When I started doing math seriously, I also feel strongly in love with "existence proof", where you were asked to prove that "something" existed, and any logical reasoning was considered fair game, even if you never found the "something".

Then, I started doing applied maths, where proving the existence of a solution is a nice bonus, but finding an approximate solution is the goal.

Here, we have an example of a funny proof of existence that does not tell you where to drill.

Some carbon was emitted during the publishing of this model - that will be so much more carbon to offset if we ever end up actually finding some real hydrogen.