Riemann can't solve his own conjecture, is it an exaggeration to say that he is a god of mathematics?
From ancient times to the present, there have been a number of well-known mathematicians in our world. Each of these mathematicians has left their own unique mark, and their contributions are like bright stars, illuminating every corner of the mathematical world. Among them, Bonhard Riemann is undoubtedly one of the dazzling and high-profile stars.
However, the controversy over his failure to resolve his own Riemann hypothesis has led some to question the mathematician's stature and abilities. Some people say that Riemann has not even been able to solve the conjectures he proposed, and he is not a mathematical god at all!
Could it be that Riemann is really just famous and not worthy of his name? Personally, in my opinion, not so! With such a profound mathematical conjecture, he has put it forward, and he is obviously not a simple original character! His mathematical thinking is very advanced, just like Yuan Tiangang, Liu Bowen and others, who can predict the future, what is such a person not a god?
Riemann should have known the answer to Riemann's conjecture, but at that time, there was no better mathematical tool to prove this conjecture completely! So much time has passed since the moment this conjecture was proposed, and thousands of mathematicians have still not solved this problem? Now these mathematicians are standing on the shoulders of giants, and they still can't solve this problem, and even many mathematicians can't understand this conjecture! As you can see from the above, Riemann is very great!
I have given a detailed answer to this question below, so please read on:
1. Riemann: A bright star in the world of mathematics
Before we talk about Riemann, we have to look back at his brilliant achievements. Riemann was one of the greatest mathematicians of the 19th century, and his contributions covered many fields such as the theory of complex variable functions, differential geometry, and algebraic geometry. He pioneered Riemannian geometry, which laid a solid foundation for the development of modern differential geometry. His work has had a profound impact on understanding the structure and nature of high-dimensional spaces. In addition, Riemann has also made important achievements in the fields of function theory and analytic number theory. His research has not only advanced mathematics, but also provided powerful mathematical tools for other scientific fields.
2. The Riemann conjecture: an unsolved mystery in mathematics
However, despite such brilliant achievements in the field of mathematics, Riemann failed to solve his own Riemann conjecture. This conjecture is a conjecture about the distribution of nontrivial zeros of the Riemann ζ function, i.e., these zeros are all located on a straight line with a real part of 1/2 on the complex plane. This seemingly simple mathematical proposition contains extremely profound mathematical connotations and wide application prospects. If the Riemann conjecture proves to be true, it will revolutionize the field of mathematics, and many mathematical problems will be solved.
However, despite the tremendous efforts of countless mathematicians to prove or falsify the Riemann conjecture, the conclusion remains inconclusive. This unsolved mystery became a major challenge for the mathematical community and raised questions about Riemann's abilities.
3. Why did Riemann fail to solve the Riemann conjecture?
First of all, we need to be clear that the Riemann conjecture is an extremely complex and difficult mathematical problem. It involves knowledge and skills in many fields such as complex analysis, number theory, and functional analysis. In order to prove or falsify this conjecture, it is necessary to have a high level of mathematical literacy and a deep mathematical foundation. Even a mathematician like Riemann may not be able to overcome this problem because of a lack of knowledge or skill.
Second, Riemann may not have fully realized the complexity and difficulty of the problem when he proposed the Riemann hypothesis. He may have only come up with this conjecture based on his own intuition and observation, without in-depth research and discussion. Therefore, in trying to prove this conjecture, he may encounter some unexpected difficulties and challenges.
In addition, Riemann's life experiences and health may also have had an impact on his research. We know that Riemann was in poor health in his later years, which may have affected the progress and results of his research. At the same time, he also needs to face various pressures and difficulties in life, which may also distract his attention and energy.
Fourth, rethinking the god of mathematics
So, should we question Riemann's status and competence because he failed to solve the Riemann conjecture? I don't think that's appropriate. First of all, Riemann's contributions to the field of mathematics are indisputable, and his achievements and status are determined by his research results and contributions, not by a particular conjecture. Secondly, the development of mathematics is a long-term process, and the solution of many mathematical problems requires the efforts and exploration of several generations. Even a math guru like Riemann may not be able to make a breakthrough on some issues. This does not mean that there is a problem with their abilities, but rather reflects the complexity and challenge of mathematical problems.
Therefore, we should respect Riemann's position and contribution in the field of mathematics, and at the same time recognize the complexity and long-term nature of the development of mathematics. As for such unsolved mysteries as the Riemann conjecture, we should maintain an open and exploratory attitude and continue to conduct in-depth research and discussion. Only in this way can we better understand the mysteries and wonders of the mathematical world.
Epilogue:
Riemann was a great mathematician in the field of mathematics, and his contributions and status are indisputable. Although he may not have been able to solve the Riemann hypothesis he proposed, this does not affect our admiration and respect for him. We should face the unsolved mysteries of the mathematical world with an open and exploratory attitude, and continue to study and explore them in depth. I believe that one day in the future, we will be able to overcome these problems and make greater contributions to the development of the field of mathematics.
Addendum: In fact, it is understandable for some netizens to question, after all, he doesn't know how to understand mathematics, and he doesn't know how advanced the Riemann conjecture is! I would have told some netizens now, or some doctors of mathematics, that you understand that mathematics may be just a little scratch of the surface, don't deny Riemann, Riemann is definitely one of the kings of mathematics! Personally, I think that characters like Perelman and Tao Zhexuan can only be regarded as middle school students in front of him!
Riemann, a pure mathematician, a mathematician who has worked hard all his life for the benefit of mankind, salutes Mr. Riemann!