After a simple lunch, which was also lackluster in Russia, Markov took Li Yu to the mathematics seminar room.
Li Yu saw that it seemed that the entire mathematics department had been invited.
Lyapunov first made an opening speech: "Dear students, as researchers of mathematics, we know that mathematics is the key to revealing everything in the world, and it is the secret method hidden in the darkness that controls the operation of the world.
“For hundreds of years, ever since Peter the Great opened the window to the west and looked at the prosperous and developed Europe through the blue Baltic Sea, we have been moving forward and following, hoping to achieve a goal comparable to Paris, London, and Gorgentia.
strength.
"But just when we had no time to look eastward, in the far east, in the mysterious country, such a great scholar was quietly born. With his profound and mysterious characters, he made us realize once again how great mathematics can be, and how hidden its hidden meanings are.
The mystery of is so close to us.
"He is the one who continued to explore X-rays, expanded thermodynamics, observed the trajectory of Pluto, and now reveals the order in chaos - Li Yu!
“Give us a warm welcome!”
The students in the audience immediately burst into warm applause.
Li Yu really didn't expect Lyapunov's speech to be so powerful. Sure enough, Russian academics also know some art.
Russia is really a magical country. On the one hand, it is full of barbarism and absurdity, and magicians like Rasputin can rise to the top; on the other hand, it longs for modernity and civilization, giving birth to Tolstoy, Mendeleev,
A world-wide great man like Pavlov.
Those who engage in magic can be so dedicated that they may even shake the foundation of the country; those who engage in academics can also shock the past and present and become famous in history.
Li Yu saw that almost all of the hundreds of students in the audience were holding a copy of "Fractals and Chaos" written by him, so he said: "When it comes to mathematics, I have only scratched the surface and can only speak in a few fields.
If something is wrong, please discuss it together and welcome corrections.
"I came here today, according to what Professor Lyapunov told me, to study and discuss new ideas in mathematics with you, such as the theory of chaos. I have written many interesting fractal structures in my book, and I want to introduce them to you today.
A kind of magic triangle."
Li Yu drew an equilateral triangle on the blackboard behind him, and then connected the midpoints of the three sides to form four equilateral triangles.
Continue to connect the midpoints of the equilateral triangle with three corners as above. This is the Sierpinski triangle in later generations.
Li Yu said: "I once wrote in a book that fractals are like Russian matryoshka dolls. They still have fine structures in an infinitely small range. I think you are the least unfamiliar with it."
Immediately, some students in the audience set up several matryoshka dolls: "Yes, Professor Li, we now privately call your fractal structure the 'matryoshka doll structure'. It's really similar."
Li Yu said with a smile: "Yes, very appropriate! You can see that if you follow this pattern and subdivide it infinitely, it is also a fractal structure. But what we want to explore today is how to use mathematics to find its dimensions."
Since he was in the Department of Mathematics, Li Yu would of course have to talk more about mathematics.
Fortunately, the dimension problem has been studied before by the German mathematician Hausdorff, and the explanation is not very difficult. The most important thing is the mathematical ideas embodied in it.
The discussion of ideas is also what Lyapunov focuses on today.
After Li Yu finished talking about fractals, he continued to discuss with them the chaos phenomenon in the field of differential equations. These were all relatively mathematical, but they were very harmonious when studying together with students from the mathematics department.
The students in the audience were very enthusiastic. Although Li Yu did not have a computer or a PPT screen, and the progress of his speech was very slow, the discussion atmosphere was very strong.
The seminar lasted for most of the afternoon, and by the end, even people from the physics, chemistry, and biology departments of St. Petersburg University came to observe.
Because there were so many people, Lyapunov had to use the school auditorium the next day, and almost turned it into a speech again.
At the end, many people came to Li Yu with copies of "Fractals and Chaos" to sign.
The past two days were almost spent on seminars and lectures in the Department of Mathematics and Mechanics. It was not until the third day that Li Yu finally had time to visit Mendeleev in the morning.
Li Yu has a habit of doing morning exercises. In fact, he happened to see the 68-year-old chemistry legend in the garden.
"Hello, professor!" Li Yu went up to say hello.
Mendeleev glanced at Li Yu and immediately understood: "Are you the Chinese Li Yu who has been lecturing in the Department of Mathematics these two days?"
"Yes, that's me." Li Yu replied, "It's an honor to meet you!"
Li Yu knew that Mendeleev had studied in Germany for many years and spoke German very well, so he started communicating with him directly in German.
Mendeleev started with some differences: "Do you speak German?"
Li Yu smiled and said: "Yes, Professor, I really haven't learned Russian well."
"It doesn't matter," Mendeleev also said in German, "I do know about you. During this period, you were often reported in the news and in the university newspaper. You are worthy of being admired by the old president, Lord Calvin. Come on.
Come on, come and sit in my office."
Mendeleev's office was as unruly as his beard. There were many books, manuscripts, and documents, and they were not very organized.
Li Yu saw a copy of Mendeleev's periodic table of elements hanging on the wall, which was his life's work.
A few decades ago, there were actually many people who made the chemical periodic table. The German Meyer published the periodic table of elements almost at the same time as Mendeleev. Moreover, Meyer's fame, prestige, and status at that time were much higher than those of Mendeleev.
Terev was great. If these two people were compared around 1880 to see who was the greater theoretical chemist, most people would probably choose Meyer.
And what is hard to believe is that Mendeleev did not believe in atomic theory, let alone electrons.
Of course, these belong to the realm of physics.
However, the reason why Mendeleev became synonymous with the periodic table of elements is indeed because he had a profound understanding of the elements. Others only tried to arrange the elements in rows. But Mendeleev spent a lot of time in the laboratory.
He has spent his whole life studying the properties of elements and how they will react. His understanding is much deeper than others.
The key is that Mendeleev was not as conservative as Meyer at all. His first version of the periodic table brought together all 63 elements known at the time.
Mendeleev went on to boldly predict many new elements, and even urged geologists anxiously: "Look hard, you will definitely find it!"
It's hard to predict something like this.
Mendeleev categorically predicted the emergence of "aluminum-like" elements (later known as "gallium" elements).
A few years later, Lecoq actually discovered it. It was the first element discovered since Mendeleev published the periodic table in 1869.
The most interesting thing is that after Mendeleev read the discoverer Lecoq's data on the element gallium, he directly told the experimental chemist that there must be something wrong with his measurements because the density and mass of gallium were different from his predictions.
.
As soon as Mendeleev said this, the entire chemical world was stunned. Everyone felt that Mendeleev was too arrogant.
But soon, people discovered that Mendeleev was right: Lecoq retracted the original data, and the republished experimental results were completely consistent with Mendeleev's predictions!
The scientific community was shocked to discover that the theoretical chemist Mendeleev actually understood the properties of new elements better than the chemists who personally discovered them.
He is definitely the God of Chemistry!
So Mendeleev is so important to the subject of chemistry. His periodic table of elements is the guiding light for chemical elements in the future. It can even be said to be a direct warning to everyone: Stop messing around and just do what I say.
Find it!
The effect is almost the same as the impact of Hilbert's 23 problems on mathematics and the impact of Kelvin's "two dark clouds" on physics.
Science is never accomplished overnight by one person. In general, Mendeleev's work is like Darwin's theory of evolution and Einstein's theory of relativity. Neither of them did all the work by one person, but they made the greatest contribution.
And it's done more beautifully than others.
As Newton said: "If I have seen further than others, it is because I stand on the shoulders of giants."
Anyway, Mendeleev became an immediate success, and even the Tsar gave him special praise.
Mendeleev's status in Russia can be seen from one incident: a few years after the discovery of gallium, he divorced and wanted to marry another man. The conservative local church told him that he had to wait seven years, but he bribed a
A priest, the wedding was successfully held. According to the law at the time, Mendeleev was suspected of committing bigamy, but no one dared to arrest him.
The reason is that the Tsar himself spoke out: "I allow Mendeleev to have two wives, because I only have one Mendeleev."
Just so arrogant.
The Mendeleev's periodic table hanging in front of Li Yu's eyes was not what he learned in middle and high school chemistry classes. Mendeleev's periodic table was a short column form, that is, a short form table.
And there are only about 70 elements now.
Li Yu looked at the watch and silently compared it with the periodic table in his mind.
After Mendeleev found out, he said: "Do you also understand the periodic law of chemical elements?"
"I did learn it once," Li Yu said frankly.
"Oh?" Mendeleev became interested, "Anyway, I don't know mathematics. If you know chemistry, we can talk more about it. Let me think about it, you are from China... Ah, by the way, China! Sweden has been here from time to time in these years.
Mentioned to me that they had found several elements similar to Cerium in my periodic table."
Li Yu didn't understand for a moment, "Cerium?"
Mendeleev stood up and pointed to position 58 on the periodic table of elements.
Li Yu suddenly realized that it was cerium.
No wonder he didn't realize it at first. This thing is the second of the lanthanide elements in the bottom two rows of the periodic table of elements.
Cerium was the only lanthanide element known when Mendeleev published the periodic table in 1869. It was not the first element "lanthanum" in the lanthanide series known to later generations.
Li Yu said: "I'm really sorry, I only know that this family of elements has similar properties, and I'm not very familiar with the others."
Mendeleev said: "Don't be sorry, I also have a headache with this family of elements. They are too similar."
Li Yu thought hard in his mind. Although he could memorize the first 36 elements very skillfully, and his various chemical properties had been very familiar with them through several years of examinations in middle school and high school, he was really not familiar with the lanthanide series elements.
Very unfamiliar.
When I was taking chemistry class, the lanthanide and actinide elements were basically in the cold palace. Who would care about them during class?
Li Yu only knew that these things were all rare earths and should not be of much use now. It was not until many new materials appeared in modern industry many years later that they began to shine.
Li Yu's mind turned around. He just mentioned China, why didn't he think of it!
Li Yu said: "You mean ceramics?"
Mendeleev nodded: "Yes. Since Sweden mastered the art of making porcelain and discovered feldspar and clay minerals decades ago, they have reported seven new elements, which can be compared with my periodic table.
Yes, because I've reserved a spot for them, but I still feel like they're a mess."
"After all, they are rare earths. I know they often mix together." Li Yu said.
"It is true that there are few, otherwise Europe would not have figured out how you Chinese can make exquisite porcelain so late." Mendeleev said.
Li Yu knew in his heart that rare earths were not "rare" at all, and it was impossible for modern industry to rely on rare elements if it wanted to develop on a large scale.
Rare earths are widely distributed in the earth's strata, but rare earth mines were indeed very few in the 18th and 19th centuries.
Mendeleev continued: "They are so similar that it is difficult to figure out. The Academy of Sciences once asked me to predict "cerium-like" just like "aluminum-like", but I can only regretfully say that I can't do anything."
Li Yu saw Mendeleev's helplessness, "You are referring to the long series of blanks on the periodic table, right?"
Mendeleev said: "Yes, I got their order wrong several times, and even Sweden later told me that the previous elements were actually mixtures."
This was a big problem in chemistry at the beginning of the 20th century, and spectral analysis was not easy to use when it came to lanthanide elements. Even if scientists have detected dozens of new color bands, they still don’t know how many new elements they represent.
Mendeleev said: "I am very curious about how the Chinese mastered these elements and then created so many brilliant and eye-catching colors on the surface of porcelain."
Li Yu's mind was full of a laughing and crying expression, and he said: "Professor, your question is really hard for me to answer. Maybe it's due to thousands of years of experience."
The bright colors are a gift from lanthanide elements, and the mineral deposits discovered in Sweden were rich in lanthanide elements.
The rare earth elements in the earth's crust were originally evenly distributed, but it was as if someone poured the entire spice rack into a bowl and stirred them, causing them to become entangled and aggregated together.
However, the Chinese people are actually much simpler when it comes to porcelain. They simply call them kaolin and feldspar, and just use them if they are easy to use. We cannot expect people a thousand years ago to understand chemical elements.
Mendeleev said: "That's true. It seems that this problem will continue to bother me."
Although Li Yu didn't know much about lanthanide elements, it seems that this issue can be considered from another angle. He said: "Professor, you can leave it aside for now. After all, at least 10 rare earth elements will appear in the future. Moreover, I know a new cycle."
The table arrangement is just right to save rare earth elements from trouble."
Mendeleev was surprised: "New arrangement?"
"I'm presumptuous." Li Yu picked up a pen and paper and started writing.
Ten minutes later, Li Yu picked up the manuscript paper and said, "Professor, take a look."
In fact, Li Yu drew the long periodic table of chemical elements that he was familiar with.
This kind of periodic table is arranged horizontally according to the atomic weight and the properties of the elements. The positions of the main and sub-group elements are clear and do not interfere with each other. It is also very friendly to beginners and easy to popularize.
Mendeleev looked at it carefully for a while, and immediately felt the advantages of this arrangement, and praised: "You are really creative. This makes it much easier to check."
Mendeleev praised Li Yu and felt a little embarrassed, because this was basically the periodic table that he was familiar with from the beginning of his exposure to chemistry, and there was nothing creative about it.
Li Yu said: "It's nothing at all, it's just changing from vertical to horizontal. If the professor thinks it's okay, given your status in the chemistry community, maybe you can promote it."
Mendeleev believed deeply: "People today have too little understanding of chemistry, and many people still think that chemistry is alchemy. If such a clear table of elements can be used, it can indeed change many people's views. Look.
When Markov came to ask me to sign, he was really right. You came to St. Petersburg and helped me a lot."
Li Yu said: "I can't say it's a big deal."
"No," Mendeleev said, "I say busy means busy! I will definitely mention your contribution to the periodic table in the new book, you deserve it."
Mendeleev was in a good mood, "You gave me such a good thing, what should I give you as a thank you? Don't refuse."
Li Yu smiled and said: "I gave the professor a handwritten periodic table, and I also hope that the professor can give me a manuscript where you wrote the periodic table of elements."
"You are so funny!" Mendeleev laughed, "No problem!"
If Li Yu had not written down the long-form periodic table in advance, Swiss chemist Werner would have done this work three years later.
In fact, this is really not an important discovery, because when it comes to the periodic table, no one will think of Werner. Of course, the one who remembers it is Mendeleev who made the original pioneering work.
As for this purely formal innovation, it is really similar to what Michelson said. An improvement would be:
The edifice of the periodic table of elements has been basically completed, and future generations are just doing a little tinkering.