purpose of super large numbers like Grahams number

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do the questions they answer have any real world applications?

In: Mathematics
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For the most part yes.

It gets quite beyond ELI5 level, but Grahams Number was constructed to answer a specific question. (Or at least place an upper bound on the answer to a question). The question involved coloring edges of cubes in various dimensions while avoiding certain patterns.

Graham’s number was an upper bound on the number of dimensions you could have before avoiding that pattern became impossible.

I don’t think Graham’s number in particular has any real-world application.

Graham’s number is from a field called Ramsey theory, which basically asks “how big does X need to be to guarantee that condition Y is met”?

Ramsey theory does have some real-world applications when it comes to graph problems. Graph problems are everywhere in computer science and engineering.

Also, if you’re interested in large numbers (that dwarf Graham’s number), I suggest reading this essay: [Who can name the bigger number?](https://www.scottaaronson.com/writings/bignumbers.pdf).