Although I would disregard the first 37 secs of the movie which are exagerated : The colors of math is a nice little intro showing the diversity yet common curiosity that one can find in math
The objective of this page is to introduce as many people as possible to the beauty of mathematics and science. The content of this section is therefore intended to be as general and accessible as possible and to help everyone interested in learning. For this reason much of the content appears as movies, short explanations, summaries, facts, or book references
Is mathematics discovered or invented ?
On the importance of mathematics for discoveries in physics. A nice paper by Edward Frenkel for the Atlantic: