If you choose one of these 6 challenges, you then will pay $ 1 million

The clay mathematics Institute is a private organization, which in 2000 called the main task of the Millennium, a decision which offered a reward of $ 1 million Over 17 years the best mathematicians in the world have managed to prove just one hypothesis.

We at the Website decided to try their hand in the remaining quests. Who knows, perhaps among our readers there's a new Isaac Newton.

Equations of the type xn + yn + zn +... = tn has been known for a long time. However, a universal method of calculation does not exist for them. We only know that each equation can be either finite or infinite number of solutions. Birch and Swinnerton-Dyer has created a method by which each such equation can be reduced to a more simple, called the Zeta function. If the value of the Zeta function at point 1 is equal to 0, has infinite number of solutions, and Vice versa. While no one has proved nor disproved this hypothesis.

  • Explanation hypotheses: wikipedia.org, claymath.org

Stephen cook formulated the question so: whether the verification of the correctness of the solution to be longer than the actual receipt of the decision, regardless of the validation algorithm? So far no one has managed to find such a task. It could lead to a revolution in cryptography and encryption systems.

  • An explanation of the problem: wikipedia.org, claymath.org

To explore any subject, mathematics first try to decompose it into building blocks. But it does not always work — sometimes there are new parts or do something with the original components. In their works Hodge has described the conditions under which these extra parts do not occur and any object can be studied as an algebraic equation. Neither prove nor disprove its hypothesis can not have more than 70 years.

  • Explanation hypotheses: wikipedia.org, claymath.org

If you go on the boat, there will be waves, and if you fly on a plane in the air will arise turbulent flows. It is expected that these and other phenomena are described by the Navier — Stokes equations. Although the equations established in 1822, no one knows how to solve them. At the same time they are actively used by designers of planes, cars and ships. If someone finds a method of solving equations, it is, for example, will make it unnecessary to aerodynamic testing.

  • Explanation of the equation: wikipedia.org, claymath.org

It is still unknown exactly how the primes are distributed according to the number of figures. In 1859, a way of finding them and checking proposed Bernhard Riemann. His method has been successfully applied to more than 1.5 trillion primes, but the hypothesis remains not proven.

  • Explanation hypotheses: wikipedia.org, claymath.org

Physicists have made their quantum equations in 1954. They found a way to unite the theories of electromagnetic, weak and strong interactions. By using the theory of Yang — mills was even able to predict the discovery of new particles. However, while nobody is able to predict the correct mass of the particles and in General to understand how these equations and whether they are true.

  • Explanation of theories: wikipedia.org, claymath.org
Source claymath.org

See also
Only 2 % of people can solve the problem that Einstein came up with in childhood
7 questions Google has stopped asking during the interview

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