Over the years, and especially from the ancient era, the mathematicians and philosophers of the time gave various contributions in terms of mathematics and its branches, many of these contributions were recorded in history, while other problems of a mathematical nature are still present today, but because they are not recorded, we do not know anything about their possible solution, nor about how to be able to consider the solution to these problems based on their historical antecedents, that of being solved of insurance They would have a great contribution to the advancement of science and technology.

The proposal I offer through this publication is to capture certain features and elements that are important when describing and evaluating the mathematical problems that have been evidenced throughout history, and that although they were left unresolved, they leave the doors open for Continue research and find possible solutions. The importance that these possible solutions describe will be taken from the already recorded and written history from which we can all have access and knowledge in detail.

Issue

Mobilizing elements within the branches of mathematics:

Within several problems that have been presented throughout history as far as mathematics is concerned, I can cite the following (just to take one as an example):

Square of the circle

This problem has an impact on the dynamism of Analytical Geometry and the infinitesimal Calculus, while at the same time the analyzes of Euclid and Archimedes are addressed to the problem of measuring and the relationship between algebra and geometry.

As I mentioned earlier in the background, there are mathematical problems that have been recorded in the history of man since ancient times and that until now have not been solved, in this order of ideas the problem of the square of the circle, although when from time old tried to solve this problem without getting concrete solutions, despite this left open the possibility through their contributions so that posterity in the framework of conceptual aspects future developers of science and mathematics can study and solve this problem.

The idea of ​​quadrature of the circle in ancient times was to take the value of the area of ​​a circle and make the equivalent to that area embodied in a square rectangle, considering exact results, all this using ruler and compass. Now giving an own contribution can say from my perspective that the way towards the solution of the quadrature of the circle is still open, although seeing the solution from a practical way can be considered to calculate the area of ​​a circle analytically by means of the formula that we all know: A = πr ^ 2, to then approximate this result to area values ​​of a square rectangle, all analytically and then taken to the construction using the classic rule or compass. We have to keep in mind that the problem may continue to persist because when we use the formula A = πr ^ 2, the number π is a transcendental infinitesimal number, which makes impossible the exact calculation and equivalent of the area of ​​a circle to that of a square. For all the above, it is worth making the following analysis, if we analyze that different bodies of matter in the physical world in which we live can be compared for their previous study in the field of physics and science, which is important for medicine and engineering, reason is that it makes us reflect that not only look for equivalent areas between the diversity of existing geometric bodies should be the object of deep research, but for the various irregular mass bodies and the relationship between their areas, we need to continue deepening about the contribution that is given to us by means of the differential and integral calculus in order to find the exact value of their areas. The depth of the exhaustive study on the infinitesimal calculus through limits, derivatives and integrals will help us more and more accurately approximate the value of the area of ​​a circle to that of a square or other geometric figures.

Even more if we continue studying and evaluating all the concepts that were opened through the mathematical history, I must say then that the theories of series and convergences give way to construct rectilinear figures starting from the number π, this even though it is a number transcendental.

I want to make clear that the problem of squaring the circle is just an example cited by me through this publication with the clearest and simplest reason to call for reflection on the various topics that remained in the mathematical history, and that should continue to be analyzed by many of us today, and that if their solution is found, then perhaps we would be finding the solution to various problems in the nature of the technological future and advancement of science in general.

When analyzing the mathematical historical event, we realize that if we investigate within the context of the emergence of new mathematical topics, we find that its evolution can be understood within the themes that we are often trying to teach in our universities. It makes us think about certain trivial aspects that can make us evolve on great contributions and results, of which history has not confirmed them to the future of our contributions to science and mathematics.

To deepen the aspects that give importance within the problems and possible solutions within the mathematical historical events, I propose to apply the following methodology that opens research fields to find solutions to these aspects:

2.1 Choose a topic of mathematical study.
2.2 Evaluate the historical evolution of the mathematical topic that we chose in 2.1.
2.3 Analyze the historical evolution of step 2.2 based on the depth of its theoretical bases.
2.4 Carry out the conclusions of the case based on deep aspects of scientific research.

Greetings friends steemians.