@MISC{December_objectoriented, author = {Klaus Grue December and Klaus Grue}, title = {Object Oriented Mathematics}, year = {} }

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Abstract

This paper shows that OO principles can be used to enhance the rigour of mathematical notation without loss of brevity and clarity. It is well known that traditional mathematical notation is not completely formal. This is so because mathematicians and other users of mathematical notation tend to sacrifice exactness to obtain brevity and clarity. The mathematician thereby leaves to the reader to guess the meaning of each formula presented based on the written and unwritten rules of the particular field of research. This works perfectly well for communication between researchers in the same field, but may be an obstacle for communication between researchers form different fields or for newcomers such as students. The lack of rigour in mathematical notation may also be an obstacle when mathematical phenomena are to be simulated on computers, where the programmer has to fill out the gaps in the notation. It is generally believed that complete formal rigour leads to an explosio...