probability at all. It can be said."

Xu Ruqing laughed, but didn't ask him what he was talking about. This simple and interesting math problem seemed to be a secret they shared, a secret waiting to be analyzed.

However, Xu Ruqing obviously didn't plan to praise him after listening to him, and didn't understand his tomorrow's senior high school entrance examination. Instead, he said leisurely: "Then I will test you again. There are three gods named 'truth' and 'hypocrisy' And 'arbitrary', you don't know who they are, truth always tells the truth, hypocrisy always tells lies, arbitrary is true and false randomly, you need to know who these three are, you can only ask three times the answer is 'yes' ' or 'no' questions, each question can only be addressed to one god, the gods can understand you, and they will only answer you in their own language, 'da' or 'jia', and you don't know which is' is' ​​which is 'false'."

"Grandpa! Where did you come up with so many weird questions?"

"The story will be read on the small frame. It's pretty good. I think it's extremely simple, but we Xinxin is a little fool. I have to test whether your brain can turn around or not, so you can't let it rust." Xu Ruqing He smiled and said that he didn't have the air of a mathematician at all.

Xu Yanxin was deflated, dangling like a balloon, and landed on the ground. He had hoped that Xu Ruqing would praise him a few words, but unexpectedly, another brain teaser came. He circled the telephone wire and complained Said: "The high school entrance examination is going to be in three hours, and you still tell me this."

Xu Ruqing laughed loudly and said, "If your math is below 150, don't come to see me, it's embarrassing!"

"Grandpa! Why are you like this! Other grandpas must make children feel less pressured."

Xu Ruqing said bitterly: "Two days ago, the old man Wang Qingshi told me that his granddaughter's math test was full every time, which proved that his genes were still very strong after three generations of dilution. How can I lose? We used to be at P University When I was studying, he always asked me questions. Xinxin, you have to prove it for grandpa!"

Xu Yanxin couldn't take it anymore and said, "If you do this again, I'll hang up the phone."

"Hey, don't, grandpa believes in Xinxin. What's the difference between the difficulty of the senior high school entrance examination and 1+1=2?"

"Isn't Goldbach's conjecture studied by many people?"

"It's all a joke about folk science and mathematics, and those who really do research don't touch that."

Xu Yanxin let out a long "Oh", and after a while, Xu Ruqing asked: "Your mother forces you to study mathematics every day, do you hate mathematics?"

"It's okay, it's just like that, I can't say whether I like it or not, it's just that there are too many make-up lessons, and I'm a little tired."

Xu Ruqing smiled, and suddenly said: "Mathematics is a very beautiful and mysterious thing, just like the ones drawn in your favorite cartoons, it is hidden deep in the palace, without any gold or silver boxes, many warriors After slaying the dragon, people forget about science when they see beauty and wealth, and it has been left in a corner, waiting for someone to discover it."

"The conjecture written down by Fermat stumped top mathematicians including Euler and Kulmer, and it was only solved after more than 300 years. Many people would say that what is the use of solving it? If there is no solution Open, isn’t it true that you can achieve nothing in your life? There are indeed more interesting and glamorous things in this world that people pursue—”

"But science has no national boundaries and is not limited by history. Countless people work hard for the same goal regardless of race, gender, and nationality. He is a beacon made of blood and sweat, only to illuminate future generations. Apart from anything else, grandpa wants to tell Xinxin more, but is Xinxin willing to listen? Do you think grandpa is an old antique who can't joke?"

"grandfather……"

"Grandpa occasionally hopes that my Xinxin will spend so many years solving the puzzle, will he notice the treasure in the corner like grandpa?"

Xu Yanxin always remembers that night, the cicadas sang continuously, the shade of the trees was dark, and Xu Ruqing's voice revealed the aging of the years.

At that time, he thought blankly, Grandpa was getting old.

But now, when he thinks about his original intention, he can't help but ask himself—is he still the Xu Yanxin who has been dormant for many years and quietly solved the problem?What exactly is he missing?If it was Jiang Yu, would he say that he was a fool who was bored and asked for trouble?

The author says:

You can think about the questions in it, it's very interesting!Then I hope everyone can watch Wenha happily and don't quarrel!Thank you for your support~