https://en.wikipedia.org/wiki/Validation_set
https://en.wikipedia.org/wiki/Smooth_function
https://en.wikipedia.org/wiki/N-simplex
https://en.wikipedia.org/wiki/Preimage_theorem
https://en.wikipedia.org/wiki/Codimension
https://en.wikipedia.org/wiki/Submanifold
I guess it depends on whether you're willing to read a textbook's worth of Wikipedia articles. (There is no shortcut. Actual 5-year-olds also require a few years until they can understand advanced mathematics.)