User blog comment:Vel!/Yudkowsky on googology/@comment-25418284-20140322200101

@Sbiis As your fictional dialogue shows, the stereotypical thought processes of googologists and mathematicians fundamentally differ. Whereas most mathematics is an act of discovery, googology is an act of artistic creation. Over time, this wiki has developed its own notions of what constitutes a "good" work of googology, a sense of aesthetic that isn't really present in the strictly goal-oriented philosophy of mainstream mathematics.

Recreational mathematics in general has a similar bent. Recreational mathematicians don't really have a generic purpose other than to amuse themselves and anyone else who happens to be interested; there may be specific, short-term goals, but in the long run it's all fun and games. For example, suppose I decide to interpret English words with septemvigintaries (base 27 with A = 1, B = 2, etc.) and write a computer program to find a set of synonyms that fall in an arithmetic sequence. If and when I find such a sequence, I have solved a specific problem just like any other mathematician, but my reason for setting up the problem in the first place is totally different. Proving the Poincaré conjecture helps us understand topology, whereas finding septemvigintary synonymous arithmetic sequences does nothing but entertain. Like googology and art in general, we also see a sense of aesthetic quality in recreational mathematics. We want number games that are simple, clever, and funny. If I make up a set of nonsense words like "zqsswtww" that fall in an arithmetic sequence, that's not very interesting as if they were real words, and especially real words that are related somehow.

Like general recreational mathematics, googology is not just math -- it's math, art, linguistics, and philosophy. And to mathematical artistic philosophical linguists, it's something very beautiful.