Problem Published
Mathematics Master David Hilbert held in Paris on August 8, 1900 23 mathematical problems were proposed in the famous speech at the 2nd World Mathematician Conference. Hilbert issued the wisdom of mathematicians in the past 100 years, guiding the direction of mathematics, and its impact on mathematics development is huge and cannot be estimated.
The 20th century is a century of the development of mathematics. Many major problems of mathematics have been completed, such as the proven of Fema, the completion of the finite population classification, so that the basic theory of mathematics is unprecedented.
At the beginning of 2000, the Scientific Advisory Committee of the University of Kreology selected the seven "Millennium Grand Prize", the Board of Directors of the Krei Mathematics Institute decided to establish a $ 7 million prize fund, each " Millennium Grand Prize issues can get a million dollar rewards.
The Selection of the Millennium Grand Prize in the Kre Mathematics Institute, its purpose is not to form a new direction in the new century mathematical development, but focus on the development of mathematics development, mathematician dreams A major puzzle that is expected to solve.
May 24, 2000, the millennial mathematics conference was held in the famous French Academy. At the meeting, the 97-year-old Philz prize winner Gameuss took a speech with "the importance of mathematics", and later, Tat and Ayia announced and introduced these seven "Millennium Awards." The Krei Mathematics Institute also invited experts in the research field more detailed detailed details. The Cier Mathematics Institute has strictly regulates the solution and winning of the Millennium Awards. Every "Millennium Grand Prize issue" gets solved and cannot be awarded immediately. Any solution to the answer must be published two years after the math magazine with the World Reputation and get the approval of the mathematical community. It is likely to be reviewed by the Scientific Advisory Committee of the Krei Mathematics Institute to determine whether it is worth a million dollars.
One has been resolved (Pang Gui guess, the Russian mathematician Grigi Perelman crack), there is still six.
"Millennium Grand Prize" has been announced, a strong reverberation in the world mathematics. These issues are about mathematical theory, but these issues will be greatly promoted to the development and application of mathematical theory. Understanding and studying the Millennium Awards issue has become a hot spot in the world math. Many national mathematicians are taking the joint research. The Millennium Grand Prize issue will change the historical process of the new century mathematical development.
Seven Polls
1. NP complete problem
Example: On a night of Saturday, you participated in a grand party. Because I feel that I am uneasy, you want to know if there is a person you already know in this hall. The owner of the banquet proposes you to say that you must know the ladies row that is in the corner of the dessert. No one second, you can sweep there, and find that the owner of the banquet is correct. However, if there is no such impression, you must look around the whole hall, review everyone one person, see if there is a person you know.
Generation problem is usually much more expensive than verifying a given solution. This is an example of this general phenomenon. Similarly, if someone tells you, number 13717421 can write two smaller numbers, you may not know if he should believe him, but if he tells you that it can be broken down to 3607, then you This is easy to verify with a pocket calculator.
People find that all complete polynomial non-deterministic issues can be converted to a logical operation problem called satisfactory problem. Since all possible answers to this type of issues can be calculated within a polynomial time, people have already guess, whether such problems, there is a certain deterministic algorithm, can be used directly in the polynomial time or search for the right answer? Is this the famous NP = P? Guess. Regardless of whether we write the program smart, it is determined that an answer can be used to use internal knowledge to verify, or there is no such tip to solve a lot of time to solve, is considered one of the most prominent problems in logic and computer science. It is Steven Coke as stated in 1971.
2. Huoge guess
The 20th century mathematician discovered a powerful way to study the shape of complex objects. The basic idea is to ask how to extent, we can form the shape of a given object by bonding the simple geometric creative blocks that have increased the dimension. This skill is so useful, so that it can be promoted in many different ways; eventually leading some powerful tools, making mathematicians to make huge progress when classifying the shapes encountered in their research. . Unfortunately, in this promotion, the geometric starting point of the program becomes blurred. In a sense, some parts do not have any geometric interpretation. Huochi appreciates that for this particularly intact space type of the so-called shooting generation, the components called the Hodg closed chain are actually a combination of geometric components called algebraic closed chains.
3. Pangola guess
If we telescide around the rubber band around an apple, then we can neither it, do not let it leave the surface, make it slow Slow movement contraction is a point. On the other hand, if we imagine the same rubber band in an appropriate direction on a tire, then there is no way to shrink it into a point without pulling the rubber band or tire. We said that the surface of Apple is "single-link", and the tire is not. About one hundred years ago, Pangola has already known that the two-dimensional spherical surface can be portrayed in nature, and he proposes a corresponding problem with the three-dimensional spherical surface (all of the four-dimensional space and the origin of the original point). This problem immediately became extremely difficult, from which, mathematicians were fighting for this.
Between November 2002 and July 2003, Russia's mathematician Griguri Pereman published three papers, and claimed to prove geometry guess.
After Pereman, there were 2 groups of researchers to publish the provisions of the proof of Perelman. This includes Bruce Klena and John Lott, Michigan University; John Morgan and Massachusetts Institute of Technology in Columbia.
August 2006, the 25th International Mathematician Conference awarded the Perelmanfield award. The mathematical circles finally confirmed that Pereman's proofs solved Pangola guess.
4. Liman assumptions
Some numbers have special nature of the product of two smaller numbers, such as 2, 3, 5, 7 ..., etc. . Such a number is known to the number of prime; they play an important role in pure mathematics and their applications. In all natural numbers, the distribution of this prime is not followed by any rule mode; however, German mathematician Liman (1826 ~ 1866) observed that the frequency of the number is closely related to a well-constructed so-called Liman Zeta function (s) 's condition. The famous Liman hypothesis asserts, all meaningful solutions of equation (s) = 0 are on a straight line. This has been verified for starting 1,500,000,000 solutions. Prove that it will bring bright to many mystery of each meaningful solution to surround the number of prime numbers.
Liman assumptions:
It is actually a factor distribution, but it is a discrimination, because the general formula of the number of perjuvenations and the number of prime numbers are Their variable sets are determined. See the number of perfumes and prime number entry.
5. Yang - Mills existence and quality gap
The law of quantum physics is established in the world's way to the macro world with classic mechanics. About half a century ago, Yang Zhenning and Mills found that quantum physics revealed the attention between basic particle physics and geometric objects. Based on Yang-Mills equation, prophecy has been confirmed in high energy experiments performed in the world's laboratory in the following laboratories: Brockhavin, Stanford, European Particle Physics Research Institute and a standing wave. Despite this, they are described in describing heavy particles, but also have known solutions in mathematical strict equations. In particular, most physicists have confirmed, and in their "quality gap" assumptions used in the invisibility of "quark", they have never obtained a mathematically satisfactory confirmation. Progress on this issue requires fundamental new ideas in physically and mathematically.
6. The existence and smoothness of the Nawell Stowe equation
from the boat that we are in the lake, the rushing airflow follows Flight of our modern jet plane. Mathematics and physicists are convinced that they can be interpreted and predicted by understanding the solution of Naweil-Stokes equation, whether it is a breeze or turbulence. Although these equations are written in the 19th century, our understanding of them is still very small. The challenge is to make substantive progress on mathematics theory, so that we can unlock the mystery hidden in Navi Leaf-Stokes equation.
7.bsd guess
Mathematologist is always compliant with all integral solutions of algebraic equations such as