# Interesting Math Facts for Layman

I am often asked why I chose to study mathematics. Especially from strangers and new acquaintances. Of course, I don't have the time to sit them down and tell them why mathematics is so marvelous and why their view of it is likely skewed by the way they learned it in middle/high school. In these instances I often pull out a simple and 'cool' fact that most people do not know, most will find interesting or make them think, and which does not take twenty minutes to explain the intuition behind it. Some of them are:

• $.9\overline{9}=1$
• $1+2+\cdots+n=n(n+1)/2$
• There are 'more' real numbers than natural numbers
• There are the same amount of natural numbers as rationals
• There are non-integer valued dimensions
• The No-Retraction Theorem

I was wondering if anyone else had a similar tool-kit and what is in it? I would like to add some more easy-to-explain-but-interesting facts.

• This thread contains a lot of cool little puzzles that might be useful.
– J.R.
Feb 3, 2014 at 23:26
• after many decades, my conclusion is that people who don't get it are unlikely to do so if given anecdotes. So, just acknowledge that your involvement in mathematics is somewhat rare in comparison with the entire population of the world, and let it go at that. If they like you, fine, if they dislike you because you are in mathematics, you cannot win anyway. Feb 3, 2014 at 23:43