So you think the whole of math is just numerical computation? You think there is nothing more to math than computing values of certain classes of functions? This is what you get when your only exposed to so called higher math is calculus and perhaps a few courses on differential equations, with emphasis on numerical methods.
There are areas of math that don't fit this simplistic view, things that don't have analytic in their name, like topology, non-Euclidean geometry, mathematical logic etc. Algebra in general is all about studying structure that ensues when you have bunch of objects and operations you can do with them with certain properties. This structure doesn't depend on the nature of object or operation. For example rotation group etc. Then there are things like measure theory, fractals, and things like non-commutative operator algebras that are useful for applications in quantum mechanics. All in all a huge chunk of math is not about computation. Bigger in fact than the part about actual computation, esp. computation of real numbers.
I had a similar reaction after reading the beginning of this article. I feel as though modern algebra uses symbolic manipulation as a means of qualitative discovery and understanding.
There are areas of math that don't fit this simplistic view, things that don't have analytic in their name, like topology, non-Euclidean geometry, mathematical logic etc. Algebra in general is all about studying structure that ensues when you have bunch of objects and operations you can do with them with certain properties. This structure doesn't depend on the nature of object or operation. For example rotation group etc. Then there are things like measure theory, fractals, and things like non-commutative operator algebras that are useful for applications in quantum mechanics. All in all a huge chunk of math is not about computation. Bigger in fact than the part about actual computation, esp. computation of real numbers.