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RESEARCH PRODUCT

On Mathematical Language: Characteristics, Semiosis and Indispensability

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Mathematicians and others often discuss mathematics as a universal language, and say that mathematics holds a special status among sciences. In particular, it is the language of science. In some way, it is the basis of the physical world, but globally it is beyond any other science, and it is not a mere servant of sciences. Apparently, mathematical language is simple, with a little grammar and a limited vocabulary, but very different from others. Unlike natural languages, it is a rigorously defined and unambiguous one. This characteristic constitutes its greatest advantage: its complete lack of ambiguity. Although it is limited in the range of things that can express, it can be adapted to the needs of any application, what constitutes a real challenge in terms of effectiveness. A language is a medium for expressing verbally or visually facts, opinions, thoughts, feelings, desires, commands, etc. Each language employs abstract symbols (verbal or visual) to represent things. Mathematics exhibits these characteristics as a language, albeit with different emphasis and importance. The range of topics communicated in natural languages and those communicated in mathematical language differ in significant ways. Feelings and emotions are not expressed in mathematical terms, and imprecisely defined terms are not allowed in mathematical language. The aim of this contribution will be to analyze some of the characteristics of mathematical language, the role of semiotic modes in reproducing the effectiveness of mathematics in science, and the relation of the problem of indispensability to the one of the reasonable effectiveness.