# Showing the beauty of math to interest undergraduate students in math

Math is not the most popular subject among students, especially in America. I have recently been thinking about giving a talk to undergraduate students encouraging them to do mathematics not because it is useful, but because it is beautiful/interesting/surprising etc. Since I feel most confident in topology and topology related fields, I would like the topic to revolve around topology/algebra, but other ideas for topics in other fields are also appreciated. The specifics are the following:

The audience: undegraduate students, a lot of them with only basic understanding of mathematics

Length: flexible, anything between $15$ minutes to $1$ hour

Purpose:

• showing the beauty of math
• overcoming students' fear of mathematics
• getting people interested in math

What to avoid: I want to avoid the argument "math is useful." I want them to appreciate math the way they appreciate music, art, or a good book. The argument "math is useful" is a very dangerous one (for example, for some it puts an equal sign between the words "good" and "useful") and I want to avoid that (The question "should math be useful" is a topic for a different discussion)

There is a similar question already posted on here:

and some of the ideas there are worth considering. However, my question is a little different since:

• I do not have the time constraint as the author of the previous post
• My audience may not necessarily consist of very intelligent students

Moreover, getting new answers to this question can help us all to get new ideas on how to persuade our students that math is beautiful and does not have to be dreaded.

Any help will be greatly appreciated.

• I gave a talk about the basics of Category Theory and realized I was being too ambitious. Since students are attracted to the fun-and-games aspect of mathematics, I would recommend a talk connecting basic combinatorics to some ideas in Algebra. – Yunus Syed Feb 1 '18 at 19:15
• A little number theory, a little modular arithmetic, cryptography. Beautiful and even useful (despite Hardy's comment). – Ethan Bolker Feb 1 '18 at 19:25