Actually that was a very interesting read for sure, thanks @BalarkaSen, it all makes sense after some looking at Forster, Miranda and Shafarevich

@BalarkaSen fundamentally think differently meaning I'm more algebraic?

Ye

@BalarkaSen You'll come to the dark side :')

Well as a joke sure but I don't think I get or appreciate the algebraic viewpoint very much

in AG or in general?

Generally

Analytic number theory is more interesting than algebraic number theory, to you, say?

I think you're misunderstanding. Everything is interesting, but my viewpoint is fundamentally geometry. I don't think I understand algebraic number theory the way algebraic number theorists would do; the motivation for ideal class groups for me comes from the Picard group

I translate things to geometry to understand them

Sure, I see

The algebraic symbols are quite literally meaningless to me, unfortunately perhaps

Similar for analytic number theory, I don't understand modular forms as just holomorphic functions satisfying this or that

They are sections of certain line bundles on modular surfaces to me

Not a critique, but maybe you got comfortable with those tools, and it made it easier to learn other notions by comparison, meaning you didn't get to appreciate the other perspectives. Could be completely wrong

That's probably true

I just think my fundamental guiding principle in mathematics is just understanding shapes

idg the other various abstract objects as separate from that viewpoint; they're still just generalizations of shapes to me