A Man of Science and Engineering in Troubled Times Wandering in the Late Qing Dynasty

Set theory sounds simple from its name, but it's actually very complex.

Didn't Hilbert solve 23 centuries of difficult problems? The first one was about set theory, that is, the continuum hypothesis.Being able to enter the 23 problem is definitely not easy to solve.

On the other hand, Hilbert's 23 problems can be regarded as the guiding light of modern mathematics, with set theory taking the lead, which already shows that Hilbert attaches great importance to set theory.

Cantor's mental state was up and down, and doctors from the hospital soon found him.

"Oh my god, Mr. Cantor! Why did you leave the hospital without permission again!" The doctor was a little angry.

"It would not be etiquette to meet in a hospital with a friend who has traveled far away," Cantor said.

"If it's a visit, what's wrong with going to the ward?" the doctor said.

Cantor said: "This Mr. Li Yu is the most brilliant supernova in the scientific world today. How can he be allowed to see what he looks like in a mental hospital?"

The doctor turned out to be a fan of Li Yu's books and said in surprise: "It turns out to be Mr. Li Yu! If I knew you were coming, I would definitely bring a book for you to sign!"

Li Yu said with a smile: "As long as you can read it whether you want to sign it or not."

Cantor said at this time: "Doctor, do you believe me now?"

The doctor was obviously not very willing and reluctantly compromised: "You must go back as soon as possible."

Cantor could only say: "I know, it won't take long."

After the doctor left, Cantor turned to Li Yu and said helplessly: "The hospital actually doesn't have any treatment methods, so we won't let you leave casually."

"Mental illness is really difficult." Li Yu said helplessly.

Cantor added: "But lately I feel more and more like I can control my dreams."

"Controlling dreams?" Li Yu said, "Is it a lucid dream?"

"Yes," Cantor said, "I can clearly feel that I am dreaming, and I can control the development of the people and things in the dream."

Li Yu said: "When he was in the United States, Tesla mentioned to me that he would have lucid dreams almost every night, and he would go to different cities in his dreams, and he could even conduct experiments in his dreams."

Many people should have had lucid dreams. Li Yu clearly realized that he was dreaming many times, but it was usually when he was about to wake up, so it did not last long.

As for people who can control dreams, they are even rarer.

(Charlotte: I’m familiar with this!)

Cantor added: "I can perform mathematical calculations in my dreams, and what I like to do most now is your game theory and chaos theory."

Li Yu said with shame: "So you can solve such a difficult thing in a dream!?"

"It's not that bad. I still have to write when I wake up," Cantor said. "I just sleep too much now, so I found that dream control is a very convenient way, which can save a lot of time."

If Li Yu didn't know that he was a super powerful mathematician, ordinary people would really think that he had a mental problem...

Li Yu reminded: "Long-term control of dreams may cause confusion in the brain and make it impossible to distinguish between reality and dreams."

Cantor nodded: "It's a noteworthy question."

"If there is a dream within a dream or a double dream in the future, after waking up from the dream, if the brain does not know that it is still dreaming, it will be very difficult to return to reality." Li Yu said.

Cantor said: "I've had a double dream, and it's really hard to wake up."

Li Yu thought to himself, I really don't know what to do in Inception.

Cantor's condition today was generally pretty good. Li Yu said, "I hope to see you in school as soon as possible."

Cantor stood up and said, "It depends on how quickly spiritual science develops."

Li Yu sighed and said nothing more. Even in later generations, the treatment of depression will be a long-term problem, but at least the pain can be alleviated through medicine.

Current patients with severe depression can only rely on human willpower and extremely limited medical means to support themselves.

-

After bidding farewell to Cantor, Li Yu went to Göttingen University again to attend Hilbert's appointment.

Göttingen is a small city, but it is currently the absolute holy land of mathematics.

At the beginning of the [-]th century, math students all over the world might have received this advice: "Pack up your backpack and go to Göttingen!"

There are even rumors that this small town is full of mathematicians.

No wonder, even 100 years later, when it comes to Göttingen, everyone knows the University of Göttingen, but few still remember that Göttingen is the name of a city.

Just like in later generations, except for people from Shandong, few people may know Tai'an City, but if you talk about Mount Tai, people all over the country know it.

The University of Göttingen has a long tradition of mathematics. Initially, Gauss, the prince of mathematics, laid a strong foundation, and then came the famous mathematics giants such as Dirichlet and Riemann.

On the corridor wall of the Institute of Mathematics at the University of Göttingen, the portraits hanging above the heads are of these three great gods.

It was Klein who truly built the University of Göttingen into a mathematics center.

Because if you want to build a world-class mathematics center, the leader must not only know mathematics, but also have charisma, organizational skills and excellent vision. Klein is a very visionary person.He actively introduced mathematical talents, the core one of whom was Hilbert; then Hilbert relied on his stronger affinity to gather a large number of mathematicians at the University of Göttingen, forming a virtuous cycle.

Not long after entering the campus, Li Yu met the young Max Born, the super boss of quantum mechanics who is currently Hilbert's assistant.

Born was wearing a hat with bright ribbons on his head. He also saw Li Yu and stepped forward and said, "Are you Mr. Li Yu?"

Li Yu shook hands with him and said, "Yes, Mr. Born, hello."

Born was surprised: "You actually know me! I'm so happy!"

Of course Li Yu knew this big boss.

Later, among the three major schools of quantum mechanics, the most famous was Bohr's Copenhagen School.And Born is the leading figure in the Copenhagen School.

Later, Schrödinger shocked the world with his wave equation, but he himself did not know how to explain the wave function.

The person who completed this work was Born, who very creatively pointed out that the essence of the wave function is probability.

Being able to have such insight is inseparable from profound mathematical skills.

Born's mathematical skills were perfected at the University of Göttingen.

Li Yu asked him: "Where is Professor Hilbert?"

Born said: "Professor Hilbert is in class, why don't you go to the office and wait?"

Li Yu said: "No, I'm going to attend the lecture too."

Born took Li Yu to a large problem-solving classroom, which was almost full.

For universities in the early [-]th century, it was uncommon to take large classes, and mathematics classes in particular were even rarer.

Because there are not that many students in the current university; and the mathematics courses are very difficult, and few students from other majors take them.

It is said that even before Li Yu traveled through time, except for students majoring in mathematics, the mathematical knowledge they learned could only be called "ancient mathematics".

Most of them only learned calculus, which was something from Newton's time. And Newton lived in the late seventeenth and early eighteenth centuries, more than 300 years ago.

Mathematics after Newton became increasingly sophisticated.

Think about it, Abel is so famous, but everyone only knows that his story is very attractive, and his untimely death is extremely regrettable, but not many people really understand the group theory he created.

As for modern mathematics, it has developed to the point where it is difficult to popularize science. It is really too difficult.

There are very few top-level mathematical problems that the general public can understand, and they are often proposed very early, such as Fermat's last theorem and Goldbach's conjecture. But if you talk about their mathematical foundations a little, they are modern mathematics, and they are no different from the Bible.

Logically speaking, most of the classes in the Department of Mathematics and Physics are in small classes, but Hilbert's affinity was so strong that too many students liked his class, so the school had no choice but to change it to large classrooms.

Li Yu was very curious about what the most famous math master in the early [-]th century was like in class, so he took advantage of the crowd and quietly slipped into the last row.

After listening for a while, Li Yu understood why everyone liked his class: Hilbert could explain profound principles in simple terms.

It is very difficult to do this, and it must be understood very thoroughly.

Students who listen to his class will feel that mathematics is "alive".

The lectures given by Klein, the head of the mathematics department, were more like a carefully prepared, encyclopedic-style "perfect speech."

The difference between the two may also be related to Hilbert's better understanding of education.

The class Hilbert was taking at this time was ordinary differential equations. Since it was closely related to physics, engineering, and mechanics, many students from these three majors came to attend the lecture.

Hilbert first wrote two equations on the blackboard: y"=0 and y"+y=0, and then said:
"Gentlemen, this is where it all begins. Through these two equations, you can learn the entire theory, even the difference in meaning between initial value problems and boundary value problems."

The starting point is very simple, but after talking for almost 3 hours, it has been pushed to a very deep level.

——This is the tradition of Western universities. If you listen to mathematics courses offered by MIT, Yale, Cambridge and other universities, you will find that they are all in a similar style.

However, because Hilbert's lesson preparation was too casual and simple, he would fail during the lecture.

Sure enough, if nothing else happens, an accident will happen.

Hilbert couldn't move at a detail. He adjusted his glasses, looked at the dense blackboard calculations in front of him, and said to himself: "What is wrong?"

A student in the front row quickly discovered the error and reminded: "Mr. Professor, the symbol is wrong, here."

Hilbert examined it carefully for a while, shrugged and said, "That's true. I should have been better prepared."

But judging from the students’ usual reactions, it’s definitely not the first time Hilbert has been like this.

Hilbert said to the student: "Anyway, Weyl, thank you for the reminder."

Usually the job of pointing out errors is done by assistant Born, but today Weyl's eyes were obviously faster.

After all, Weyl was also a great mathematician later on, and one of the few mathematicians who could make significant contributions to both the theory of relativity and quantum mechanics.

Weyl then went to the Institute for Advanced Study in Princeton, where he was a colleague of Einstein and provided him with great help.