User blog comment:Primussupremus/What are the limits of Googology?/@comment-30754445-20170531225910/@comment-30754445-20170605011416

There are very simple mathematical problems whose answer are googological. For example: The length of the longest possible sequence of numbers which uses 1,2,3 and has the Friedman property (look it up) is greater than 10[7190 arrows]10 (or J7190 in my letter notation). Larger examples include Hydras and the TREE function.

So yes, these numbers do have uses in mathematics.

And they aren't too difficult to work with, either... at least not once you get used to them. The problem is that many googologists just love the sense of mystery that comes with the craft, and tend to complicate things way beyond what's actually needed.