**Mathematics** (from al-Greek research, science) is the science of structures, procedures and relationships, which has historically been based on the operation of counting, measuring, and describing the forms of real objects. Mathematical objects are created by the idealization of property of real or other mathematical objects and describing these properties in a formal language. It can be described as a set of knowledge resulting from abstract logic reasoning applied to various objects such as numbers, the figures, the structures, and transformations. Mathematics is also the field of research developing this knowledge, as well as the discipline that teaches them.

It is likely that humanity has developed mathematical skills before the appearance of the writing. The first objects recognized certifying computational skills are counting sticks, such as the Ishango bone (in Africa) dating back 20 000 years before our era. The development of mathematical knowledge in the early civilizations is linked to their practical applications: the trade, management of crops, measuring surfaces, predicting events astronomical and sometimes executing religious rituals.

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The word “mathematics” comes from the Greek via Latin. The word mathematical means “science, knowledge” and “mathematics,” he gave birth to the term mathematikos – “relative knowledge” and “for the mathematical sciences.” This word was adopted into Latin (mathematicus) and the Romance languages.

Mathematics is distinguished from other sciences with a special relationship to reality. It is entirely intellectual nature, being based on axioms declared real (that is to say that the axioms are not subject to experience, even if they are often inspired by reality) or on assumptions provisionally admitted. A mathematical statement – usually called theorem, proposition, lemma, fact, scholium, or corollary – is considered valid, when the formal discourse that establishes its truth follows a certain structure called rational demonstration, or logic-deductive reasoning.

For college students, who write their research paper on the subject, it is necessary to indicate that although the mathematical results are true purely formally, they find applications in other sciences and in different areas of technology. Thus, Eugene Wigner speaks of “the unreasonable effectiveness of mathematics in natural sciences.” In addition to that, the investigators have to emphasize the fact that mathematics is not a natural science, but is widely used for the exact wording of natural science content and to obtain new results. Mathematics is a basic science, which provides (general) language means to other sciences, thus it reveals their structural relationship and contributes to finding the most general laws of nature.

If your knowledge is no not enough for composing a good research proposal on mathematics, you may want to consult free research paper topics. You can consider them as an example of scientific writing, providing you the set of rules necessary for proper research project composition.

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