From failed candidate to chief scientist

Chapter 82: Have you completed the proof of Kakeya’s conjecture?

"Oh, Lin, this won't work, this won't work..."

"Topology simply cannot solve the problem of single Unicom."

"The Peilong tree seems to be possible, but it cannot be single-connected, and the topology itself is not a single-connected domain. This is a paradox!"

"We chose to use topology to solve the single-connection problem in Peilongshu, but we are going in the wrong direction."

"Unless you make the stick into a topological structure, this is impossible. This contradicts Kakeya's conjecture itself."

"I don't think we should waste any more time on this..."

Birkar slumped in the armchair and helplessly spread his hands on the table, with a depressed look on his face.

Lin Mo dragged his chin and frowned deeply as he looked at the topological model that he and Bill Carr built together.

What's the problem?
Is it true that topology cannot solve the problem of Peilong tree?

Lin Mo thought for a long time, but he didn't have any good ideas to solve this problem.

The research has indeed reached a dead end. In the past few days, Lin Mo and Bill Carr have constructed the corresponding topology based on the Peilong tree. However, as Bill Carr said, this topological model cannot solve the problem that the Peilong tree is not a single connection. problem, unless the samurai stick in Kakeya’s conjecture is made into the topological structure they involve.

But this is obviously impossible. If you do this, it will violate the proposition of Kakeya's conjecture. Even if you can achieve the desired result of Kakeya's conjecture, it will not prove the Kakeya's conjecture.

So what about dancing sticks to form such a topology?

This is theoretically possible, but unrealistic.

Because it is impossible for a samurai to complete the construction of the topology every time he swings a stick before swinging it.

Converted into theory, that is, it is impossible for a stick to complete the construction of the topological structure and complete the 180-degree U-turn of the stick.

This is the so-called single-connection problem.

In layman's terms, there is no guarantee that the stick will always have a fixed point, just like the hand of a samurai holding a stick, the topological structure cannot guarantee that the hand of a samurai can always maintain a relatively fixed position.

Lin Mo scratched his head, was he really going to give up like Bill Carr said?
Then wouldn't all my efforts these days have been in vain?

Lin Mo thought for a while and decided to struggle again.

The next moment, Lin Mo activated his keen talent.

A large amount of information quickly flashed through Lin Mo's mind, and suddenly, a flash of inspiration flashed across Lin Mo's mind.

He thought of the previous discussion with Bill Carr about using the three-point inward-swinging method to fuse the Peilong tree and realize the single connection of the Peilong tree. However, after many attempts, he found that the complexity of the Peilong tree is three-dimensional. Sharp inward angle cannot be solved.

However, the failure of Peilongshu does not mean that the topological model constructed by him and Birkar is not good. If the tricuspid inward angle is combined with topology and the topological structure is drawn using the tricuspid inward angle, the single-connection problem can be successfully solved.

Thinking of this, Lin Mo took up his hands and started writing and drawing on the whiteboard on the wall with a whiteboard marker.

Bilkar on the side shook his head.

He felt that Lin Mo was doing useless work and wasting time, but he still set his sights in Lin Mo's direction.

At first, Birkar didn't pay much attention, but as Lin Mo continued to write, Birkar's eyes slowly turned from dull to solemn, and then from solemn to surprised, and finally a look of joy appeared on his face.

Birkar suddenly jumped up from his chair and rushed to Lin Mo's side, but at this time Lin Mo was still writing. Birkar did not dare to interrupt Lin Mo and continued to look at Lin Mo.Lin Mo paused occasionally, and Birkar's voice sounded at the right time.

"Here, it seems like this..."

As he spoke, Bill Carr grabbed the whiteboard marker on the side and started writing on the side.

The two of them faced the white wall like this, sometimes writing, sometimes stopping to think, sometimes discussing a few sentences.

I don't know how long it took.

Lin Mo and Bill Carr put down their whiteboard markers at the same time and looked at each other with satisfied smiles on their faces.

"finished!"

"It's really finished?"

The previous sentence was Lin Mo's sigh of relief.

In the latter sentence, Birkar's tone still contained a bit of surprise and disbelief.

"What's done?"

Shan Gang has been in a difficult mood for the past two days, wondering whether he was wrong and whether he should resign. Recently, he has been sitting in the office in a daze.

At this moment, a voice suddenly sounded in the quiet office, which pulled Shan Gang out of his thoughts and asked subconsciously.

But Shan Gang reacted quickly and turned to look in the direction of Lin Mo and Bill Carr.

"Have you completed the proof of Kakeya's conjecture?"

Shan Gang asked with some uncertainty.

"No, no, no, we didn't prove Kakeya's conjecture, it was Lin who completed the proof. Lin is really a genius!"

At this time, Bill Carr still had a bit of surprise on his face, and he still looked at the densely written content on the whiteboard on the wall with some disbelief.

"No, no, no, Coucher, this proof also has your share of credit. Without you, we wouldn't be able to prove it."

Lin Mo also came back to his senses, and when he heard Birkar's words, he hurriedly spoke modestly.

Lin Mo didn't dare to take credit. Although he had just used his keen talent to get inspiration from a large amount of information, these inspirations had actually already existed in his discussions with Bill Carr, so Lin Mo felt that, Now being able to prove Kakeya's conjecture is inseparable from the help of Bill Carr.

"No, no, no, this is your proof, I just made some small suggestions in it."

Birkar is an honest man. He feels that Lin Mo came up with this all by himself. Even without him, Lin Mo will be able to complete the proof sooner or later.If you have to say what Bill Carr did, Bill Carr felt that at most he could only be regarded as an assistant on the side, helping Lin Mo eliminate wrong answers and saving some time.

Moreover, Birkar had already given up just now, and even advised Lin Mo to give up.If Lin Mo hadn't listened to him and continued to think and research, such a great proof might have been obliterated by himself.

Therefore, Birkar's heart was full of guilt and luck at this time. He felt guilty that he had not persisted and persuaded Lin Mo to give up. Fortunately, Lin Mo did not listen to him, so this great proof was not aborted.

"No, no, Coucher, without you, I wouldn't have been able to complete this proof. You see, the idea of ​​using three inner corners was also proposed by you at the time. Therefore, you deserve the most credit for this proof."

Lin Mo was telling the truth. He knew the source of his inspiration, so he did not dare to take credit for it. He also felt that he had taken advantage of Bill Carr. Without Bill Carr, he would not have been able to prove Kakeya's conjecture.

(End of this chapter)