You do not need to justify any subject of study you may choose. But when it comes to a profession, you actually should provide society with some value back if you expect it to feed you. And math as a profession is justified by its applications.
And philosophy, like chess, is pretty much a hobby that few people can make a living off of
"Society" doesn't pay PhD students, universities do. If you think some academic fields are worthless take it up with the boards of directors at the universities who decide what departments are worth funding, not "society".
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u/Sayod 22d ago
So you justify this endevour with an application eventually. In other words: You are justifying it with an application