Categories of “Interesting” Mathematics

‘Interesting’ is a subjective notion. One might distinguish several different categories of ‘interesting’ mathematical statements or problems. This article talks about a few of these categories with examples.

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Cubes and Tesseracts on Paper

A tesseract is a ‘four dimensional cube’, that is projected into three space. The qualifier may be unnecessary, but of course you’ll never see an example of a tesseract for which this isn’t the case.

Source from wikipedia article of regular 4 polytopes

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Notation Stifles Arithmetic Intuition Building

There are a multitude of ways to represent additive and multiplicative operations. Typically students will learn something like the following for addition, subtraction, multiplication and division respectively. Where a,b are real numbers.

a+ b, a - b, a \times b, a \div b

Here I am just going to enumerate the problems with these basic notations and why similar notations do not work either, and then conclude with modern notations that are well suited to these operations.

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