User blog comment:Primussupremus/Why isn't Googology taught in schools?/@comment-172.58.83.157-20170530181640/@comment-27513631-20170531201615

I don't think that's terribly surprising, honestly, though. I've done a rough summary of what I think are significant parts of (finite) googology (see comments for limits of googology blog post), and the only parts which are particularly complex, if I haven't missed anything, are either too specific and useless to study as they are based on a particular theory, rely fairly heavily on meta-definability (which as far as I am aware hasn't been studied much at all, unfortunately) and wouldn't be very interesting in their own rights, or the same but for proof-theoretic analysis.

Other than that, googology is mainly an end, whereas the remainder of mathematics may (in principle) be a means, which reduces its interest.