Professor Garland, one of the most famous mathematicians today, also studies the problem of number theory and has made many achievements in this field.
The problem he is studying now is also the famous Riemann conjecture of prime number problem.
The famous mathematician Gauss once said, "Mathematics is the queen of science and number theory is the queen of mathematics."
The prime number problem is the core of number theory, and the Riemann conjecture is the most dazzling pearl of the crown.
Many people may have heard of Riemann conjecture, but few people know what Riemann conjecture is.
It is also very simple to say that the real parts of all nontrivial points of Riemannian zeta function are 1/
You may be puzzled by this sentence. What is the Riemann zeta function? What is the extraordinary point?
If we want to introduce Riemann conjecture from the beginning, we should start with the study of prime numbers by mathematicians.
Before introducing the conjecture of twin prime numbers, we have already said what a prime number is, and mathematicians have never stopped studying prime numbers since ancient times.
Catalan conjecture, Pillay conjecture, twin prime conjecture and well-known Goldbach conjecture are all researches on the distribution law of prime numbers.
As we all know, there are finite primes, and we can also calculate finite primes, but it will be difficult to calculate whether a number is prime or not when it is large enough. We don’t have a general formula to determine whether a number is prime or not.
And if we can find this general formula, then all the problems of prime numbers will be solved.
Many mathematicians have studied this problem and come up with some general formulas of prime numbers, including many famous mathematicians such as Euler and Equus, but all these general formulas have been proved to be wrong in the end.
At present, the largest prime number known to mankind is 7739171, which was discovered by mersenne prime in 17 years by the "Internet mersenne prime Search" project, and it is a spherical project.
What is mersenne prime? This is also a relatively complicated problem. It is unknown here for the time being. It can be simply understood that mersenne prime is a special kind of prime number.
After discovering the method and finding the general formula that can express all prime numbers, mathematicians turned to another question: Can you know how many prime numbers there are in a fixed range?
For example, we all know that there are four prime numbers in ten, so can we calculate how many prime numbers are 10 million or more through a formula?
The expression for calculating the number of prime numbers in this range is called prime number calculation function.
Here we must introduce a great German mathematician Georg Friedrich Bernhard Riemann, who is the founder of Riemannian mathematics and one of the founders of complex variable function theory.
In 1859, Riemann handed in his only paper on number theory, which was also his only paper with few concepts. The title of the paper was "On the number of prime numbers less than a given value"
Just like the title of the paper, in this nine-page paper, Riemann directly gave the accurate expression of the prime number calculation function, but his paper was too brief and did not confirm the process. Even today, we have proved a small part of it
What is even more regrettable is that in 1866, Riemann, a talented mathematician, died of lung nuclei at the age of four.
Otherwise, perhaps Riemann conjecture is no longer a conjecture today.
The expression π () given by Riemann consists of two parts, one is J (), which is the prime number calculation function given by Riemann, and an approximate value of π () can be calculated by this function.
The other part is the correction term μ(n)/n for j ()
The value obtained after correction by the correction term is the accurate π ()
But here, it seems that we haven’t talked about the two problems mentioned above: Riemannian zeta function and its nontrivial point.
Next, let’s first talk about a Riemannian zeta function, which can represent zeta (s). This function is expressed in the complex field function independent variable s instead of it.
What is a complex number? If we expand it, it will be too long. Let’s skip it here.
Anyway, when we solve the equation ζ(s)=, we can get two types of solutions.
The first and simple solution s=n is all negative even numbers.
Obviously, this is very simple, which is also called ordinary solution or ordinary point.
The second s=a+bi is obviously a complex solution.
Complex solutions are very complicated. Today, if all the answers are not found, they are also called nontrivial solutions or nontrivial points.
Now that we know what Riemann zeta function is and what its nontrivial point is, what does it have to do with Riemann’s prime number calculation function?
Simply put, Riemann gives the prime number calculation function, some of which contains the nontrivial point ρ of Riemann zeta function, and if we can know all ρ, we can get the exact π ().
That is to say, to prove Riemann conjecture is to prove that all real parts of ρ Re(ρ)=1/
And if we can prove Riemann conjecture, we will be able to make a big step forward in understanding the distribution of prime numbers. It can be said that Riemann conjecture is the most important conjecture in the field of prime numbers at present.
Some people think that if Riemann conjecture is proved, we will open the door to the new world.
But it’s really hard to prove this conjecture. More than a hundred years later, we still don’t know anything about Riemann. Mathematicians want to pick this pearl, but no one has done it. Professor Garland is one of them at present.
For Chen Song himself, of course, he is also interested in Riemann conjecture. It is difficult for a mathematician to be uninterested in Riemann conjecture, but at least for now, he feels that he has no strength to study it for the time being, and maybe later.
At this time, Chen Song sat quietly on the stage listening to Professor Garland’s report and remembering some sum formulas from time to time.
Professor Garland’s report was also left for questioning, but Chen Song didn’t ask him if he was sorting out Professor Garland’s report in his mind, but he didn’t catch it at the moment, which made him unable to immerse himself in his thoughts until everyone in the lecture hall left and he was still sitting in the same place.
Professor Garland saw him coming. "What seems to be your problem?"
Chen Song sighed and said naively, "I was inspired by your report, but some inspiration flashed by and I haven’t caught him yet."
Professor Garland smiled and said, "I’m glad I can help you, but in my experience, you might as well rest your brain for a while and then comb it again. Maybe you can find something then."
Chen Song nodded mainly because he found himself unable to find inspiration for Yankee for a while, and there will be a report here soon.
He got up and walked out with Professor Garland and said, "Thank you for your suggestion. I will try-your report was very successful. Congratulations!"
Professor Garland smiled and shook his head and said, "It’s not successful. I’ve been studying Riemann conjecture for two or three years, but I haven’t gained much. It’s rare for me to doubt myself. There are so many mysteries waiting for us in the field of mathematics. I wonder if I can see Riemann conjecture proved in my lifetime."
Chen Song was also a little silent for a while. In 1637, the famous mathematician Ma came out. Now everyone is familiar with Ma Da Theorem, and there is no reason not to write the proof process because Bai Xiao is too small.
It took later mathematicians more than 300 years until 1995, when it was proved by mathematician wiles.
When Riemann wrote his nine-page paper, he also thought it was obvious that it needed more proof. However, the reality is that other mathematicians don’t think it is simple, and it is difficult to prove even a small step.
Chen Song thought it might be like he couldn’t understand such a simple thing when he was tutoring his sister Chen Xinyu in math and physics. What would Chen Xinyu not understand?
Chen Song reported that Professor Garland also went. In addition to Professor Garland, Chen Song also saw many familiar faces in Taiwan, all of which he had or had not been in contact with famous mathematicians.
However, Chen Song did not have stage fright. He calmly nodded to Taiwan and began to give his report step by step.
His expression is as plain as ever, but it has brought great surprises to Taiwan mathematicians, especially the mathematical tool he gave a speech at the Xia Guo Mathematicians’ Conference before. Although it was simply summarized this time, it also made these top mathematicians realize its value.
So when the question session was held, a famous mathematician asked, "Dr. Chen, have you ever published a photo paper in that mathematical tool before?" Or can I introduce one? "
Hearing the unexpected question, Chen Song smiled and said, "I once made a special report at Xia Guo Mathematicians’ Congress, and it was included in the journal of Xia Guo Mathematicians’ Congress. If you are interested, you can subscribe to it yourself."
After the mathematician got a satisfactory answer, he sat down, and then some mathematicians who were also interested in the conjecture of twin prime numbers asked some questions, and Chen Song also explained them one by one.
However, there is no doubt that mathematicians are more interested in his design of that mathematical tool than his research progress on the conjecture of twin prime numbers, and it is natural that Xia Guo Mathematicians’ Congress suddenly received many words.
For Chen Song, the biggest gain from attending the International Congress of Mathematicians this time is that besides winning the Philippine Prize, he got to know more mathematicians and listened to many valuable reports.
In order not to increase the security pressure on Wu Fan, Chen Song immediately returned to China with other mathematicians after the nine-day mathematician conference. I haven’t seen Tong Yihuai pick him up at the airport for ten days. Of course, all kinds of media have not missed this opportunity when they heard the news.
Coincidentally, they arrived at the airport at about the same time as Chen Song and others, and there was an entertainment star stuck in the airport. The media not only came to interview Chen Song, but also went to see the little star on a bigger scale.
The exit is so big, a bunch of media crowded together, and some fans who came to pick up the plane naturally attracted the attention of ordinary passengers. Some of them were not in a hurry and also gathered for sightseeing. The scene suddenly got a little messy and Tong Yihuai was squeezed out.
Ronaldinho "…"