Do you like math? Are you good at solving equations and theorems? Well here you will find some good challenges. Today you will know the most famous mathematical problems with no solution in history. Surely when you finish this article you will run to find paper, pencil and a calculator.

The
most famous mathematical problems and theorems without solution of the
history

Hodge's conjecture

Hodge's conjecture is one of the unsolved mathematical problems that is closely related to algebraic geometry. In fact, the best current scientists They have expressed that this is one of the most difficult theorems without solution for the general public.

Hodge's conjecture somewhat seeks to break down all complex algebraic equations into others that are much simpler. This mathematical problem wants to see mathematical equations as units that can be divided into smaller fragments.

Riemann's hypothesis, of the oldest unsolved mathematical problems

This is a work of the German mathematician Bernd Riemann in which he suggests that there is a very close relationship between how prime numbers behave and Riemann's zeta function. What Bernd Riemman said has not yet been proven in concrete terms.

Of all the mathematical problems without solution, this is the one that has not been solved for a long time. Riemman's hypothesis was raised in the year 1859. Many mathematicians have been the ones who wanted to prove it, but so far the work of German is only given a hypothetical role.

Yang-Mills and the mass jump

This mathematical problem is based on the existence of a mass jump or mass gap as a solution to the Yang-Mills theory. The latter talks about the elementary particles of matter, and the existence of gluons at the quantum level.

The interactions between the elementary particles of matter are, in large part, explained by the mass jump that Yang-Mills poses. In these mass jumps or mass intervals the quantum particles have positive masses, while the classic waves travel at the speed of light.

Specifically, what you want to solve are the gaps or questions that still exist in the Yang-Mills theory. In some computerized simulations it has been possible to verify the proposed, but in theoretical and experimental works not yet.

The Navier-Stokes equations

Another of the most famous unsolved mathematical problems in the world. The Navier-Stokes equations try to explain the behavior of atmospheric liquids and gases, ocean currents and other flows around moving objects.

There are still many questions about these equations and how they try to explain the passage from turbulent to non-turbulent behaviors in fluids. It is expected that with future work and research the missing pieces can be found to solve this puzzle.

The importance and usefulness of solving these equations is that predicting the behavior of gases and liquids can help to know how storms, tornadoes and hurricanes will form and develop.

Birch and Swinnerton-Dyer conjecture, another of the unanswered mathematical problems

The Birch and Swinnerton-Dyer conjecture is one of the unsolved problems in the mathematical world that has managed to beat the brightest minds of today. This mathematical problem is a combination of algebraic geometry and number theory.

The Birch and Swinnerton-Dyer conjecture studies solutions to equations aimed at defining an elliptical type curve. It has always been wanted to know how to distinguish an elliptical or gender 1 curve from those of other types.

There is a classification of the algebraic curves that group them into curves of type 0, which have no or infinite solutions. And also, type 1 curves that have a finite or infinite number of solutions. Thus, it is elementary to identify the type of algebraic curve to perform an operation.

mathematical problems unanswered

P versus NP

The problem P versus NP is one of the theorems with no solution found that marvels at its difficulty, complexity and possible mathematical applications. This theory suggests that there are problems in which there is a greater complexity in finding an answer than in checking whether the solution is correct or not.

In mathematics, those with a solution that can be found in a time considered reasonable are known as P-type or polynomial problems. On the other hand, NP-type problems, also called non-deterministic in polynomial time, are in which it can be somewhat complex or difficult to find a solution, but when it is found it is a simple matter to check if it is correct.

Then, when you have a problem in which the solution is easily found (type P), you will also have one in which the solution will be checked in a simple way (type NP). Scientists do not know if there are NP-type problems that are not P-type, but they think it is likely to be so. The truth is that no one has been able to prove this.

The
Poincaré conjecture, one of the mathematical problems “without
solution ”solved

The Poincaré conjecture is the only former member of the list of unsolved mathematical problems. The one that at one time was one of the most difficult hypotheses to verify, in 2006 it was solved by the Russian mathematician Grigori Perelman.

In this way, Perelman managed to demonstrate with his work that the surface of a three-dimensional sphere is characterized by being the only surface simply convex, compact and closed. Before this statement had only been accepted for two-dimensional spheres.

Solve one of these
unanswered mathematical problems for a million dollars

Still don't dare to try to solve one of these mathematical problems without solution? Do not you dare to try for the modest figure of 1 million dollars ?. That's right, by solving one of these mathematical problems of the century you can earn a small fortune.

The only person so far who has managed to solve one of these problems has been the Russian Grigori Perelman. He refused to receive the award, and did not want to be listed as a genius or anything like that. This surprised quite a few, who would dislike a million dollars?

You know what are the math problems for now without solution. If you are good at math you should start calculating what you would do with that money. Maybe you become a mathematical genius today with just one exercise.

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