Chapter 237 New Proof Idea
Compared with the lively worship ceremony in the village ancestral hall, the full moon banquet held by Xu Yuan for his daughter two days later attracted more people. Even the leaders from the city came accompanied by Wang Jianan, although they only gave gifts and blessings and did not stay for dinner.

And the next one is the Mid-Autumn Festival.

Thinking that I haven’t celebrated the Mid-Autumn Festival in my hometown for a long time, I thought about returning to Yanjing a few days later.

September 2013, 9, Thursday, Mid-Autumn Festival.

night.

Because of the weather, I couldn't see the bright moonlight when I looked up.

Xu Yuan simply ate some mooncakes, and while his family was sitting in the living room chatting, he got up and went into the study upstairs.

There are not many people living in the house in my hometown, and there is only a desk and a solid wooden bookshelf against the wall in the study.

There are less than twenty books placed on it.

However, there were a lot of draft papers scattered on the desk.

If you look closely, you can see all kinds of complex formula symbols, and not just mathematical formulas.

It also includes physical aspects.

"It's really not easy to find a suitable way of thinking. It really deserves to be the most abstract mathematical problem in the world."

Xu Yuan sat on the chair and started to organize the manuscripts.

Muttering to himself.

During the days he is at home, he will still sit in the study when he has time in the evening.

Take the opportunity to demonstrate the new method you came up with.

See if we can push forward the proof of the Hodge conjecture and spark some inspiration.

Unfortunately, there was no gain.

Since completing the design of the hypersonic missile's appearance and participating in the calculation of the missile's trajectory, he has used mathematical analysis and other mathematical branch methods to successfully make the panel progress bar reach 50%.

In a sense, he was already halfway to proving the Hodge conjecture.

Originally, at this pace, we would have been able to completely prove the Hodge conjecture, a world-renowned mathematical problem, before next year's International Congress of Mathematicians.

As a result, we encountered a bottleneck again.

This is like forgetting an important formula halfway through a problem.

Only by remembering this formula can you continue to solve the problem.

But the problem he faced now was not to remember the formula, but to create it.

And make sure it is logical.

After all, after the proof of each difficult mathematical problem in the world is announced, mathematicians around the world will conduct a long period of argumentation. Even if any loophole is found, it will be considered an unsuccessful proof by the mathematical community.

Of course he doesn't need to worry about this.

As long as the progress bar reaches 100%, it means that he has completely proved the Hodge conjecture.

Don't be afraid of anyone's arguments.

Previously, he recalled that he had used physical methods to promote mathematics when studying the Monge-Ampere equation and proving the optimal transmission theory.

Finally, remarkable results were achieved.

He has tried many branches of mathematics to prove the Hodge conjecture.

However, the arguments are not valid.

In this case, perhaps using physical methods can be effective, after all, physics and mathematics are inseparable.

Many physical formulas can be applied in mathematics.

For example, when learning calculus, you can understand it in a physical way.

The thought stopped here, and he didn't waste any more time. He immediately picked up the pen and continued to deduce based on his previous train of thought.

Soon I was immersed in it and entered a state of deep learning.

All the sounds from the outside world seemed to be isolated, and my thoughts seemed to be galloping on a highway.

Will not be affected by surrounding factors.

Even the passage of time seems imperceptible.

At this time, Xu Yuan was completely in his own world, with mathematical knowledge and physical knowledge constantly colliding in his mind.

Just to find the critical point that can solve the Hodge conjecture.

"The basic framework of homology algebra is realized by taking the sum of morphisms and objects and using commutative categories."

"You can try the Abelian category."

"We have to find conditions that ensure that a shape can be described by a polynomial after topological transformation."

"Only by finding this condition can topology and algebraic geometry be connected."

“It completely opens up a new world of mathematical research.”

……

With a large number of thoughts constantly colliding in his mind, Xu Yuan finally focused his attention on the Abelian category.

Try to extend it through related concepts such as Abelian gauge field theory in the quantum field of physics.

Hoping to find the conditions that connect topology and algebraic geometry.

As time passed, the expression on Xu Yuan's face became more and more serious.

There are even some surprises occasionally.

I don’t know how much time has passed.

Just as he was holding the pen and writing down another formula on the draft paper, his hand suddenly stopped the next second.

The whole arm is suspended above the draft paper.

Like something was discovered.

At this time, his eyes were no longer on the draft paper, but on the progress bar on the panel.

-

Task: Proof of Hodge conjecture

Subject: Mathematics

Progress: 52%
Result: Not completed
"The progress has actually increased!" He murmured subconsciously as the content information came into his eyes. The progress of proving Hodge's conjecture has been stuck at 50% for quite some time.

No matter how he used the previous method to deduce, he couldn't make the progress bar grow.

I didn't expect that after using physical methods, the time increased by 2% in such a short time.

Although this 2% may seem small, its significance is immeasurable.

At least it shows that his current general direction is correct.

This represents hope.

He originally thought that the progress of proving Hodge's conjecture would be put on hold and that he might not be able to realize what he had said before.

Although this is not a big deal, it will at most be discussed in the mathematics community.

But now his confidence has greatly increased.

If we continue researching in this direction, we will be able to complete the proof soon based on the growth rate of the progress bar.

Abelian gauge field theory belongs to the field of quantum mechanics, and the most important mathematical aspect is the commutative category.

Although the study of quantum mechanics originated very early, more than a hundred years ago, it has only recently begun to gain popularity in China, and the number of scholars engaged in research has gradually increased.

It is believed that quantum mechanics has great research value and can promote the development of human civilization.

Although Xu Yuan was not unfamiliar with quantum mechanics, it was not his area of ​​expertise.

If I want to continue my research and apply it to mathematics, it may not be efficient to just read the materials and study on my own.

It’s best to ask the right person for advice.

This will help the progress bar grow and help solve this world mathematics problem as soon as possible.

The thought stayed in his mind, and a figure quickly emerged in his mind.

"It seems that I have to visit Mr. Yang after I return."

As a Nobel physicist, Mr. Yang proposed the Abel gauge field theory as early as the 1950s, for which he won the Nobel Prize.

At the same time, it has opened up new research directions for quantum integrable systems and many-body problems.

He had met Mr. Yang when he was just starting to make a name for himself in mathematics, and the other party also hoped that he would study physics.

Now that I have taken the initiative to ask for advice, I am sure the other party will not refuse.

Just as I had decided on the next itinerary, a shout from outside the door suddenly reached my ears.

"Xiao Yuan."

Hearing his mother Liang Yanli's voice, he immediately got up and walked over, opening the door from the inside.

"I called you just now but no one answered. I was a little worried." Liang Yanli was relieved when she saw Xu Yuan appear in front of her and said with concern, "It's getting late. You should go back to your room and rest."

Xu Yuan knew that he was immersed in deep learning just now, and he didn't hear it because of the door.

So he explained:

"I'm quite absorbed in studying a question. I'll finish now."

Now that the new direction for studying the Hodge conjecture has been determined, there is no need to pay too much attention to this short period of time.

I'd better wait until I get back to Yanjing to ask questions first.

As he said this, he closed the study door and walked towards the bedroom.

Liang Yanli did not ask too many questions about this. After all, she knew very well what her son was exposed to now, and she would not be able to understand it even if she knew.

Why should I bother my son to explain himself?

It’s enough to know that my son is healthy and our family is harmonious.

……

After the Mid-Autumn Festival, and with the progress bar still on his mind, Xu Yuan decided not to delay any further.

After arranging the vehicle, we returned to Yanjing.

On the day he left the village, many villagers spontaneously came out to see him off, creating a warm scene under the stone archway of Xuzhai Village.

As for the local specialties and other things that everyone gave him, due to their overwhelming enthusiasm, Xu Yuan could only accept a few symbolically.

Then we got in the car and headed to the city station.

On the second day after returning to Yanjing, Xu Yuan arrived at the campus of Qinghua University in the morning.

But he wasn't going to his own office.

The Institute for Advanced Study is located in the Science Museum on the Qinghua campus, and Professor Yang’s office is located on the second floor.

Although Mr. Yang is already 90 years old, he still insists on going to the office to work every day.

Consult academic materials and conduct academic exchanges with younger generations.

Fortunately, the other party lives in the master's residence on campus, which is not far from the Science Museum.

Soon Xu Yuan arrived at the Science Museum, and just as he was about to go upstairs, he saw a familiar figure.

It was Qiu Chengtong who joined the Institute for Advanced Study.

"Why did you think of this today? Do you have something to talk to me about?"

Qiu Chengtong noticed Xu Yuan's figure, walked over and greeted him.

Upon hearing this, Xu Yuan answered truthfully:

"I have some questions that I would like to ask Mr. Yang for advice."

Hearing Xu Yuan's words, Qiu Chengtong looked a little confused, wondering why Xu Yuan was interested in physics again.

Although he really wanted to ask about the proof of Hodge's conjecture, he swallowed the words back when they came to his lips.

I was worried that it would bring unnecessary pressure to Xu Yuan and have a negative impact on him.

So he just nodded in the end and mentioned Mr. Yang's situation: "Then you should go over quickly. He happens to be in the office right now."

After being reminded by Qiu Chengtong, Xu Yuan did not delay any longer and immediately went upstairs.

Qiu Chengtong, who stayed on the first floor, looked at Xu Yuan's back until he disappeared from his sight.

He shook his head and sighed softly: "Will I really have the chance to witness another difficult mathematical problem being proven in my lifetime?" He himself was unsure when he said this.

……

(End of this chapter)