Jiang Shuiyuan learned every day that the main source of the school's big and small incidents was the mouth of the annoying spirit Wu Zichen, and if he didn't say anything about He Tiantian's descendants besieging him after school, Jiang Shuiyuan would not know about it in a short time. What's more, Jiang Shuiyuan has recently had to deal with the homework of teachers in various subjects, preview the textbooks of the second year of high school, go to the Chinese Studies Lecture and Talk Club to read books, and study the classics of Chinese studies by himself, so he is almost too busy to touch the ground, how can he have the time to care about these idle things?

On the evening of the announcement of the Olympiad list, the mathematics team couldn't wait to convene the students for their first meeting.

The new members rushed to the classroom of the mathematics group of the Olympiad with pen and paper, and when they entered the door, they saw a short and fat young man lying comfortably on the podium, looking at everyone who came in with great interest, and humming a popular vulgar song in his mouth. On the side was a helpless senior, rubbing his hands and not knowing how to deal with such an embarrassing scene.

After all 20 people arrived, Ge Juntian jumped up, straightened his crumpled shirt, and said with a smile: "Hello everyone, I am the instructor of the mathematics group of the Olympiad Society, named Ge Juntian, you can call me Uncle Ge, Brother Tian or anything." I'm calling you here today for one main purpose, to see if you have the talent to learn mathematics. ”

Test whether you have the talent to learn mathematics? I have only heard that you need talent to study music, art, sports, etc., and you also need talent to learn mathematics? The 20 people who had just sat down in their seats were obviously short-circuited in their heads.

Ge Juntian seemed to see everyone's doubts: "That's right, whether it is studying now or embarking on the road of scientific research in the future, talent is the decisive factor! For example, at the same age of twenty-three, in the face of a group of middle school students, Mr. Sun Baixi, the father of the country, can write the emperor's masterpiece "Principles of Chemistry", while I can only whistle at the girls passing by, this is the difference in talent. Although I did not like the famous Comrade Edison, he said something that I agreed with very much. He said that genius is one percent inspiration and ninety-nine percent perspiration, but if there is no one percent inspiration, no amount of sweat is just sweat. In fact, the inspiration he is talking about is talent, without good talent, no matter how much sweat and tears are shed, even blood, it is useless. So I'm going to test your talents first, so that you don't waste your time and mine too!"

The group of students below immediately looked at each other, and at the same time, there was a deep curiosity in their hearts: what does the so-called talent look like, and how is it detected?

The senior on the side smiled bitterly and said, "Teacher Ge, I'm afraid it's not as exaggerated as you say, right? As the old Chinese saying goes, 'diligence can make up for clumsiness', I believe that as long as you work hard, you will definitely be rewarded." Maybe you can't reach the heights of those geniuses, but it's impossible to work for nothing and achieve nothing!"

Ge Juntian glanced at him: "If you work hard, you will definitely be rewarded?" Then give you a gorilla, a set of textbooks from kindergarten to university, and another fifty years, so that you can train the world's first orangutan college student. How?"

"Uh......" The senior was speechless for a moment, and it took a long time to retort: "I'm talking about people, you're talking about orangutans." If you are an ordinary person with a normal IQ, a set of textbooks and fifty years of time, there is absolutely no problem in cultivating you into a college student!"

"In the face of genius, ordinary people are no different from gorillas!" Ge Juntian retorted mercilessly: "What is a genius? It is that Newton published a treatise entitled "Mathematical Principles of Natural Philosophy" in 1687, which laid the scientific view of the physical world for the next three centuries and became the foundation of modern engineering; Mr. Sun Baixi wrote a series of articles for more than ten years starting in 1898, which thoroughly framed the framework of physics, chemistry, and astronomy for nearly a hundred years. As for ordinary people, at most, they are doing some tinkering and bits and pieces of work in these structures. ”

The senior's brain teaser turned: "What about Mr. Zhao Jinghui, the mother of the country? I haven't heard how outstanding her talent is, hasn't she still made epoch-making contributions in the field of medicine?"

"Oh, that's because there is a genius behind her that you and I both know about the past and the present!" replied Ge Juntian, "We call this kind of accidental and unrepeatable success 'luck', and luck is an indispensable part of talent! For example, some talented mathematicians have been plagued by a world-class conjecture all their lives and cannot make an inch, while some mathematicians have just stepped into the field of mathematical academic research and have found a wonderful way to solve this problem.

Ge Juntian immediately turned his face and said to the 20 freshmen who had just stepped into the door of the Olympiad Club: "So you must pray for good luck for yourself! A good scientist must establish a lofty ideal and have a core research problem. After the problems are determined, it is necessary to persist in independent thinking, focus on the core issues step by step, and gradually improve the level. This requires you to identify a world-class problem as your goal in order to have a chance to make a name for yourself, otherwise you will only become a mediocre pastemaker and never become a scientist in the annals of history!

For example, the ancient Greek philosopher Aristotle proposed in the third century BC to construct space with congruent polyhedra, which has not been completely solved for 2,200 or 300 years. Another example is the square of the circle, one of the problems of ancient Greek ruler and gauge drawing, which also bothered mankind for nearly 2,000 years, until Lindemann proved that pi is beyond the number before completely denying its possibility. In addition, well-known mathematical conjectures, including Fermat's theorem, Goldbach's conjecture, and the four-color conjecture, are still unresolved, and it is unknown how long they will plague mankind in the future. It's all up to your luck!"

Ge Juntian's flickering suddenly made the teenagers in the classroom excited, eager to start a world-class problem with a pen now, hoping to completely solve it in three or five years, and make a sensation in the world in one fell swoop, and then won the Sun Yuanqi International Outstanding Young Scientist Award and wrote his name into the mathematics textbook.

"Very well, boys, I will see the burning fighting spirit in your eyes! But whether you are qualified to enter the temple of mathematics and choose a topic worth fighting for a lifetime depends on whether you have the talent to study and study mathematics. Ge Juntian raised his arms and spat and said, "What is talent? I think the deeds of Ramanujan, the most famous genius mathematician in Tianzhu, are enough to prove what talent is." Ramanujan's highest education was in high school, and like you, he did not have a formal higher education in mathematics, but he loved mathematics and was obsessed with number theory outside of work, especially the summation formulas involving mathematical constants such as π and prime numbers, as well as integer splitting.

"Ramanujan's talent is evident in his strong intuitive insight, which often foresees certain mathematical conclusions, although he does not like to prove, and often turns out to be right after the fact. Before his death in 1920, he wrote a letter to his friend, the famous British mathematician Hardy, describing a mysterious function that people had never heard of before, and saying that he had a strong intuition about the properties of this function. After decades of research, researchers recently said they proved Ramanujan's intuition right because this function could be used to explain part of the mystery of the cosmic black hole. And that's a great talent for mathematics!"

Ramanujan's magical talent shook the hearts of all the students, and even the senior who had been refuting Ge Juntian before was fascinated.

After Ge Juntian gave everyone a lot of energy and whetted his appetite, he began to ask the question: "The so-called 'mathematics' is the knowledge of numbers, so the sensitivity to numbers is very important, like the Ramanujan mentioned just now, he likes all kinds of mathematical constants very much, but the content of our test today is integers. For example, the famous German mathematician Kronecke believed that arithmetic and mathematical analysis must be based on integers, saying: "God created integers, and all the rest of the numbers are man-made." You have certainly not heard of the name Kronecke now, but when you become mathematicians in the future, you will definitely know the Kronecker function, Kronecker product, Kronecker-Weber theorem and other mathematical theories named after him.

"Burkhoff, the most important American mathematician of the early 20th century, also said: 'The simple composition of integers has been the source of new life in mathematics for centuries.' The rules of the game we played today were that I would write down a random integer on the blackboard, and you would have a minute to think about it, and then write down what was special about it on a slip of paper and give it back to me. Do you understand?"

"Understood!" the students replied in unison.

Ge Juntian picked up the chalk and wrote a number on the blackboard: 1729.

Many people are frowning and pondering: it has factors of 7, 13, 19, 91, 133, 247, and 1729, and the sum of the factors is 511, which is less than 1729, so it is a loss. But what's so curious about this?

Jiang Shuiyuan thought for a while, and wrote on the paper: 1729 = 1^3 + 12^3 = 9^3 + 10^3, which is expressed by the sum of two cubes, and 1729 is the smallest of the two expressions.