TITLE: Useless math that became useful
QUESTION [13 upvotes]: I'm writing an article on Lychrel numbers and some people pointed out that this is completely useless.
My idea is to amend my article with some theories that seemed useless when they are created but found use after some time.
I came with some ideas like the Turing machine but I think I'm not grasping the right examples.
Can someone point me some theories that seemed like the Lychrel numbers and then become 'useful'?

REPLY [2 votes]: The solutions of the closest-packing problem, of how to most densely pack non-overlapping congruent $n$-spheres in $\mathbb R^n,$ have, for some  $n>3,$ been found to have applications to error-detecting and error-correcting codes in digital transmissions.
In the book Knots by Kaufman there is an example of an application of knot theory (the study of homeomorphic embeddings of $S^1$ into $\mathbb R^3$) to statistical mechanics.