[I am not an mathematics educator; but because the process of learning is educating yourself, I'm posting it here]
In Visual Complex Analysis's preface, the author gives an analogy with pseudo-deaf musicians and follows the same to mathematics. Mathematics today, he argues, is mostly build on abstract symbolic manipulation rather than much more stronger visual (intuition) method.
Is it a good notion to rely on visualization and intuition solely on graduate and postgraduate mathematics on topics like Analysis, Abstract Algebra and other fields (Topology and differential geometry is pretty obvious - it is probably visual per se) ?
If yes, then how to visualize and develop intuition in graduate and postgraduate mathematics in fields mostly relying on (stupid; ?) symbolic manipulation ?