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

"That's what I'm going to say next!" Ge Juntian was so familiar with Hilbert's problem that he was very familiar with. He roughly outlined the remaining few unsolved problems, and then asked: "How about it, young men? Have you picked out the girl you like? If you want to say that you are really the same as choosing a wife, it will basically be a lifetime, so you have to think carefully.????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????. Don't go together. Change the question half

Jiang Shuiyuan instantly became happy: "Then Teacher Ge, which question are you choosing?"

Ge Juntian's originally unrestrained face immediately collapsed, and after a long time of gritting his teeth, he replied: "I chose the 18th question, 'Use congruent polyhedral to construct space'!"

Jiang Shuiyuan immediately smiled happily: No wonder Ge Juntian is so bitter and deeply revenge. It turns out that he has a deep feeling of the same!

It is said that the history of Hilbert's eighteenth question is longer than the Riemann conjecture. As early as the third century BC, the ancient Greek philosopher Aristotle made such a guess: stacking a regular tetrahedron of the same size should fill the entire space. In the following 1800 years, Aristotle's statement was questioned many times by famous scholars, but a strict argument for its error did not appear until the 16th century. In other words, when the regular tetrahedron is surrounded by a circle along a edge, there will definitely be gaps, and no porcelain solid can be filled.

After Aristotle's guess was denied, another question followed: if the porcelain is not filled, how big is the remaining gap? Or, what range is the gap? This is Hilbert's eighteenth question: use congruent polyhedron to construct the space and determine its maximum stacking (or directional stacking) density.

To deal with this problem, it is not only necessary to deal with extremely complex operations, but also to consider various structures that may appear in space by conglomerate polyhedrons, which is not ordinary brain-strapped. Academician Hui Chengze clearly stated in his book that in addition to the German mathematician Biberbach and Reinhardt made some achievements in 1910 and 1928, the research on this problem has been in a state of stagnation for a long time!

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

Ge Juntian said: "My suggestion is one, don't choose open questions, such as the 23rd question "Research on the Method of Expanding Variational Difference". Although the variational method has been greatly developed since the 20th century, as long as mathematics exists for one day and the variational method still has its value, then this question is not finished. Can you wait for which day? For example, the sixth question "Axiomatic of physics, which plays an important role in mathematics". Although it has been successful in quantum mechanics and quantum field theory, many people are skeptical about whether all branches of physics can be fully axiomatic. Even the foundation of existence has been questioned. Who knows whether it will be a splash of water and a moon in the future, and a waste of water in the bamboo basket?

"Suggestion 2: It is best not to touch long-term indecisive questions. Teacher, I am the most vivid negative teaching material. If you don't have a high talent, you still want to touch Rieman's guess. I advise you to have a long time to die!

"Suggestion 3: Try to choose the issue that has important results in the near future. This means that there are still people who are concerned about studying this issue, and there is room for further discussion and development of this issue. If no one has discussed the paper recently, it means that this issue is either in a dead end or too difficult. If you choose such a topic, there is not even a person discussing each other. How can you continue to study it? Isn't it just that everyone can discuss and exchange ideas and then do it over time? It's really like Newton and Sun Yuanqi who are hardworking and striving to the world. There are few people in the world who can understand their academics. Isn't it that one of them will not be released in two or three hundred years!

"In addition, if possible, try to choose questions that scholars have studied in China. You can get the month before getting close to the water. Of course, this is not a requirement. Moreover, if you have a problem that you like at first glance, you can also not be restricted by the above rules and regulations. It is hard to buy a lot of money to be happy! How about it, tell me your choice?"

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

"The eighth question? The problem of prime number distribution? It is a good choice!" Ge Juntian nodded in praise: "You should know that there are many simple forms and difficult and interesting sub-problems under this question, such as the Riemann conjecture we just mentioned, as well as the famous Goldbach conjecture and twin prime number conjecture, which are worth investing a lifetime of energy to crack. However, I suggest that you should avoid the Riemann conjecture and choose the Goldbach conjecture or twin prime number conjecture, because the difficulty of the former is well known, and the latter two have been studied by many scholars in China, and have made gratifying results. With your perseverance and hard work, you may not be able to come from behind and win a jewel in the crown of mathematics!"

"Yes!" Zhang Jin nodded vigorously.

"Where are you in Jiang Shuiyuan?"

Jiang Shuiyuan took a deep breath: "I will choose the tenth question!"

The accurate expression of Hilbert's tenth question is: Given an integer coefficient Diopian equation with any number of unknown numbers, can we use finite steps to determine whether there are rational integer solutions for indefinite equations? It's a bit confusing to put it bluntly, just like solving equations in junior high school, which is to find the integer root of an integer coefficient equation, but now this equation is a little more complicated.

"The tenth question? Is the solution of the uncertain equation?" Ge Juntian was stunned and continued after a long time: "If it wasn't a coincidence, then it must be destined!"

"?" Jiang Shuiyuan and Zhang Jin were confused.

Ge Juntian said slowly: "When talking about this issue, we must first mention one person - Sun Yuanqi of our Huaian Prefecture. As we all know, he has three wives, the mother of the country, Zhao Jinghui, Vera and Lilith. But there are two American women who almost became Mrs. Sun on the same day. You should know who it is?"

"Elena and Nina!" As natives in Huai'an, Jiang Shuiyuan and Zhang Jin naturally knew this story well.

"Yes, it's them! Elena never married after returning to the United States. She worked in education at Boston University and later adopted a girl. Jiang Shuiyuan, you have read Mr. Hui's book "Hilbert Problem and Research Progress" and you should know this girl."

"Who? Could it be Mrs. Robinson?" Because Mrs. Robinson is 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 smiled and said, "Mr. Hui wrote serious textbooks, how could he get involved in such gossip? Mrs. Robinson's real name is Julia. She has been weak and sick since childhood. However, influenced by Ms. Elena, she likes studying very much. She has been fond of mathematics since middle school. Later, she entered the Barnard College of Columbia University to specialize in mathematics, obtained a bachelor's and master's degree, and met and fell in love with Mr. Robinson, who was an assistant in the number theory course in school. In the end, Miss Julia became Mrs. Robinson.

"Short after marriage, the doctor found that Mrs. Robinson could not have children, which almost destroyed her life and caused her to fall into long-term depression. In the end, Mr. Robinson rekindled her interest in mathematics, which made her come out of the shadow of despair. From then on, she regarded mathematics as her own child. The direction of her research was Hilbert's tenth question!"

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

Ge Juntian shook his head: "This is just the beginning! Since then, Mrs. Robinson has been obsessed with research on Hilbert's tenth problem and has made important achievements, but her weak body has repeatedly troubled her. The doctor believes that due to the impact of childhood illness, the heart function is severely damaged and it is very likely that she will not live to be 40 years old. But year after year, Hilbert's tenth problem has not been perfectly solved. So every year on her birthday, Mrs. Robinson will make a wish when she blows out the candles, hoping that in her lifetime, she can see that Hilbert's tenth problem is solved, no matter who can solve it, because she said: 'I can't bear to leave the world with confusion!'

"Time passed by year, and Mrs. Robinson's wishes were also faded again and again, and her body became weaker. When she reached the end of her life at the age of 39, she asked again: 'Where is the person holding the last key in her hand?' The elderly Ms. Elena next to her comforted her and said: 'Don't worry, that would be a smart and handsome young Chinese man.' Because in Ms. Elena's heart, the smartest person in the world was the young and handsome Chinese man back then, and will always be, and will definitely solve the problem that troubled her daughter! Then Mrs. Robinson passed away with such an answer.
Chapter completed!