In Récoltes et semailles, Grothendieck writes
observe that the concept of the group (notably of symmetries) appeared only in the last century (introduced by Évariste Galois), in a context that was considered to have nothing to do with Geometry. Even in our own time it is true that there are lots of algebraists who still haven't understood that Galois Theory is primarily, in essence, a geometrical vision, which was able to renew our understanding of so-called "arithmetical" phenomenon.
I don't understand why Galois theory (which is a theory that connects field theory and group theory) is a "geometrical vision". Isn't it more an algebraic theory in the sense that it connects two different kind of algebraic structures (fields and groups)?