Defeating the No. 1 Middle School Team, the biggest opponent, is equivalent to clearing the biggest obstacle on the road to winning the championship. Everyone in the Huai'an Mansion Squadron was in a good mood and felt that the future was suddenly brighter. Jiang Shuiyuan was also relaxed, thinking that he could calm down for a while in the next few weeks, read the book and write. Who knew that after pressing the gourd, Ge Juntian summoned him and Zhang Jin a few days later, and asked in a scattered manner: "How are you reading the book I gave you?"

Jiang Shuiyuan widened his eyes: "Didn't you say you're giving us a month? If I remember correctly, it's only less than two weeks since that day!"

Ge Juntian did not feel ashamed at all, but instead said with a striking remark, "That's right, but later I overestimated your abilities a little. Not to mention giving you a month, even if you give you a semester or a school year, you may not be able to see any tricks. And the longer you look at it, the greater the blow to you, which will affect your confidence and determination to devote yourself to mathematical research. It is precisely because of this that teacher, I decided to tell you about what Hilbert's problem is, and the most promising research directions at present, and give you appropriate help and guidance. Of course, before this, I want to see how much you know about the Hilbert's problem? Zhang Jin, come first!"

Zhang Jin was already stuttering, but now he was nervous and stuttering even harder. He stared at his toes and said, "I, I haven't even finished reading the first 'continuous hypothesis' problem..."

"Do you understand?"

"Finally, I can't understand..."

Ge Juntian was slightly disappointed, turned his head and asked Jiang Shuiyuan, "Where are you in Jiang Shuiyuan? You shouldn't have participated in the Chinese studies difficult competition again, didn't you read my book?"

"I read the book you gave me, but like Zhang Jin, I didn't understand it at all." In fact, Jiang Shuiyuan took the time to finish the book in the first week after getting it, but he only finished it. This thing is completely different from the Chinese classics such as "Thirteen Classics" and "Twenty-Four Histories". The latter can basically understand it after reading it. Even if the 10 or two of them are not understood, you can keep it in your mind and compare it with other classics and chew it carefully. Once you understand it, it will be an excellent paper; while the former can basically understand what you can understand after reading it, and the ones you can't understand will not understand it from the first page.

Jiang Shuiyuan's memory is unlimited. After self-studying the high school mathematics textbooks, Ge Juntian read many introductory books on advanced mathematics. However, after reading this book "Hilbert's Problem and Research Progress", I remember the word "Shadow's Problem and Research Progress". The content is simply unintelligible, and the brain hurts a lot when I think about it.

"Oh? Is that right?" Ge Juntian said, picking up chalk and writing down Arabic numerals from 1 to 23 on the blackboard, and then continued to ask: "Then tell me what have been solved now?"

Ke Me? Jiang Shuiyuan rolled his eyes: "The second problem is 'the non-contradiction of arithmetic axiom system'. First, the American Czech mathematician Kurt Godel proved Godel's theorem of incompleteness in 1931, and then the German mathematician Gentz ​​used limit induction to prove the non-contradiction of arithmetic axiom system in 1936, thus properly solving this problem."

"Not bad!" Ge Juntian wiped off the word "2" on the blackboard, "What else?"

Jiang Shuiyuan said: "The third problem is that there are two tetrahedrons with equal height and bottom, which cannot be decomposed into a limited small tetrahedron, making these two groups of tetrahedrons congruent to each other'. Hilbert's student Max Dern proved that it was impossible as early as 19oo, and this problem has been solved."

"It's totally correct!" Ge Juntian wiped off the word "3" again and asked again: "Continue to say."

...

Until Jiang Shuiyuan sorted out all the problems that had been solved in Hilbert's problem, Ge Juntian sat down with satisfaction, his eyes full of praise: "Very good, very good! It takes this outstanding talent to study mathematics. Of course, Zhang Jin, don't be discouraged. The talent between people is incomparable. Your advantage lies in "ten years of hard work". Just like building a house, you need talented designers, and also a builder who turns the blueprint into real objects. By the same token, mathematical research also requires an ascetic monk like you!"

It is rare for Ge Juntian to comfort others once, but why did Zhang Jin feel that he was trying to curse himself in different ways?

Ge Juntian pointed to the remaining numbers on the blackboard and said loudly: "As you can see, although there are 23 problems in the Hilbert problem, after nearly a hundred years of continuous efforts by mathematicians around the world, more than half of the problems have been properly solved so far, and the remaining problems have also achieved a series of important research results. However, it is worth noting that among the 12 problems that have been solved, our neighboring country, Japan, made important contributions, including the fifth question, "Whether all continuous groups are differentiable groups", Japanese mathematician Hidehiko Yamaeba gave a complete affirmation result in 1953; on the fourteenth question, "Prove the finiteness of some functions in the complete system", Japanese mathematician Masahito Nagada gave a negative solution with a beautiful counterexample in 1959. In addition, Japanese mathematician Sadao Takagi also gave partial answers to the ninth and twelfth questions.

"Compared with the outstanding achievements of the Japanese mathematics community, the contributions made by our Chinese mathematicians seem to be lackluster. They mainly achieved some globally influential results on the eighth problem, "the problem of prime distribution" and the sixteenth problem, "topological research on algebraic curves and surfaces". But this is far from enough, because the status of Chinese mathematics in the international academic community is far from comparable to disciplines such as physics, chemistry, electrons, biology, and astronomy!

"We all know that mathematics is the mother of all sciences. If mathematics falls behind, the exhibition of other disciplines will definitely be more or less affected. After all, all problems are ultimately mathematical problems. Therefore, in recent years, domestic research institutions with the Chinese Academy of Sciences and the World University of Science have proposed a grand 'twenty-year plan', which is to mobilize the whole country to concentrate the best mathematicians on the remaining Hilbert problems, strive to make breakthrough progress on one or two problems in twenty years, and achieve important results on three to five problems. Therefore, you should regard participating in the Olympics and winning the gold medal as the direction of your efforts in the past one or two years, and also regard solving the Hilbert problem as the goal of your lifelong struggle in the next one or two years!"

Zhang Jin was so excited by this great plan that he was so excited that he stuttered: "It's going to take twenty years!"

"Yes, twenty years!" Ge Juntian was also full of emotion, "Ten years of reunion, ten years of lessons, twenty years of time should be enough to cultivate a large number of world-class mathematicians, so you students who are now in college and high school are blessed. As long as you are not bad in talent and calm down and seize the opportunity, you may not be unable to solve a Hilbert problem and thus win the Sun Yuanqi International Youth Science Award! As for the mathematical researchers who are now thirty or forty, they are missed. They missed a good opportunity and were destined to be a stepping stone for their younger generations. Of course, the age of thirty is the golden age of mathematicians. They are now unknown, and they are probably going to be like this in their lives!"

"Twenty years!" Jiang Shuiyuan also sighed, but his feelings were a little more sad: for others, twenty years may be a period of time in life. For him, twenty years is the length of all his remaining lives!

Ge Juntian looked at the two students who sighed with dissatisfaction: "What's wrong with twenty years? If you can solve a Hilbert problem, it will be worth it even if it takes twice as much time!"

"The key is that even if you spend twice as much time, it may not be able to solve a sub-problem in Hilbert's problem in the end!" Jiang Shuiyuan put aside his sentimentality and retorted tit-for-tat, "Just as Academician Hui Chengze wrote in his book, Riemann proposed the famous "Rymann Conjecture" in his paper as early as 1859; in 19oo, forty-one years later, Hilbert included him in the Hilbert problem; in three years, Danish mathematician Gram calculated the values ​​of 15 zero points, which is the specific existence that people have seen at zero points.

"Since then, people have begun the arduous journey of finding zero points and counterexamples, from more than a dozen to more than a hundred, and then to more than a thousand, from the current Riemann-Sigel formula to the introduction of electronic computers, and then to distributed computing. Now the conjecture has been proposed for more than a hundred years, and the zero points found have exceeded ten trillion, but what can it do? Ten trillion evidence is not as good as one proof. Now the Riemann conjecture still exists!"

Ge Juntian immediately took a breath of cold air like a toothache: "Ryman guesses! That is a human problem that exists as long as cancer and is irresistible!"

The Riemann conjecture is indeed difficult. Hilbert once said that if he woke up after a slept for 100 years, the first question he would ask was: Has the Riemann conjecture been proved? However, such a difficult Riemann conjecture is just a sub-problem in Hilbert's eighth problem, "Primary Distribution Problem". Similar sub-problems include the Goldbach conjecture, which China Minke favorites to crack, and the twin prime number conjecture that was famous not long ago. The difficulty of the Hilbert problem can be imagined!

Ge Juntian changed his tone: "It is precisely because of such hard bones that mathematics is so exciting and charming! It is because of such hard bones in Hilbert's problem that I have come to give you some advice: Are you planning to know that there is a tiger in the mountain, or to go to the tiger mountain, or to pick the soft persimmons? Of course, no matter how soft the soft persimmons in Hilbert's problem is also diamond-level, otherwise they would have been slapped by others!"
Chapter completed!