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

After all, how can you measure the difficulty of something that has not been proven to be true at all?

This in itself is a pseudo-logic.

However, it is not impossible to classify mathematical conjectures and mathematical conjectures.

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 today's mathematical community", then thousands of mathematical conjectures can be roughly divided into several echelons.

The first echelon is undoubtedly the millennial puzzle such as the Riemann conjecture, the NP complete problem, the Yang-Mills gauge field existential and mass interval assumptions, the so-called seven mathematical problems of the world, and some of the problems in Hilbert's 23 questions, and so on.

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

The second echelon is naturally the most well-known of the three major mathematical problems of modern times, Goldbach's conjecture, the four-color problem, and Fermat's theorem. Two of them have been resolved, and the remaining one, Mr. Chen, has achieved "1+2". In addition, some questions from the Longlands Program and some of the questions from Hilbert's 23 questions can also be listed in this list.

In the third tier, the distinction between conjectures at this level and the second tier is not obvious, and when it comes to subjective opinions, there may be large differences. Typically, the Jacobian conjecture can be counted in this category.

And the question of proving this level is not far from the Fields Medal, at least it can be nominated...... Provided, of course, that is, under forty years of age.

As for the fourth echelon, Zhou's conjecture can be counted in this list, and all sub-problems of the first, second, and third echelon problems, or the "weak conjecture" of a certain conjecture, can also be stuffed into it.

There are even more in the fifth tier, some unpopular branches that no one cares about, conjectures put forward by a little-known mathematician, and all conjectures that do not reach the fourth tier, can be included in this echelon.

According to this grading method, the Polliniac conjecture can be counted as the third echelon, and the twin prime conjecture can be regarded as the "K=1 special form" of the Polliniac conjecture, but considering that the academic value is higher than the "study of the distribution law of Mersenne primes (Zhou's conjecture)", it is between the third and fourth echelons, and infinitely close to the side of the third echelon!

Regardless of the final result, with this outstanding contribution, the nomination for the 18-year Fields Medal, Lu Zhou will definitely be stable. His biggest rival is probably the 13-year Ramanujan Prize winner, Peter Scholz, who is said to be challenging the famous weight-monodromy conjecture, the progress of which is unknown.

Of course, the study of mathematical conjectures is only a part of theoretical mathematical research, not the whole story. Many people have never proved any major mathematical conjectures in their lifetime, but this does not prevent him from contributing to the entire mathematical community.

For example, Mr. Grothendieck, who laid the foundation of modern algebraic geometry and revolutionized the face of functional analysis, these two contributions alone are probably incomparable to any mathematical conjecture. After all, many of today's mathematical conjectures are based on his "generalization theory".

There is still a long way to go to climb the heights of mathematics.

The proof of the twin prime conjecture is just a small step on the road to Mount Everest.

Lu Zhou knew deeply that his research results were only answers to some of the questions in Hilbert's eighth question.

Although his heart was excited, his heart was about to beat out of his chest, but it did not swell above it.

The more you know about the world, the more you have in your head, the more you can feel small.

In fact, Lu Zhou is not very clear about what his true feelings are at this moment. Whatever he thinks, though, one thing is for sure, his name is on fire in Princeton.

Everybody knows.

At yesterday's presentation, a young man from Asia eliminated a world-class mathematical conjecture in front of all the audience in the presentation......

……

Shaking his groggy head, he got out of bed.

Pushing open the door of the bathroom, sitting in the bathtub and taking a hot bath, Lu Zhou, who had changed into new clothes, stood in front of the mirror and took a look.

Well, not bad.

It's still as handsome as ever, but it's a pity that there is no meat.

Hey, this physique that can't eat fat no matter how much you eat is really nerve-wracking.

After enough mirrors, Lu Zhou walked to the window and opened the curtains that had not been opened for a long time.

This night, he slept very comfortably.

This is probably the most comfortable sleep he has slept in the past few days in North America.

It's just that looking at the sky outside the window, it doesn't seem to have changed much.

If it weren't for the fact that he couldn't be better in a good mental state, he would have to wonder if he had slept or not......

Lu Zhou's face changed suddenly.

Wait, what time is it?

Looking at the time on my phone, it was already half past three!

Thinking that there was still a closing ceremony waiting for him, Lu Zhou ran to the entrance without saying a word, put on his shoes, and rushed out of the door.

I got off the elevator and walked through the lobby, and I didn't see anyone along the way except the waiter at the hotel.

There was an ominous premonition in his heart, and Lu Zhou, who ran to the door, accidentally bumped into a white guy who was looking down at his phone. Before he had time to explain, he threw a "sorry" and immediately asked, "How many days is it for the academic conference?" ”

The little brother said with a dissatisfied expression: "On the sixth day, man, be careful when walking!" ”

It's dangerous!

Lu Zhou breathed a sigh of relief.

It seems that this closing ceremony has not been missed.

But think about it, even if he bursts his liver for a few nights, it can't be so exaggerated as sleeping for two days and two nights.

At this moment, the white little brother stared at Lu Zhou for a long time, and suddenly came back to his senses, his eyes widened: "Wait, you ...... Could it be a braised elbow? ”

it?

Lu Zhou almost sprayed him in the face.

MMP！ You still want to marinate me!

Ruthless enough!

glanced at the phone, probably confirming the photo from Twitter, the white brother's eyes suddenly lit up, and he pulled the landing boat and didn't let him go.

"Hey, listen, you scrapped my dissertation, guess what my dissertation was written about? I cleverly found a Lambda function and proved that there are infinite pairs of primes that are all less than 242 apart, which shortens the gap between 2 and 246 by one step! And just yesterday, you not only killed this hen that lays golden eggs, but also ruined the research results of my two months! ”

Lu Zhou didn't know what to say, just looked at this Yankee with a neurotic look, and was ready to wave to the security guard next to him at any time.

But fortunately, this little brother didn't make any drastic moves, just pulled him and beeped.

“…… Damn, but well done! I guess it's the same method of proof, using the method of topology...... It's just that I didn't expect the sieve method to work like this. Meet me, my name is Callister, and we have a drink together in the evening? For the sake of you delaying my graduation, you owe me this glass of wine anyway, hey, don't run, hey! ”

Lu Zhou didn't look back, and ran away decisively.

……

Inside the auditorium, it was crowded.

The closing ceremony is about to begin, but it doesn't feel like there were as many people as it was at the beginning.

Lu Zhou remembered that he seemed to have heard Senior Brother Luo say that many people who participate in academic conferences do not stay honestly until the end, and many people go out to surf the world after completing their own reports, listening to the lectures they want to hear, or talking about like-minded objects.

Lu Zhou looked around, but he didn't find Senior Brother Luo, but he saw an unexpected person, the Indian brother named Di Jean.

Surprisingly, this product hasn't left yet?

Is it so resilient to pressure?

Noticing Lu Zhou's gaze, the Indian brother didn't say anything, just responded with a resentful curry-style look, and then looked to the side and ignored him.

Lu Zhou made a helpless expression.

If he cites someone else's unpublished research, he will feel a little guilty, but this ...... This pot can't reach him.

The closing ceremony began.

The hall soon fell silent.

After a while, an old man who didn't look very reliable, with a black cane, walked slowly up to the podium.

Francis, President of the Federal Mathematical Society, is also a member of the International Union of Mathematicians.

The reason why he doesn't seem very reliable is because his slow movements always make people worry about whether he will suddenly fall asleep while talking, or fall down while climbing the steps.

"Introduce yourself, Francis, there's nothing else to introduce...... Besides, the lads should be impatient, so let's get straight to the point. The old man smiled kindly and said.

The audience also smiled kindly and gave encouraging applause.

The old man pushed his glasses, flipped a page of the speech, and read it in pieces.

"First of all, thank you very much for participating in this math conference, and thank you to Parker, Amazon Inc...... and other corporate sponsorships. No matter how noble the cause, without the help of good people, our cause cannot move forward......"

“…… In the face of great causes, we do the same work, no matter how high or low, even if your conclusions are temporarily wrong, even if you are refuted with fierce words, it does not mean that you are not good enough. On the contrary, you standing here are already more courageous and talented than 99 percent of the people in the world. I hope that this time next year, I can still see you energetic young men and girls...... Of course, bad old men like me are also welcome, always welcome. ”

"There's still a party ...... in the evening"

"By the way, I almost forgot the most important thing." The old man pushed his glasses, smiled slightly apologetically, cleared his throat, and continued, "The best young speaker of this academic exchange conference will receive a $10,000 prize sponsored by Amazon Group and a certificate from the Federal Mathematical Society...... The winner is Lu Zhou. Doesn't seem to have much suspense? After I thought about it, I won't sell it. ”

The crutches stomped the wooden floor, and Mr. Francis lifted his spirits and said with a smile to everyone in the audience.

"So, have fun!"

"Plus, the championship belongs to the Philadelphia Eagles!" (Super Bowl)

The young man in the audience whistled.

In the thunderous applause and relaxed atmosphere, this academic conference came to a successful conclusion.