>>12313278Yes exactly, in analysis you carve deep paths into unkown territory of what an algebraic structure can do. People generally say that we dont have an overarching theory of PDE.
In algebra you focus on what you are given to start with and make deductions from that.
Sometimes in analysis a bit lf structure is discovered and things become more algebra-like. For example we now know that many analytical objects like to live on Hilbert spaces, so we can study abstratc Hilbert spaces, classify them etc.
It's actually the same with vector spaces. I bet in the past people considered the study of finite dimensional vector spaces analytical, It was analytical geometry. Now we know what makes them tick and we study the axioms of abstratc vector spaces.
And I think even with PDE this might happen. I dont know this topic but arent there D-modules? That sounds exactly like trying to find a minimal set of axioms which make PDE tick and then studying these algebraically
