‘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.
Category: Mathematics and Science
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.
Without a source I recall a text I read which described the invention of the Monte Carlo Method, and how it “was dignified with a name” after being used extensively during the Manhattan Project. This is a fantastic phrase that fits this method well.
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 are real numbers.
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.
This semester I’ve taken a course covering, again, introductory point set topology. This is a fairly standard and basic subject to cover in an undergraduate mathematics course. There is something fascinating about point set topology; it invites conjectures and then dashes those conjectures in satisfying and clever ways.
Problems from Chapter 4: Linear Operations, Section 1: The Dimension Formula
Problems from Chapter 3: Vector Spaces, Section 3: Vector Spaces