Ultimate Scholar

God knows how much Li Mu wanted to scold his mother when he saw this task was announced.

What a joke!

Randomly pick a math problem to solve, and then you randomly pick four famous problems in mathematics?

Needless to say, the Riemann conjecture, since Bernhard Riemann proposed this conjecture in 1859, mathematicians all over the world have wanted to solve this problem, but they have stumped the entire mathematical community for nearly two century.

As the most important conjecture among all current mathematical problems, one of the important reasons why Riemann's conjecture is so attractive to mathematicians is that it has very accurate predictions for the distribution of prime numbers.

For mathematicians, they dream of knowing the specific distribution of prime numbers.

It is also due to the day and night research of mathematicians that there are now more than 1,000 propositions in the mathematics world, all of which are based on the establishment of the Riemann Hypothesis.

In other words, once the Riemann Hypothesis is proven, all of these more than 1,000 propositions can immediately become theorems, greatly enriching the mathematical knowledge base.

So Li Mu never expected that the system would put this kind of problem on this kind of task.

Obviously don't let him solve it!

The same goes for the other questions.

For example, the Hodge conjecture, although the history of this conjecture is not as long as the Riemann conjecture, its importance to the mathematical world is no less than that of the Riemann conjecture, and it is even second only to Riemann in terms of difficulty of proof. guess.

As for the difficulty of BSD conjecture, it is also not low.

These three conjectures belong to the seven major mathematical problems of the millennium, which are the problems that all scholars in the field of mathematics are committed to solving.

However, in terms of popularity, Goldbach's conjecture is the highest. The first three conjectures are only famous in the mathematics world, while Goldbach's conjecture is famous all over the world.

If the crown of mathematics is number theory, then Goldbach's conjecture is the jewel in the crown.

It didn't make the list of the top seven math problems of the millennium, but that doesn't mean it's any less difficult.

The problems that can be included in the seven major mathematical problems of the millennium are of great substantive significance to the academic world. Once solved, they will be able to bring a huge boost to the development of the academic world.

And if Goldbach's conjecture is solved, it will not be of great significance to the academic world like those problems.

However, as a saying goes, number theory is a game for geniuses, and if Goldbach's conjecture is solved, it means that this game has been cleared by a genius.

This is a symbolic meaning.

And in terms of difficulty...

Perhaps Goldbach's conjecture is slightly simpler, but how much simpler?

Nobody knows.

In the end, Li Mu couldn't hold back anymore, and scolded his mother again: "System! You come out to me! Is this kind of task a human can enact?"

Oh, the system is really not human.

Damn.

Just when he was complaining wildly in his heart, Andrew Wiles saw his student's expression of displeasure, and couldn't help wondering: "What's wrong with you."

Li Mu regained his senses, quickly restrained his expression, and said, "It's nothing, I thought of something happy."

Wiles was taken aback for a moment. Could that expression be because he thought of something happy?

"What joy?"

"My wife...cough cough, that's, that's..."

"Okay, you don't need to say any more, I understand." Wiles waved his hand and said with a smile.

Li Mu: "??"

What do you know?

Did he say anything?

...

Walking out of Wiles' office, Li Mu guessed that Professor Wiles might have misunderstood something, and his expression was not right when he left.

"Forget it, why not think about which problem to choose to solve."

Shaking his head, the thinking in his mind returned to that task.

Whether it is Riemann's conjecture, Hodge's conjecture, or BSD conjecture, the difficulty is much higher, while Goldbach's conjecture is easier for Li Mu.

After all, Goldbach's conjecture is a problem of number theory. For him who has already solved several problems of number theory, he really needs to understand it better.

"Then, choose the Goldbach conjecture."

He has picked off two of the jewels in the crown of mathematics, the Hailstone Conjecture and the Twin Prime Number Conjecture. Now, he will also aim at this biggest pearl.

...

If you want to talk about history, Goldbach's conjecture is probably the oldest one among the four conjectures in this task.

In 1742, Christian Goldbach, who worked in the Russian Foreign Ministry, discovered such an interesting problem: any integer greater than 2 can be written as the sum of three prime numbers.

And this is also the original statement of Goldbach's conjecture.

Goldbach couldn't solve this problem, so he wrote to ask the famous mathematician Euler at that time.

In this regard, a letter sent from Russia to Switzerland officially set off a revolution in the study of prime numbers in the mathematics world.

In his reply to Goldbach, Euler approved this conjecture, but he could not give a proof, but he also gave a more complete statement: every even number greater than two can be written as the sum of two prime numbers .

Goldbach's conjecture, which modern mathematicians are committed to solving, is Euler's statement.

It is interesting to say that Euler started his research on the distribution of prime numbers just because he found that he could not prove this problem, which has influenced later generations, including the Riemann conjecture, which has a certain relationship with this matter. relation.

"It's really a long enough question."

In the library of Oxford University, Li Mu sat on a desk leaning against a corner. After carefully studying the history of Goldbach's conjecture, he couldn't help but sigh with emotion.

Before solving this famous problem, it is also his habit to read the development history of this problem.

In the past three hundred years, the achievements of the mathematics community on the Goldbach conjecture have been very rich. In 2013, the weak Goldbach conjecture has been solved, and the solver is Harold of the Paris Normal University. · Hoofgot.

But Jon Goldbach's conjecture still makes the whole mathematics community scratch their heads.

"The statement of weak Goldbach's conjecture is... Any odd number greater than 5 can be written as the sum of three prime numbers. It seems interesting, but this is about odd numbers. Strong brother's guess is about even numbers. It is slightly different. .”

"But whether it is an even number or an odd number, there is always something that can be connected in the use of the method..."

Groping his chin, the computer in his mind at Level 4 was filled with numbers.

Suddenly, at this moment, a girl sat down on the seat next to him.

"Hey, Li, long time no see."

Li Mu was taken aback for a moment, then turned his head to look over, and recognized it immediately.

He also greeted with a smile: "Isa, long time no see."

The girl's name is Isa Grosvenor, who is also a graduate student in mathematics at Merton College, but her advisor is not Andrew Wiles.

As for why they knew each other, it was simply because they were neighbors.

Merton College's postgraduate dormitories are not divided into men and women, after all, they are all single rooms, so there are not so many particularities.

"Recently, you have turned the world upside down for Miss Physics. I've heard of it. Is Weili really so magical?"

Li Mu said with a smile: "Whether it is the dimensional force or other basic forces, they are all amazing, because it is these basic forces that give birth to various phenomena in our universe."

"So what's really amazing is actually the universe."

Isa Grosvenor nodded half-understanding, "The universe is really incomprehensible, just like mathematics."

Li Mu smiled: "The most intelligible part of the universe lies in its incomprehensibility, but similarly, the most incomprehensible part of the universe lies in its comprehensibility, and the mathematics we study is for us to better understand it."

"Anyway, it's quite a headache. It's like the subject that Professor Richter wants to study recently. He actually plans to study Goldbach's conjecture!"

Isa sighed helplessly. Richter was her mentor. Although he was not as well-known in the mathematics world as Andrew Wiles, he had quite a lot of heavyweight achievements.

"By the way, what are you studying?"

As she spoke, Yisha glanced at Li Mu's draft paper curiously.

Then she was taken aback, "Why do I feel that what you wrote...is a bit familiar, this seems to be Goldbach's conjecture?"

Li Mu: "Uh... yes, I'm also preparing to study Goldbach's conjecture."

Yisha's blue eyes widened immediately, "You actually want to study this question?"

"My God, it seems that I have to persuade Professor Richter to give up as soon as possible."

"You are a math conjecture smasher!"

…………

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