I think that one main issue is that many people unfortunately equate math with routine calculations or rote memorization. I think it's valuable to communicate that actually math is the art of creative thinking. To do this, it helps to share some "gems", or examples with powerful "Aha" factors.

Along these lines, I have a very fresh one: last week, I just had a very shocking (mathematical) realization while thinking about football:

There is a way to instantly see the optimal running angle when evading an equal-speed defender in football: eyeball the line which runs through the midpoint between you and the defender, and see where it hits the edge of the field - run straight there.

I was immediately floored by this observation, because it is so easy in retrospect that it should be common knowledge. Yet literally everybody I've told this to has said that it was new to them - mathematicians & people from the general public. I quickly threw together a video to share it across the community:

https://youtu.be/9sxVgJ_wPaM?list=PLqv4sKOD1bsUoSs-SbzlA2BE1...

I think that by thinking of and packaging cool nuggets of "math" like this to share, we can help rebrand the image of math. :)