Mathematics
Image Compression Using Singular Value Decomposition
Quick fact
Using SVD, you can compress an image by storing only a handful of singular values and their corresponding vectors—sometimes just 10-20 singular values per color channel can reproduce an image that is visually nearly indistinguishable from the original.
Why this is interesting
You've probably stored and sent thousands of images, each a massive grid of numbers. What if you could throw away most of those numbers without anyone noticing the difference?