The Collatz Conjecture is the simplest math problem no one can solve — it is easy enough for almost anyone to understand but notoriously difficult to solve.
Toward the end: “If anything it shows that all the things we can solve are miracles.”
More on the Collatz Conjecture.
Hat tip: Heather Zeiger
See also: Things exist that are unknowable: A tutorial on Chaitin’s number
and
Yes, you can manipulate infinity in math. The hyperreals are bigger (and smaller) than your average number — and better! (Jonathan Bartlett)