"Algebraic Geometry".

He has been looking forward to this course.

In the past, whether it was "Partial Differential Equations", "Functional Analysis", or other courses, the mathematics taught in it can be said to be mathematics from a hundred years ago.

Those knowledge contents existed hundreds of years ago, or even hundreds of years ago.

Undergraduate mathematics courses in colleges and universities may sound very advanced. To put it bluntly, the contents were all studied by mathematicians a hundred years ago. Even mathematicians a few hundred years ago studied much more advanced mathematics.

For example, Bornhard-Riemann studied Riemannian geometry 170 years ago, but the knowledge areas covered in undergraduate courses are far from the level of Riemannian geometry.

"Algebraic Geometry" is the real modern mathematics.

"Algebraic Geometry" studies the geometric properties of the set composed of several common zero points of algebraic equations in dimensional space.…

This explanation sounds complicated, but it is easy to understand with an example.

X2 Y2=1 (square), a standard plane equation, and the corresponding geometric figure is a circle.

This is a high school mathematics level understanding, which studies the real solutions of equations.

If placed in the content of "Algebraic Geometry", what is studied is not the real number solution, but the complex number solution. In the real number solution, it is a standard circle, but if it is a complex number solution, it becomes a ball.

Expanding further, what about X3 Y3=1 (cubic)?

The graph of this equation becomes a ring. When the power n is greater than 3, the corresponding graph becomes very complicated and difficult to understand by relying on imagination.

This is "Algebraic Geometry", which studies the graphics formed by the corresponding solutions of equations, and studies algebraic problems in a geometric way.

"Algebraic Geometry" is related to many fields of mathematics, such as number theory, analytic geometry, commutative algebra, differential geometry, topology, etc. Some of the methods it contains are great references and references for other disciplines.

Value.

The reason why Wang Hao is looking forward to this course is mainly because he wants to expand his knowledge field.

His main research directions are partial differential equations and number theory, and many mathematical disciplines are related. Expanding the field of knowledge is very helpful for studying mathematical theories.

At ten o'clock, the students all arrived in the classroom.

Wang Hao's courses are very popular, and students are looking forward to them.

After entering the new semester, Wang Hao's mentality became much calmer. Because it is a postgraduate course, there is no need to ask students to do anything, and most students will listen carefully.

In addition, many of the students were not new faces, and most of them were even familiar faces. He did not teach anything about classroom discipline and went directly into the course.

Wang Hao stood on the podium, walked down and said, "This course is called "Algebraic Geometry". Some students know the content, and some don't, but you must first understand one question. "Algebraic Geometry" is the real

of modern mathematics.”

"And a lot of the mathematical content you have learned before cannot be said to be ancient mathematics. The content is also the knowledge gained by mathematicians hundreds of years ago, or even hundreds of years ago."

"To study "Algebraic Geometry", first we must understand a mathematician. Most people have never heard of this person. His name is Grothendieck. He is a stateless Jew and a very legendary mathematician."

"His research has made the Institute of Advanced Studies in Paris recognized as the world's research center for algebraic geometry. At the same time, many of the algebraic geometry content we can learn now are the results of Grothendieck."

Grothendieck was a very thoughtful super genius and one of the most influential mathematicians of the 20th century. He is even considered by some to be one of the greatest mathematicians of the 20th century.

He has been studying algebraic geometry for a total of about 12 years. In these 12 years, he has written tens of thousands of laws of algebraic geometry. One person has almost built the entire system of algebraic geometry.

Grothendieck's ideas are also important.

At that time, mathematics was considered a method of solving problems. If there was a problem, then a mathematical method should be used to solve it. Grothendieck believed that mathematical research should not just solve mathematical problems, but should study a whole set of mathematical theories.

If the problem is found directly in theory, everything can be solved.…

His thinking has played a very important role in promoting the research and development of current mathematical theory.

Unfortunately, geniuses often have radical personalities.

Because of the war he experienced when he was young, Grothendieck was a radical pacifist, and he was willing to give up his mathematical research for the sake of the war.

Grothendieck, who was only 42 years old, gave up his favorite mathematics research because of the YUE war, and simply went to Hanoi to give lectures on mathematics.

Later Grothendieck simply went to the Pyrenees in southwestern Europe and became a reclusive Buddhist. He even refused the Crawford Prize and the US$250,000 bonus on the grounds that he believed the money should be spent on

On the young and promising mathematician.

After that, Grothendieck remained in seclusion until his death quietly a few years ago, with few media even reporting on it.

Wang Hao explained the development history of "Algebraic Geometry", which also made the students immersed in it, and they felt the greatness and radicalness of Grothendieck. At the same time, they also realized that "Algebraic Geometry" is indeed modern mathematics.

The emergence and development of this discipline are very recent, and it can only be traced back for only fifty years.

…

While Wang Hao was taking his own course, Xia Guobin was in the office of the Navitas laboratory, carefully reading every word of the message he received.

The news above made him feel refreshed.

That was news from the Aeronautical Materials Institute. They had formed a team of experts and were preparing to visit the NanoVis laboratory.

This seems a bit uninvited. Even the Institute of Aeronautical Materials and the Nano Laboratory are on the same level. They are just scientific research institutions, and there is no superior-subordinate relationship.

But Xia Guobin doesn't care about coming uninvited. What's important is that the other party is the Institute of Aeronautical Materials. What are the experts from the Institute of Aeronautical Materials doing in the NanoLab?

This is probably to check the laboratory conditions, and there may be a big project!

For NanoVis Laboratory, the aviation group only allocates a small amount of R&D funds, which is enough to make them full.

Project is one aspect.

On the other hand, Xia Guobin also felt that his efforts to develop the laboratory had yielded results, which had been noticed by the aviation group, and a team of experts was specially sent to inspect.

This is so exciting!

Xia Guobin couldn't control his emotions. If he were ten years younger, he might have jumped up and cheered in celebration.

He immediately went out and seriously asked everyone to cheer up.

"The expert team from the Institute of Aeronautical Materials will be here in a few days. We must let them see the capability level of the Nanolab, let them see our mental outlook, our focus, devotion and seriousness in treating research projects...

"

Xia Guobin made a series of remarks, which meant that he must leave a good impression on the expert team of the Institute of Aeronautical Materials.

…

The next day, the complex office.

Wang Hao was sitting in the office, drinking coffee leisurely and chatting with other people. He was not talking about the Kakutani conjecture, but he also paid great attention to the submission status.

When you open the submitted manuscript and check the status, you will find that the manuscript has quickly entered the second review stage.

This progress still makes him satisfied...

"Second review? What experts will be the reviewers?"

"Princeton? The Clay Institute? Or the Swedish Academy?"

These are all possible.

For a top mathematics journal such as "New Advances in Mathematics", the review expert team is not limited to one country.

at the same time.

Qiu Chengwen was sitting in his office, checking newly received email messages. He found that the editorial department of "New Advances in Mathematics" had sent a mathematical proof.

Below is a message from Bruce Pulitzer, "Professor Qiu, this is part of the proof of the hail conjecture.

Thanks again!"

Qiu Chengwen downloaded the content with interest. Looking at the two pages of proof content above, he found that it contained a very subtle conversion method. After a quick glance, he knew that there should be no problem.

He couldn't help but wonder again, "Is the Kakutani conjecture going to be proven?"

"Maybe……"

"That's just part of it."

Qiu Chengwen couldn't help but think of Wang Hao. He remembered that when Wang Hao came to the Mathematical Science Center, he said that he was studying a new mathematical method that could be used to prove the Kakutani conjecture.

Now the Kakutani conjecture is about to be proven.

"This is interesting."

"It seems that Wang Hao's research is too slow! If he knew this proof, he might give up his research."

Qiu Chengwen thought and sighed.

Scientific research is sometimes like this. Someone spends several years studying a problem, but before the research is completed, it turns out that it has been proven by others.

Several years of hard work were in vain...

"I hope Wang Hao won't be too hard hit..."
Chapter completed!