Chapter 244 Entering the Highest Hall of Mathematics

It can be said that Rotter's arrangement was very effective. During the nine-day International Congress of Mathematicians, hundreds of famous mathematicians gathered together to discuss the proof of the Hodge conjecture.

Use various methods to verify whether the conclusion is valid.

Even many domestic mathematicians attending the conference joined the argument.

And the areas that everyone is good at are basically algebraic geometry, topology and mathematical analysis.

Because of this, they all hoped that Hodge's conjecture could be completely proven this time.

After all, turning the conjecture into a theory will open up new methods and expand their research in algebraic geometry and topology in the future.

Therefore, he was very attentive during the entire argumentation process.

Even at night, I would choose to work overtime to verify the calculations.

Perhaps it was precisely because mathematicians were studying the proof process that only ordinary people discussed it online in the next few days.

It was rare to see mathematicians speaking.

But the more this happens, the more everyone feels a sense of anticipation before the storm.

As long as the international mathematics community announces that it recognizes the validity of Xu Yuan’s proof of the Hodge conjecture.

Then the whole world will surely fall into carnival in an instant.

Sunday, August 2014, 8, in the Seoul Exhibition and Convention Center Auditorium.

There were no one-hour or forty-five-minute presentations in this large lecture hall.

Look around.

You can see many mathematicians finding the right posture and doing a lot of calculations on scratch paper.

There were even a lot of manuscripts scattered on the table.

Even my hair became messy because I didn't have time to clean it.

If I had to use two words to describe it.

The best is madness.

I was completely attracted by Xu Yuan's proof process and immersed in the ingenious ideas therein.

It lasted for a whole week without any pause.

After all, the main Hodge conjecture brings together the most abstract concepts and can be said to be the most counterintuitive.

In this case, not only is the proof unimaginably difficult, but even the reverse deduction is quite complicated.

It cannot be completed in a short time.

Even though there were so many famous mathematicians present.

At this moment, Martin, professor at the University of Warwick and winner of this year's Fields Medal, suddenly stopped what he was doing, stood up straight and looked at the draft paper in his hand.

A very excited expression appeared on his face.

"Perfect."

“It’s just perfect.”

"This is simply a great work of art. Xu is truly the most gifted mathematician I have ever met."

While shouting to himself with a big smile on his face, he quickly attracted the attention of others around him.

The next second, someone seemed to have thought of something and started asking impatiently.

"Martin."

"Have you completed your argument?"

Martin calmed down when he heard someone calling his name and turned his head to look at the other person.

Then he nodded heavily.

"I think so."

"After deducing and arguing in the reverse direction, we can confirm that the conditions given by Xu in the proof do establish a connection between algebraic geometry and topology to a certain extent."

“This will be a major academic achievement in the mathematics community.”

"Xu has entered the highest hall of mathematics and deserves everyone's admiration."

Martin was not stingy with his praise for Xu Yuan. Although he was much older than Xu Yuan, at this moment he had transformed into a little fan with a face full of admiration.

As Martin was the first to bring the good news, others in the lecture hall were unwilling to lag behind.

Soon, the results of the demonstration were obtained one after another.

Basically the same as Martin's.

Confirming that the conditions given by Xu Yuan are valid indeed establishes a connection between algebraic geometry and topology.

This also marks the complete resolution of the Hodge conjecture, a world mathematical problem that has remained unsolved for so long.

Since the Clay Mathematics Institute proposed the seven Millennium Prize problems, after Perelman solved the Poincare conjecture, the Hodge conjecture was successfully proved after all these years.

There are only five of the world's most difficult mathematical problems left for the mathematical community to solve.

Faced with such a grand event in the mathematics world, everyone was undoubtedly very excited.

"It's incredible that Xu could come up with such a method to prove the Hodge conjecture. It was beyond the expectations of the entire mathematics community."

“His inspiration never seems to run out.”

"It's hard to imagine that such a mathematician could be born in China!"

"Forgive me for not thinking highly of him before. I didn't expect he would give me such a big surprise."

"It seems that as long as he says something, he can definitely do it. From now on, this conjecture will be called the Xu-Hodge Theorem."

……

Since Rothar learned that Xu Yuan had completed the proof of the Hodge conjecture, he has been very concerned about whether his conclusion is valid.

After all, this is related to whether the International Mathematical Union can officially announce it to the mathematical community.

Seeing that tomorrow is the day when the International Congress of Mathematicians ends, he is quite anxious about it.

I will follow the progress of the demonstration when I have time.

Today, as soon as he arrived outside the lecture hall, he found that it was not as quiet as before. Instead, it seemed very lively.

After standing at the door and listening for a while, I learned that someone had already completed the argument, so I walked in impatiently without even saying hello.

He immediately asked, "What is the result of the argument?"

There was no attempt to hide the anticipation on his face.

Martin was somewhat familiar with Rotter because it was he who was awarded the Fields Medal.

Answer immediately when asked:

"Mr. Rothel, we are sure that Xu has completely proved the Hodge conjecture and his conditions are valid."

The voice just fell.

The next second, someone else took over the conversation and added something.

"We used different methods to verify the derivation, but ultimately did not find any errors. These steps not only completed the proof, but were more like a piece of art carved out with great care."

"It is clear that Xu, like Perelman, has made indelible contributions to the mathematical community."

"I propose that it should be announced to the world immediately."

Rotter was naturally aware that he had to maintain the authority of the International Mathematical Union and could not rashly announce the news that the Hodge conjecture had been solved.

But he knew better that the people in the lecture hall were all well-known mathematicians in the field of mathematics.

Their conclusions can, to a certain extent, represent the international mathematics community.

So the thought stayed here, and he no longer hesitated and made a decision immediately in front of many mathematicians.

"This is indeed good news, and this event is not just for our mathematics community, but something the whole world should know about."

After saying this, he did not stay in the lecture hall for the rest of the time and left quickly to do this.

Perhaps it was Rotter's personal order, and the International Mathematical Union also showed a rare high efficiency. It issued an announcement through official channels that day, announcing that Xu Yuan had proved the world's mathematical problem Hodge conjecture.

Openly support Xu Yuan.

However, even so, it will not affect others' continued argumentation and research on the proof process.

If you can find loopholes or errors, your reputation in the mathematics community will also be quickly enhanced.

Of course, the premise is that you can really find it.

The International Mathematical Union's statement undoubtedly caused a new sensation in the mathematical community.

All we can say is that Xu Yuan’s value is still rising.

As for the Clay Mathematics Institute, which provided the prize money, there was rarely any news about it at this time.

Because they are also urgently arguing.

The Clay Mathematics Institute proposed seven world-problems in the millennium and prepared a prize of one million US dollars for each problem. They must also confirm the authenticity of the proof process of the solution before they can respond and issue the prize.

In fact, under normal circumstances, their Clay Mathematics Institute should be the first to announce the results.

Unfortunately, it happened to be the day when the International Congress of Mathematicians was held, and more mathematicians gathered at the International Mathematical Union.

So much so that the International Mathematical Union was the first to complete the proof.

-

Wells had never felt so good before, and the smile on his face had been hard to wipe off in recent days.

From having hope for Xu Yuan to feeling regret over his fading away from the mathematics community.

Then there was the surprise of the public live broadcast proving the Hodge conjecture.

He finally made up for the regret in his life and saw a world mathematical problem being solved again.

He even thought that since Xu Yuan was able to prove the Hodge conjecture so quickly, he might be able to solve the most famous Riemann hypothesis in the future.

There is no doubt that he trusts Xu Yuan and knows that the other party will never write nonsense during the live broadcast.

Therefore, in order to clear Xu Yuan's name as soon as possible, he immediately formed a research team.

Provide deductive reasoning for the proof process.

Although the progress was slower than that of the International Mathematical Union, at least the final conclusion was reached.

"Professor Wells, based on the results of our argument, prove that the conditions in the proof process are established."

"Hodge's conjecture has been solved."

"I knew that anyone who is favored by Deligne will not let us down." Wells took the proof and the smile on his face became even bigger.

Then he did not forget to instruct:

"We should hurry up and officially announce this result to the world. We have fallen behind the International Mathematical Union this time."

"Okay, Professor Wells." The other party nodded in response.

Hearing this, Wells finally breathed a sigh of relief, and the next second he murmured to himself with a smile on his face.

"This time we can finally pay out the bonus."

Although Xu Yuan was the second person to solve the world's most difficult mathematical problem, Perelman did not accept the prize.

So for their institute, this is the first time that a million-dollar prize has been awarded to a mathematician.

As for Deligne, since he is studying the proof process alone, his progress will definitely be much slower.

However, when he saw that the International Mathematical Union and the Clay Mathematics Institute had successively published papers confirming that the Hodge conjecture had been solved, he was completely relieved and continued his research at a leisurely pace.

After all, with the confirmation of two major authorities in the mathematical world, there is no need to rush to publish the results of his argument.

In addition, he was not surprised by this result. After all, since Xu Yuan decided to study the Hodge conjecture, he believed that the other party would be able to do it.

It turned out that his vision was very accurate.

As the news spread back to China, netizens were excited and their emotions were extremely high.

Everyone congratulated Xu Yuan on successfully entering the highest hall of mathematics and becoming a world master of mathematics.

As for the protagonist Xu Yuan, he had just finished writing the paper proving the Hodge conjecture and was preparing to publish it globally as the cover of the latest issue of the Journal of Mathematics.

……

(End of this chapter)