Mathematics Panorama
What is Matématica? Given the difficulty of giving an adequate answer to this question, some have proposed: "Mathematics is what mathematicians do." It does not clarify the issue much, but it is therefore a good starting point. The best explanation of what mathematics is today is obtained, effectively, penetrating the workshop of the mathematician and observing carefully what it does. Therefore, use limit calculator we will try, in the first place, to explore some of the different areas of activity that we currently call mathematicians. Later we will proceed to analyze a little more deeply the general sense of this activity.
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Pure Mathematics and Applied Mathematics
It is sometimes tried to pigeonhole mathematicians into two large groups, that of the mathematicians "pure" and that of the "applied". The "pure" would be those who only care about the study and development of mathematical structures by themselves; The "applied", those who confront the realities of nature that admit some form of mathematical treatment, with the intention of understanding, exploring and exploiting such realities through the knowledge that can be detached from such mathematical treatment to which more or less adjusts that reality. Thus, it is often spoken of pure mathematics and applied mathematics. Conceiving such a division as two watertight chambers is completely inadequate
From a historical point of view and highly detrimental to the development of these two types of mathematics. The most eminent mathematicians, Archimedes, Newton, Gauss, Poincaré, Hilbert, von Neumann, Weyl ... have developed both aspects of mathematics, and it is clear that a healthy development gives this can not be obtained but by an interaction of these two types of activity within it.
The same name of pure mathematics seems to imply an introverted and morbid attitude, and therefore it is preferable to describe the activity around the same mathematical structures with the name of fundamental mathematics, and that of those who consider especially the applications, with that of mathematics of the applications. The process of interaction
Between one and another can be described as follows: Nature presents a physical, chemical, biological, social reality .... it seems desirable to explore and control. From the observation of this reality a mathematical model is extracted which appears to be adjusted in its functioning. This model is developed with existing appropriate mathematical tools and techniques, or new mathematical structures are created that allow for their deeper knowledge. In this study the mathematician, driven by the desire to know in depth the mental structure underlying the model, goes on many occasions much farther than the mere dominion of the initial reality would require. Once you know the model and the laws that govern it, it is a question of rehearsing this conceptual domain in the reality of departure. The attained knowledge of the model, partly perhaps superfluous for the moment, is stored and maybe one day will be used.
From a historical point of view and highly detrimental to the development of these two types of mathematics. The most eminent mathematicians, Archimedes, Newton, Gauss, Poincaré, Hilbert, von Neumann, Weyl ... have developed both aspects of mathematics, and it is clear that a healthy development gives this can not be obtained but by an interaction of these two types of activity within it.
The same name of pure mathematics seems to imply an introverted and morbid attitude, and therefore it is preferable to describe the activity around the same mathematical structures with the name of fundamental mathematics, and that of those who consider especially the applications, with that of mathematics of the applications. The process of interaction
Between one and another can be described as follows: Nature presents a physical, chemical, biological, social reality .... it seems desirable to explore and control. From the observation of this reality a mathematical model is extracted which appears to be adjusted in its functioning. This model is developed with existing appropriate mathematical tools and techniques, or new mathematical structures are created that allow for their deeper knowledge. In this study the mathematician, driven by the desire to know in depth the mental structure underlying the model, goes on many occasions much farther than the mere dominion of the initial reality would require. Once you know the model and the laws that govern it, it is a question of rehearsing this conceptual domain in the reality of departure. The attained knowledge of the model, partly perhaps superfluous for the moment, is stored and maybe one day will be used.
In the description that follows from the different fields of the current mathematics we will try to indicate specifically some of the points in which this interaction is presented.
In describing the diverse environments of the fundamental mathematics and the mathematics of the applications it is necessary to bear in mind also that the mathematics nowadays constitutes an organic unit in which the interdependence between its diverse fields is perhaps one of the most striking notes of the contemporary mathematics. One cannot, for example, speak of mathematical logic without taking into account the modern computer science, nor of geometry ignoring the analysis. At the end of our journey we will briefly examine the deep sense of mathematical activity and its role in human culture.Edit this text to make it your own. To edit, simply click directly on the text and start typing. You can move the text by dragging and dropping the Text Element anywhere on the page. |