In Visual Complex Analysis's preface, the author gives an analogy with pseudo-deaf musicians and follows the same to mathematics. Mathmatics 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 ?
The best way to develop intuition is to practice, as far as I know. At that level, it's best to read some research papers and implement them on your own. After 30-40 times, you will yourself understand that you got some intuition into things.