When it comes to "Zeno's tortoise", not many people may know it, but when it comes to "Schrödinger's cat", I believe most people have heard of it.

In fact, the level of "Zeno's tortoise" is the same as that of "Schrödinger's cat". Together with "Laplace's beast" and "Maxwell's demon", they are called "the four mythical beasts of physics".

It is well-known in the physics community.

"Zeno's Tortoise" is also known as "Zeno's Paradox". It originally told the story of a race between God and a tortoise. We might as well change it back to the familiar tortoise and hare race.

The tortoise said to the hare: "Although you run very fast, as long as I run first, you will never be able to catch up with me."

The rabbit didn't believe it, and the tortoise gave an example: "For example, I ran 100 meters first, and you chased me again. Assume that your speed always maintains 10 meters per second, and my speed always maintains 1 meter per second. Then when you spend

After running 100 meters in 10 seconds, I walked forward 10 meters, and I was still in front of you. After 1 second, you ran another 10 meters, and I walked 1 meter, and I was still in front of you. And so on, no matter you

No matter how close you are to me, I will always be in front of you."

When the hare thought about it carefully, he realized that he could never catch up with the tortoise.

So the tortoise and the hare won the race with the tortoise's rhetoric, while the hare gave up without a fight.

Is this really the case? Everyone knows that when it comes to running, the hare can overtake the tortoise in no time, but why does such a paradox occur?

This problem is finally described in mathematical language, that is, a finite length is divided into infinite parts, but the infinite parts do not add up to infinity.

Zhuangzi also mentioned a similar divine hammer in "Zhuangzi·Tianxia Chapter" - "One-foot-long hammer, half of it is taken every day, and it will be inexhaustible for eternity." This is exactly the same paradox.

Doctoral student Hua Hong couldn't help but ask: "Junior Qin Ke, I have heard of this 'Zeno's tortoise', but does it have anything to do with our problem?"

“How is the paradox of ‘Zeno’s tortoise’ solved mathematically?”

"The concept of 'limit' through calculus."

Qin Ke smiled and said: "Yes, you used the 'maximum' and 'minimum' methods here, which is theoretically correct, just like the assumptions made by the tortoise, but the problem is the result of the final demonstration.

It is very different from reality and even contradicts it. Is this essentially the same as 'Zeno's tortoise'?"

Chen Licheng, Hua Hong and others' eyes lit up at the same time. If they thought about it carefully, it was indeed true!

"The maximin method is indeed a very excellent mathematical method, but it is not suitable to be used in this situation. In the case of both intraspecific and interspecific attraction, the solution of the Schrödinger equation in the nonlinear partial differential equations represents the wave function. The solution

The square of represents the probability density of particles appearing at a certain spatial location at a certain point in time. Using the maximin method can easily lead to distortion of the probability density due to limiting."

"So that's the case, it's true!" Chen Licheng's eyes lit up, and then he said angrily: "Why didn't we discover this problem?"

"You are a fan of the authorities. You only want to use such a sharp tool to solve this problem as quickly as possible. Instead, you unknowingly fell into a paradox similar to 'Zeno's tortoise'."

Qin Ke found a way out for everyone in a gentle tone. In fact, if a genius mathematician like Chen Licheng is not anxious to make the most dazzling results in the shortest time, he just needs to study in a down-to-earth manner using different methods.

This problem can definitely be solved within two months.

But due to mentality problems, haste has the effect of making waste...

Hua Hong subconsciously asked: "What mathematical method is most suitable to use?"

As soon as the words came out, several people cast strange looks at him.

It's amazing that Qin Ke can see the problem so quickly, but you still expect him to give the correct answer? Doesn't this make it impossible for him to step down?

Chen Licheng coughed slightly and was about to change the topic when he heard Qin Ke say thoughtfully: "If you want me to give you some advice, you can try it from two directions."

"The first one is to use the 'divergence' method to determine the parameter range of the existence of the normal solution through fine constraints, and then verify the existence of the normal solution."

"Another way to try the 'variational method' is to determine the existence of the normal solution by introducing the 'equivalent functional', the 'mountain road lemma', and the 'surround method'." Qin Ke took a pen and roughly wrote on the whiteboard.

He wrote two directions and then said:

"Of course, there is a third optimal method in theory, which is to start from the 'isomorphism theorem of solutions' and try to combine it with the 'divergence' method. This kind of calculation may be the least. In three pages

This will solve the problem of the existence of the formal solution that you want to prove."

quiet!

The entire research room fell into a state of absolute silence!

The three methods proposed by Qin Ke were like bombshells, which shocked all six people including Chen Licheng.

Qin Ke actually pointed out the direction to solve this problem!

Even if it's just the direction, it's incredible enough, because Qin Ke only read the relevant information for three minutes!

This is simply unbelievable, but Qin Ke pointed out the problem easily just now, which indeed made several people unable to despise his suggestion!

Chen Licheng murmured: "Is the 'divergence' method a widely praised new mathematical method published in the previous year? I didn't even think of trying this method..." He held Qin Ke's hand excitedly

: "Thank you, Junior Brother Qin! You can be said to have woken me up from my dream with just one word. If it weren't for you, our project would have been stagnant for another two months before we could discover the problem!"

Chen Licheng said two months. In fact, he knew in his heart that as long as it lasted for another half month, the team would basically fall apart. It was not difficult to judge such an outcome from the fierce quarrel among the team members before coming in.

After all, studying a subject for which there is no hope for a long time is a test of one's will and mentality.

This chapter is not finished yet, please click on the next page to continue reading the exciting content! So this time Chen Licheng was really grateful to Qin Ke from the bottom of his heart, and at the same time he was also reflecting on the fact that he was really too impatient.

After all, I am still young and energetic... I still have a lot to learn on the road of cultivating my mind.

Qin Ke hurriedly said: "Senior Chen, you are too polite. I am just a bystander. If I were in your position, I might not be able to get around this paradox for half a year."

Qin Ke's lack of taking credit and humility endeared him to several doctoral students in Chen Licheng's team. Even the two doctoral students who had previously been silent and somewhat ostracized Qin Ke took the initiative to shake hands with Qin Ke and thank him.

Chen Licheng repeatedly tried to invite Qin Ke to join his scientific research team, but Qin Ke politely declined.

He knew that this project was very important to Chen Licheng, and when he estimated the results would be the time when his paper proving the twin prime conjecture was published.

At that time, I was afraid that my reputation would be far greater than that of Chen Licheng. If I were in this scientific research team, how would people outside criticize me? Will I take the spotlight? As soon as he considered this, Qin Ke knew that even if he was not interested in this

Even if you are interested in the topic, you cannot join it.

Chen Licheng and others expressed deep regret. Chen Licheng could only say that he would thank Qin Ke for his help in the acknowledgments at the end of the paper, and made an appointment to have a good meal at a hotel outside to thank Qin Ke.

Qin Ke shook his head and said: "Senior Chen, I see that you are all gearing up to try to solve the current difficulty in a new direction, so I won't take up your time. And there is a special training for the school basketball team in the evening, and I have to attend.

Okay, I won’t disturb you anymore, I’ll go back to class in about time.”

Several people personally escorted Qin Ke out of the scientific research center before reluctantly waving goodbye.

Looking at Qin Ke's walking back, Chen Licheng said with emotion: "The mathematics world in the next few decades will probably belong to this junior Qin."

Hua Hong and other graduate students nodded with deep understanding.

…

Hua Hong sent a WeChat message to his sister at night:

"Sister, I met your male god Qin Ke today."

"Wow, is it true? Are you handsome or not? Am I awesome?"

"He is really handsome, and God is really God. Didn't I say before that our research has encountered a big problem. The entire project has been stalled for a month because of this problem. We are all desperate. What do you think the result will be?"

"How?"

"Your male idol came over as a guest. He looked at it for three minutes and then discovered the problem. He also pointed us in three directions with the highest probability of success. Since the afternoon, we have been experimenting separately. From the results obtained so far

Inferring that these three directions may be correct. No wonder you call him a "god" all day long. Junior Qin Ke is a real god. I am completely convinced. Our team leader originally wanted to give him a bonus, but he thought it was just a small effort.

, simply refused to accept it.”

"Wow! My boyfriend is so handsome and awesome! Brother, you have to work hard to become friends with him and introduce him to me!"

"You? Just forget it. You are three years older than him and you are not pretty. Junior Qin Ke has a girlfriend called Ning Qingyun."

"Ugh... the smelly old man is ignoring you!"

Hua Hong's sister burst into tears.

But soon, she cut off the first part of the conversation (cut out the part that said she was not beautiful), and then posted it to Qin Ke’s fan group "Ke Ke’s God who will always protect us", causing a blockbuster

's scream.

Soon, the screenshot of this conversation was forwarded everywhere, and someone even forwarded it to a bib and @several well-known media, causing a sensation on the Internet.

[I saw news about my boyfriend again, he is indeed my boyfriend!]

[Mathematics is very dependent on talent. I guess Qin Shen’s talent in mathematics is the ceiling among young people, right? 】

[Qin Shen is honest, helpful, and does not ask for anything in return. Ah, I like him more and more! 】

[If you don’t know it, you won’t know it for a lifetime. If you know it, you will know it at a glance. That’s right, I’m talking about mathematics.]

[Some people ask if it is true or false? How can this be false? Looking at this style and strength, it is definitely true. 】

[Only geniuses can reach the top. I look forward to the day when Qin Shen will reach the top of mathematics. 】

[With basic skills, Qin Ke can defeat mathematicians all over the world with his own strength. What does a mere scientific research problem mean?]

[Speaking of which, this is the second hot search related to Qin Shen today. Qin Shen is too popular, but I suggest not to overspend on him and let him study in peace.]

[That is, I hope reporters will not disturb Qin Shen.]

…

Qin Ke didn't notice that there was another hot search for him on his scarf. He returned to the new study room and continued to guide Ning Qingyun's "To Ning Qingyun II".

This new study room is nearly 100 square meters. When you open the window, you can see the Spring Garden. You can see the moonlight of the lotus pond. It is a VIP location.

Ning Qingyun didn't pay much attention when Qin Ke talked about Chen Licheng's project. She was used to Qin Ke's mathematical level. After all, they were all attacking the Polignac conjecture. Senior Chen's project was no longer surprising.
To be continued...