Over de Taal Van de Wiskunde

Abstract

The professional mathematician employs in his writings a special language, which we call 'the language of mathematics'. It has two components: on the one hand (a fragment of) natural language, and on the other hand a highly specialized artificial language. The latter part attracts the eye in a mathematical text, because of its deviating form: it contains symbols, formulae and the like. Yet almost all peculiarities of mathematical language, including those of the artificial part, can be embedded in the usual natural language frame. This different appearance of mathematical language originates from a mathematicians urge for efficiency, clarity and compactness. A noteworthy advantage of mathematical language is found in its treatment of coreferences. The artificial part of mathematical language employs a highly developed reference mechanism, called binding. A formula like 'εx IR(x > x2)' for instance, contains a bound variable 'x' of which only the category (viz. the set of real numbers) is fixed. The variable 'x' can be replaced by another one without changing the meaning of the formula: 'yε IR(y > y2)'.This mechanism of binding makes all kinds of referential words, as used in natural language (such as relative pronouns), superfluous. Mathematical language is still in full development. Especially at the word and word group level, many interesting linguistic features can be observed. At the sentence and text level, however, mathematical language is not very revolutionary. Here improvements are possible, and some of these are proposed in the article.