Zhang Jin said weakly: "Old, teacher, but, but I still don't know what are the problems that have not been solved?"

"That's what I'm going to say next!" Ge Juntian was really speechless about Cheng Dù, who was familiar with Hilbert's problems, and lightly sketched out the remaining unsolved problems, and then asked: "How is it, boys? Have you picked out the girl you like? To say that you are really no different from choosing a daughter-in-law, it is basically a lifelong choice, so you have to think about it carefully." Don't go back and forth halfway through the time and change the topic halfway, it will hurt your muscles and bones!"

Jiang Shuiyuan instantly blessed his soul: "Then Mr. Ge, which topic did you choose?"

Ge Juntian's originally uninhibited face immediately collapsed, and it took a long time to grit his teeth and reply: "I chose the eighteenth question 'Constructing Space with Congruent Polyhedra'!"

Jiang Shuiyuan suddenly smiled happily: No wonder Ge Juntian is so bitter and hateful, it turns out that he deeply sympathizes!

As early as the third century B.C., the ancient Greek philosopher Aristotle made a guess that a tetrahedron of the same size should fill the entire space. Over the next 1,800 years, Aristotle's assertion was repeatedly questioned by prominent scholars, but the rigorous argument for his error did not appear until the 16th century. In other words, when the tetrahedron is enclosed along a ridge, a gap will inevitably be created, and it will not be filled.

When Aristotle's speculation was rejected, another question arose: if the porcelain was not filled, how large would the remaining void be, or in what case, in what extent? This is Hilbert's eighteenth problem: construct space with congruent polyhedra and determine its maximum packing (or directionally packed) density.

Dealing with this kind of problem requires not only extremely complex calculations, but also the various configurations that may occur in space of congruent polyhedra, which is not an ordinary brain-consuming task. Academician Hui Chengze made it clear in the book that except for some of the results made by the German mathematician Bibelbach in 1910 and Reinhardt in 1928, the research on this problem has been at a standstill for a long time!

Zhang Jin scratched his head and asked, "Then, what do you have to say, teacher?"

Ge Juntian said: "My proposal is one, don't choose an open topic, such as the twenty-third question 'the development of variational methods of research', although the variational method has made great progress since the twentieth century, but as long as mathematics is stored for a day, the variational method still has the value of saving zài, then this problem is not over." For example, the sixth question, 'The axiomatization of physics, which plays an important role in mathematics', is a matter of success in quantum mechanics and quantum field theory, but many people are skeptical about whether the various branches of physics can be fully axiomatized. Even the foundation of the zài has been questioned, who knows if it will be a water splash in the future, and the bamboo basket will be empty?

"It is best not to touch the long-term unresolved problem, and the teacher is the most vivid negative teaching material. If you don't have the extreme talent and extraordinary perseverance to touch the Riemann conjecture, I advise you to die of this heart a long time ago!

"The third is to try to select issues that have important results published in the near future, which means that there are still people who pay attention to the research of this issue, and there is still room for further discussion and development of this issue. If no one publishes a paper to discuss it recently, it means that the problem has either reached a dead end, or it is too difficult for anyone to dare to touch. If you choose such a topic, there is not even a single person in the world to discuss with each other, how can you continue to study it? Isn't this kind of thing just a matter of people exchanging ideas and colliding with each other, and then accumulating over time? It is really like Newton and Sun Yuanqi who worked so hard and alone to ride the dust, and there are few people in the world who can understand their academics, but I am afraid that there will not be a single one in two or three hundred years!

"In addition, if possible, try to choose a problem that has scholars in China to study, and you can get the moon before the water. Of course, this is not required. And you have a problem at a glance, and you can not be restricted by the above rules and regulations, and it is difficult to buy a happy heart!

Zhang Jin rubbed his hands and said, "Old, teacher, I, I want to choose the eighth question." ”

"The eighth problem, the problem of the distribution of prime numbers, is a good choice!" Ge Juntian nodded approvingly: "You must know that there are many concise sub-problems under this question, which are difficult to prove and interesting, such as the Riemann conjecture we just mentioned, as well as the famous Goldbach conjecture and the twin prime conjecture, all of which are worth investing a lifetime of effort to solve." However, I suggest that you better avoid the Riemann conjecture and choose the Goldbach conjecture or the twin prime conjecture, because the difficulty of the former is well known, and the latter two have been studied by many scholars in China, and both have made gratifying results. With your perseverance and hard work, you may not be able to catch up and win a jewel in the crown of mathematics!"

"Hmm!" Zhang Jin nodded vigorously.

"What about you?"

Jiang Shuiyuan took a deep breath: "I'll pick the tenth question!"

Hilbert's tenth problem is accurately formulated as whether an indefinite equation with an integer coefficient Diophantine plot with any number of unknowns can be determined in a finite step to determine whether the indefinite equation has a zài rational integer solution. It's a bit of a twist to put it bluntly, just like solving an equation in junior high school, that is, finding the integer root of an integer coefficient equation, but now this equation is a little more complicated.

"The tenth question?, the solvability of indefinite equations?" Ge Juntian was dumbfounded, and only after a long time did he continue: "If it is not a coincidence, then it must be fate!"

Jiang Shuiyuan and Zhang Jin were both puzzled.

Ge Juntian said slowly: "Speaking of this issue, we must first mention one person - Sun Yuanqi of our Huai'an Mansion. As we all know, he has three wives, the mother of the country, Cho Kyung-hye, Vera, and Lilith. But there are rumors that there were two American women who almost became Mrs. Sun that day, you should know who they were, right?"

"Elena and Nina!" As Huai'an people, Jiang Shuiyuan and Zhang Jin naturally knew everything about this story.

Among them, Elena never married after returning to the United States, worked as an educator at Boston University, and later adopted a girl, Jiang Shuiyuan, you have read Mr. Hui's book "The Hilbert Problem and Research Progress", you should know this girl. ”

"Who? Could it be Mrs. Robinson?" Because Mrs. Robinson was one of the few female mathematicians mentioned in the book, Jiang Shuiyuan immediately recalled: "It seems that Academician Hui did not mention this in the book?"

Ge Juntian said with a smile: "Mr. Hui wrote a textbook of Yan Sù, how could it be mixed with such gossip things? This Mrs. Robinson's real name is Julia, she has been frail and sickly since she was a child, but under the influence of Ms. Elena, she likes to study very much, and has been enthusiastically fond of mathematics since middle school, and later entered Barnard College of Columbia University to specialize in mathematics, and has obtained bachelor's and master's degrees, and met and fell in love with Mr. Robinson, who was a teaching assistant in the number theory class at the school, and finally Miss Julia became Mrs. Robinson.

Soon after the marriage, doctors discovered that Mrs. Robinson was infertile, which nearly destroyed her life and plunged her into a long period of depression. In the end, it was Mr. Robinson who rekindled her interest in mathematics and brought her out of the shadow of despair, and she has since regarded mathematics as her own child. And the direction of her research is Hilbert's tenth question!"

"That's it?" Jiang Shuiyuan and Zhang Jin were both a little disappointed. If this is also fate, then fate is too cheap, right?

Ge Juntian shook his head: "This is just the beginning! Since then, Mrs. Robinson has been obsessed with the study of Hilbert's tenth question, and has made important achievements, but her weak body has repeatedly troubled her, and the doctor believes that due to the influence of childhood diseases, the heart function is impaired, and it is very likely that she will not live to be 40 years old. But year after year, Hilbert's tenth problem was never perfectly solved. So every year on her birthday, Mrs. Robinson would blow out the candles and make a wish that she would see Hilbert's tenth problem solved in her lifetime, for whoever would solve it, for she said, 'I can't bear to die in confusion!'

As the years passed, Mrs. Robinson's wishes were frustrated again and again, and her body became weaker and weaker. At the end of her life at the age of 39, she asked again, 'Where is the man who holds the last key?' and the elderly lady Elena comforted her, 'Don't worry, it will be a smart and handsome young Chinese boy.' For in Lady Elena's mind, the smartest man in the world was the young and handsome Chinese lad who was, and always will be, able to solve the problems that plagued her daughter!

"Now it's up to you to choose Hilbert's tenth question, and there is no doubt that it is predestined from heaven!"