Watching some YouTube videos of the biggest numbers ever used in a legitimate calculation usually gets you things about Graham’s number or Tree(3) (as an example).

The numbers represented in those things is beyond huge. Indeed while Graham’s number is truly ridiculously huge Tree(3) makes Graham’s Number seem a spec.

As is noted in the Graham’s number video, if you could hold that number in your head your head would literally collapse into a black hole. Tree(3) is waaaay bigger.

My question is, while it is fun to think about these things, are they of any use whatsoever? Or are they just play things? The explanation of Graham’s number, while a real calculation, seems completely random and more a math puzzle than anything that is useful.

Am I missing something? Is working these sorts of problems out a useful effort in advancing mathematics?