"Ling ring ring~~"

The alarm clock kept ringing, waking up Liu Yichen who was sleeping soundly. He opened his hazy sleepy eyes and his head was still a little heavy.

After washing up, I felt a little more awake.

Looking at the time, it was almost time for the banquet. He put on a suit and tie to look more formal.

He is not in a hurry to sort out the papers as soon as possible. No one will be stupid enough to plagiarize his research results in academic seminars like this.

There are so many well-known scholars, including at least seven editors-in-chief and associate editors of professional mathematics journals. People who can do such stupid things will probably not be able to submit articles to journals or academic conferences.

Even if you upload your paper to a website such as arxiv, it will be downloaded quickly. After all, there are so many math masters here, and no one dares to commit a crime.

When Liu Yichen arrived, the reception had already begun. In addition to Professor Tian, ​​there were four Chinese mathematicians participating. As for Xu Chenyang and Yun Zhiwei, they were not seen. Obviously, they were not qualified to participate in this kind of event.

A layered cocktail party.

As far as I can see, there are about a hundred people attending the reception, and every one of them is famous. They are at least first-class mathematicians, and many of them are Philippine Prize winners.

Qiu Chengtong and Tao Zhexuan came over in person, holding a goblet in their hands. Then they chatted with Liu Yichen for a while and gave some instructions.

"Liu Yichen, this is a special reception. The special thing is that everyone participating is a world-class mathematician. This reception can be said to be specially set up for you. You are also invited. It means that from today on, you can also be regarded as a world-class mathematician."

He is a first-class mathematician." Qiu Chengtong said to Liu Yichen in Chinese: "You will have to remember the names of these people in the future. How many connections you can accumulate in the future depends on how many of them you become friends with and how much mathematics you can gain.

The award also depends on them!"

"Tao Zhexuan had this advantage in the first place, and he was able to win the Fields Medal in 2006. Otherwise, he might have won the Fields Medal in 2010, but who knows whether there will be more outstanding mathematical results in the meantime."

Qiu Chengtong gave an example.

Liu Yichen looked thoughtful.

It seems that if you want to win big prizes in mathematics, in addition to having excellent results, you also have to work hard on your background and connections!

But think about the same principle. For the same level of achievement, one is an unknown mathematician, and the other is a world-renowned mathematician. Naturally, the latter has a higher probability of winning the prize.

Unless your results are overwhelming, such as Wiles proving Fermat's last theorem and Perelman proving the Poincaré conjecture.

After talking for a while, Qiu Chengtong, Tao Zhexuan and Professor Liu Yichen were among the crowd, talking and laughing happily, not at all as geeky as they usually behave.

Some of the mathematicians who participated in this special banquet were in the field of number theory, algebraic geometry, partial differential equations, topology, and mathematical analysis...

"Liu, you are just like Tao back then, full of incredible things!"

"It's incredible. When I was young, I also studied the 'Hail Conjecture', but unfortunately I failed in the end and failed to prove the 'Hail Conjecture'!"

"The mathematical method you used to prove the 'Hail Conjecture' is very good. I think it will be of great help to my research!"

"..."

Liu Yichen was a little surprised. He did not expect that these well-known mathematicians were all so kind and humble. They were not at all like the arrogant and self-respecting people in the legend.

The descriptions of pure mathematicians in the outside world are that they are geniuses, unconstrained, arrogant, arrogant, etc., as if they are a special group of people who are immersed in mathematics and cannot extricate themselves, reclusive and independent.

On this day, he saw about a hundred mathematicians. These mathematicians came from various countries in the world, mainly in Europe and the United States, and some were Russian mathematicians. From this aspect, we can also see the various aspects of mathematics in the world today.

In terms of the strength of foreign forces, if divided by country, China is still far away from a first-class mathematical country, while the United States, France, and Russia have the most mathematicians and are the most confident.

And he had to lament that it is not without reason that the United States can be called the center of mathematics in the world. Almost 40% of the world's famous mathematicians are concentrated in the United States, either as mathematics professors in major universities in the United States or as mathematics research institutes.

researchers, or serve as editor-in-chief or deputy editor-in-chief of professional mathematics journals.

In comparison, China is far behind, and it will probably take at least 30 years to catch up!

This kind of catching up is much more difficult than industrialization, and engineering catching up is even easier. Just like China today, it has completed modern industrialization and can be said to be an industrial country and the world's factory.

However, there is a big gap between China and China in mathematics, and it is not easy to catch up.

It was also on this day that the name Liu Yichen entered the eyes of every mathematician present. From then on, Liu Yichen became a figure in the world of mathematics.

...

At twelve o'clock in the evening, in the dead of night, Liu Yichen, who had changed into his pajamas after taking a shower, leaned on the pillow on the bed, squinting his eyes slightly, showing a thoughtful look.

There may be a distinction in academic value between mathematical conjectures and mathematical conjectures, but it is difficult to use a certain standard to measure the difficulty of a conjecture.

After all, there is no way to truly measure the difficulty of a conjecture that has not been proven at all!

However, the number of unproven mathematical conjectures in the world is currently greater than the number of axioms and theorems. There are more than a thousand mathematical conjectures based on the proof of the Riemann Hypothesis alone. In other fields of mathematics,

There are countless mathematical conjectures.

And if these mathematical conjectures have to be classified into different levels, it is not impossible.

If we put aside all non-academic factors such as political significance, economic significance, news rendering, etc., and only talk about the academic value "to the current mathematics community", then thousands of mathematical conjectures can be roughly divided into several levels.

The first level is like the "Seven Major Mathematical Problems in the World" proposed by the Millennium Clay Mathematics Institute, namely Riemann's Hypothesis, NP-Complete Problem, Yang-Mills Theory, Poincaré's Hypothesis, Hodge's Hypothesis, and Navier

-Stoke's equation, BSD conjecture. The Clay Mathematics Institute offers a high reward of one million US dollars for every mathematical conjecture. You can imagine its difficulty and value. In addition to the "Seven Major Mathematics Problems in the World"

, there are also some problems in Hilbert's 23 questions such as the compatibility of arithmetic axioms, the shortest line problem between two points using a straight line.

Once these conjectures are proven, they will not only promote the development of mathematics, but will also have a profound impact on other subject areas.

For example, the Riemann Hypothesis. Once the Riemann Hypothesis is proven, it means that more than a thousand mathematical conjectures based on the Riemann Hypothesis being true will be promoted to mathematical theorems; and once the Riemann Hypothesis is falsified,

That would also be a devastating blow to mathematics. The lifetime efforts of thousands of mathematicians would be ruined in one go, and many edifices built in the field of number theory would collapse and turn into ruins.

For example, Yang-Mills theory. The Yang-Mills equations that appear in this theory are a set of very meaningful nonlinear partial differential equations that have not been considered in mathematics. Solving it will play a great role in the development of pure mathematics.

Effect. Of course, the biggest effect of solving it is not in mathematics, but in physics. It will provide the most solid support for the unified theory of strong electricity in physics.

The second level is naturally the three most famous modern mathematics problems, Goldbach's conjecture, the four-color problem, and Fermat's last theorem. Two of them have been solved, and the remaining Goldbach's conjecture has stopped the best results.

The proof of '12' made by Chen Jingrun is only one step away from capping the building of Goldbach's conjecture. In addition, it is some of the problems in Langlands Program and some of Hilbert's 23 questions.

!

The third level includes some of Hilbert's 23 questions, as well as the Hailstone Conjecture, Zhou's Conjecture, Twin Prime Conjecture, etc.

The fourth level is some "weak conjectures" of the first, second and third level conjectures or some conjectures that are more meaningful for research.

The fifth level is the 'weak conjecture' or sub-conjecture of the fourth level conjecture, as well as mathematical conjectures like Sitapan's conjecture.

At the sixth level, this type of conjecture is the most numerous. Some may have research value, but the research value is not great. Some simply have no research value. This type of mathematical conjecture accounts for 90% of all mathematical conjectures. This

Many first-level conjectures are proven every year, and several papers can be published on the proof of a conjecture. At the same time, more conjectures are proposed every year.

If he can solve the first-level conjecture, then all the honors will be given to him. Even if the other party does not come to accept the award, it will be no problem. Just like Perelman, if it were not for his weird personality and maverick, he might have been eliminated long ago.

Promote him to be a god-like man. And for solving the second-tier conjecture, he will not be able to win any heavyweight mathematics awards such as the Fields Medal and the Wolf Prize in Mathematics.

Those who solve the mathematical conjectures of the third level are qualified to compete for the Fields Medal. Of course, this is just a competition, and it is not guaranteed to be obtained.

Liu Yichen has successively proved Zhou's conjecture and Hail's conjecture. It can be said that the nomination for the 10-year Fields Medal is stable. As for whether he can win the award, it depends on whether he is lucky enough. If he is lucky enough, he will win the award in one fell swoop. If he is not lucky enough, then

Just wait and work harder!

Of course, awards are only one aspect. There are also some figures who do not need any awards at all to show their greatness. For example, the 'Pope of Mathematics' Grothendieck laid the foundation for modern algebraic geometry and completely changed the field of functional analysis.

These two contributions made him the first person in contemporary mathematics, even though he had been living in seclusion for nearly twenty years!

However, a figure like Grothendieck may not be born in a hundred years. Even compared with Euclid, Descartes, Leibniz, Poincaré, Hilbert and others, Grothendieck

Tendyk was no less impressive.
Chapter completed!