All-round mathematician

Chapter 104 The Solitude of Mathematics

Feng Yao looked across the corridor of time. In that year, his first teacher of Mathematical Olympiad, under the same circumstances, said some indelible words.

"When we were in elementary school, we learned about prime numbers. What do you think of its properties?"

Ye Haoran didn't talk much at first, and he was even more unwilling to talk after being hit. Yang Fan replied: "2, 3, 5, 7, 11...prime numbers are also called prime numbers, which can only be divisible by one and itself. In fact, it is useless. It has nothing to do with applied mathematics, it seems to be a simple concept.”

Hearing the students' contempt for numbers and involving the sacred professional field, Feng Yao said in a cold tone, "Any discovery of mathematical laws is a flash of light among mathematicians who have failed thousands of times."

"Euler used the Riemann function to prove that the sum of the reciprocals of all prime numbers is divergent, and Harry Furstenberg used topology to prove the infinity of prime numbers. Are those mathematicians full of food?"

"Master Chen Jingrun proved that 1+2 is a sufficiently large even number that can be written as a prime number plus a composite number composed of at most 2 prime factors."

"Yang Fan, if you want to prove the conjecture, you must pay attention to any possible mathematical laws, which will benefit your life."

"Okay, Mr. Feng, I understand." Yang Fan accepted humbly. Old Feng is a good person. When it comes to mathematics, he is very tall and does not allow others to object, and has a bad attitude.

Perhaps it is such a person who can go far.

Feng Yao knows that this state is not enough, but today is not mainly to talk about the history of the masters, but to adjust the mentality of the students.

"We go on with the prime numbers, that is, the prime numbers. In the infinite series of natural numbers, they take their place, like all other numbers, squeezed by two numbers before and after them, but they are one step further from each other than the other numbers .”

"They are suspicious and solitary numbers that have strayed into the sequence and are held there like tiny pearls on a necklace. It is sometimes doubtful that perhaps they wish to be like all other numbers. Ordinary, it just doesn't work out for some reason."

Feng Yao's quiet voice spread throughout the office. He made this passage extremely sacred, even anthropomorphizing prime numbers.

It's too sentimental, and it's not like what an engineering man should say.Not to mention Yang Fan was surprised, even the expressionless Ye Haoran was slightly weird.

"Well, this is not what I said, it is the original words of other masters." Feng Yao felt that the combination was not good, and this passage really did not match his personality.

"The important thing is that there are some more special members among the prime numbers. Mathematicians call them twin prime numbers. What kind of phenomenon can you call this?

"Twin primes?"

Yang Fan whispered, twins are twins, they have similar attributes.He counted down a few numbers until 11 and 13, and he had some inspiration, which seemed plausible.

He continued to count, and when he reached 17 and 19, he understood that it was near and far away.

Both Ye Haoran and Feng Yao heard the sound of counting. Feng Yao smiled slightly and said, "You should have discovered that these are two prime numbers separated by an even number."

"Then Mr. Feng, are they useful? The prime numbers are infinite, so there must be many more." Yang Fan said.

"Now that you have discovered it, can't you feel that loneliness? They are a pair of prime numbers very close together, almost adjacent to each other. There is only an even number between them, which prevents them from truly intimate contact.

"If you have the patience to keep counting, you will find that such twin prime numbers will become more and more difficult to come across. What you often encounter are those lonely single prime numbers, which get lost in the silent and rhythmic world composed purely of numbers. in the space."

"At this time, you will have an uneasy premonition that until there, the appearance of those twin prime numbers is just an accident, and loneliness is destined to be their real destiny. Then, when you are about to give up, you will meet again. A pair of twin prime numbers hugging each other tightly.

"Therefore, mathematicians have a common belief, that is to count as much as possible, and sooner or later they will encounter a pair of twin prime numbers. Although no one knows that they will appear there, one day, they will be discovered again."

"That's the . . . loneliness of mathematics."

The office was silent, Yang Fan was counting silently, one by one prime numbers flashed in his mind, they were arranged there quietly, and the distance from the numbers of the same type was getting farther and farther away.

After counting the number to 809, the quality of the twins was very low, and when it reached 811, [-], Yang Fan's eyes lit up again, hopeful.

It will be very difficult to appear again later, so keep counting, there will be.

The two students were looking for that epiphany in their hearts, Feng Yao smiled, as if seeing himself back then.

"Yang Fan, the path of mathematics is really lonely. After entering university, it is difficult for you to communicate with others except your classmates, so you can only study alone. Chemistry is applied to medicine, and physics changes technology. Only mathematics, Theories are everywhere. In solitude, go on and hold on."

"Teacher Feng, I understand." Yang Fan responded seriously.

Feng Yao was relieved, nodded to him, patted Ye Haoran on the shoulder again, and said: "Ye Haoran, don't act like the whole world has abandoned you, I received a message, the physics group, you have entered the training list. "

The surprise came too suddenly, Ye Haoran lost his extension slightly and almost fell down again.

Yang Fan was happy for this science genius to be shortlisted, and said: "Work hard, give up other subjects, and take physics to the top first."

Mathematics in high school is the best. After college, physics is the best. It is simply the most outstanding science in the world.

Ye Haoran, who had been expressionless for a long time, squeezed out a smile. The movement of his face showed that he was really happy.

"How did you learn "Linear Algebra and Its Applications?"

Just as the two students were happily preparing to leave, Feng Yao stopped Yang Fan.

"It's okay, I read a small part." Yang Fan didn't tell the truth, the progress of this book has already passed 50%, he was afraid of scaring Feng Yao.

"You don't have much time, enjoy your high school life." Feng Yao smiled mysteriously, without breaking the word, and changed the subject, "March 3, the national team training. After the end, at the end of March, I will take you to the capital one trip."

Going to the capital is to settle matters related to admission, and to visit Feng Yao's teacher.

This was agreed a long time ago, Yang Fan nodded: "Teacher Feng, I will hurry up and read math books."

Of the three-year mathematics textbooks, only two in the third semester of high school are at 82%. Work hard, and it will be perfect in a week or two. From then on, you will be proficient in high school mathematics.

(End of this chapter)