God knows how much Li Mu wanted to scold his mother when he saw this task was announced.
What a joke!
Pick a random math problem to solve, and then you randomly pick four famous problems in the math world?
Needless to say, the Riemann Hypothesis. Since Bornhard Riemann proposed this conjecture in 1859, mathematicians all over the world have wanted to solve this problem, but it has stumped the entire mathematical world for nearly two years. century.
As the most important conjecture among all current mathematical problems, an important reason why the Riemann Hypothesis is so attractive to mathematicians is that it has a very accurate prediction of the distribution of prime numbers.
For mathematicians, it is their dream to know the specific distribution of prime numbers.
It is precisely because of the day-and-night research of mathematicians that there are now more than 1,000 propositions in mathematics, all based on the premise that the Riemann Hypothesis is true.
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.
You obviously won't let him solve it!
The same is true for several other questions.
Take the Hodge Hypothesis, for example. Although the history of this conjecture is not as long as the Riemann Hypothesis, its importance to the mathematical world is no less than that of the Riemann Hypothesis. 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 are all among the seven major mathematical problems of the millennium, and are problems that all scholars in the field of mathematics are committed to solving.
In terms of popularity, Goldbach's conjecture is the highest. The first three conjectures are only famous in the mathematical community, but 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.
Although it is not included in the seven major mathematical problems of the millennium, this does not mean that it is not 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 bring huge promotion to the development of the academic world.
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 solved by a genius.
This is a symbolic meaning.
And in terms of difficulty...
Maybe Goldbach's conjecture is a little simpler, but how much simpler?
Nobody knows.
Finally, Li Mu couldn't stand it any longer and scolded his mother again: "System! Come out! Can this kind of task be issued by a human being?"
Oh, the system is really not a human being.
Damn it.
Just as he was complaining crazily in his heart, Andrew Wiles saw his student's unhappy face and couldn't help but wonder: "What's wrong with you?"
Li Mu came back to his senses, quickly calmed down his expression, and then said: "It's nothing, I thought of something happy."
Wiles was stunned for a moment. Could that expression mean he was thinking of something happy?
"What happy thing?"
"My wife...ahem, just, just..."
"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 understand?
Did he say anything?
…
Walking out of Wiles' office, Li Mu guessed that Professor Wiles might have misunderstood something, and his expression didn't look right when he left.
"Forget it, let's think about which problem to choose to solve."
Shaking his head, his mind returned to that task.
Whether it is the Riemann Hypothesis, the Hodge Hypothesis, or the BSD Hypothesis, it is much more difficult, and the Goldbach Hypothesis is easier for Li Mu to get started with.
After all, Goldbach's conjecture is a problem of number theory. For him who has solved several number theory problems, it really needs to be better understood.
"Then, choose Goldbach's conjecture."
He has already won two of the jewels in the crown of mathematics: the Hailstone Conjecture and the Twin Prime Conjecture. Now, he has to set his sights on the biggest pearl.
…
If we talk about history, Goldbach's conjecture is probably the oldest of the four conjectures on this task.
In 1742, Christian Goldbach, who worked in the Russian Ministry of Foreign Affairs, 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 Euler, a famous mathematician at the time, for advice.
In this regard, a letter sent from Russia to Switzerland officially launched a revolution in the study of prime numbers in the mathematical world.
In his reply to Goldbach, Euler acknowledged this conjecture, but he could not provide a proof. However, 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 overcoming, is Euler's statement.
What’s interesting to say is that Euler began his research on the distribution of prime numbers precisely because he found that he could not prove this problem, and thus influenced later generations, including the formulation of the Riemann Hypothesis, which was all related to this matter. relation.
"It's such a long-standing problem."
In the Oxford University library, Li Mu sat on a desk in the corner. After carefully studying the history of Goldbach's conjecture, he couldn't help but sigh.
Before solving such a famous problem, it is also his habit to read the development history of this problem.
Nearly three hundred years have passed, and the mathematics community has achieved very rich results on Goldbach's conjecture. In 2013, the weak Goldbach's conjecture was solved, and the solver was Harold of the Ecole Normale Supérieure in Paris. ·Heoffgot.
But Goldbach's conjecture still makes the entire mathematical community scratch its head.
"The statement of the weak Goldbach conjecture is... Any odd number greater than 5 can be written as the sum of three prime numbers. It seems a bit interesting, but this is about odd numbers. Brother Qiang guessed it is about even numbers, which 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 methods..."
Fumbling his chin, Level 4's mental computer was filled with numbers.
Suddenly, at this moment, a girl sat down on the seat next to him.
"Hey Lee, long time no see."
Li Mu was stunned, then turned around and looked over, recognizing him immediately.
He also smiled and said hello: "Isa, long time no see."
The girl's name is Isa Grosvenor, who is also a mathematics graduate student at Merton College, but her tutor is no longer Andrew Wiles.
As for why they knew each other, it was simply because they were neighbors.
Merton College’s graduate dormitories are not divided into male and female dormitories. After all, they are all single rooms, so there are not so many details.
"You've been causing a lot of trouble for the physics sister recently. I've heard about it. Is dimensional force really that magical?"
Li Mu said with a smile: "Whether it is dimensional force or other basic forces, they are all magical, because it is these basic forces that gave birth to various phenomena in our universe."
"So what is truly magical is actually the universe."
Isa Grosvenor nodded in understanding, "The universe is really difficult to understand, just like mathematics."
Li Mu smiled: "The most understandable thing about the universe is that it is incomprehensible, but similarly, the most incomprehensible thing about the universe is that it is understandable, and the mathematics we study is to allow us to better understand it."
"Anyway, it's quite a headache. It's like the topic 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 community as Andrew Wiles, he also had quite a lot of important achievements.
"By the way, what are you studying?"
With that said, Isha glanced at Li Mu's draft paper curiously.
Then she was stunned, "Why do I feel that what you wrote... is a bit familiar. It seems that it is also Goldbach's conjecture?"
Li Mu: "Uh... yes, I am also preparing to study Goldbach's conjecture."
Isa immediately opened her green eyes, "You actually want to study this problem too?"
"Oh my God, it seems I have to persuade Professor Richter to give up as soon as possible."
"You are a mathematical hypothesis crusher!"
…………
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(End of chapter)
