I think "a phd in algebra" is shorthand for "I did my doctoral research on an apocryphal subject that is only understood by a sub-sub-sub field of the mathemati

I think "a phd in algebra" is shorthand for "I did my doctoral research on an apocryphal subject that is only understood by a sub-sub-sub field of the mathematics research community and I wrote a thesis with a title that would simultaneously melt your brain and mean nothing to you, so I'm saying it in a way that you would kind of get more or less what my PhD was approximately about ish, with caveats". In the same sense, I "have a PhD in AI". You have a PhD in "what could be said to be the Landlands problem itself". It happens.