Steven Diaz has part of the answer at his blog Be Aware Math is Everywhere! The other part of the answer is because Mathematics is beautiful. Its patterns are often intricate and can give the “Aha” feeling when discovered.
Unfortunately, school mathematics is often mainly focussed on skills practice rather than investigating and searching for new patterns. Over the past few days, I have been a practicing Mathematician, albeit as an amateur. In the next few posts I will outline a couple of these investigations, and my feeble attempts.
As an Art teacher may try to show the beauty of a piece of Art, I want to excite students to be passionate about investigating and discovering Mathematics! Then they will never think to ask: “when will we ever use this?”