Here’s one that’s so common that we don’t give it a second thought: Every picture you see today is nothing but math. You know, there was a time not that long ago that movies, TV and still pictures were “analog” media.” Photos were the easiest to understand — Light hit a piece of plastic with chemicals on it. The chemicals were affected by the light and after a lot of this or that, and some projection, paper and more chemicals, you got to see what the camera saw, exactly how the camera saw it. It didn’t take a lot of brain power to understand.
Now you point your phone at something and a chip the size of a pinhole somehow captures differences in voltage created by different wavelengths and intensities of light. Then, faster than you can even think about it, those differences are converted to a string of ones and zeroes, and then run through incredibly complex filters that eliminate 90% of the numbers then still keep the image intact (somehow.)
The numbers that remain are stored either on a chip or on a spinning disc, and when you want to see them, almost instantly complex mathematical processes spring into action enabling those missing 90% of the numbers to reappear so that when your computer reads them one at a time, they can be reassembled and rejiggered into an image on your screen (which is another technological marvel in and of itself.)
Seriously, does any of that seem like it could actually work? It all does, and that’s a tribute the math involved.