Automatizing computational skills

Solution 1:

I too am a self-learner of mathematics working in a field where I have to use math professionally. In my experience speed or automatism has not been important. The trouble in using or learning math comes from not being able to figure out what line of reasoning to follow or how to adequately model a real-world phenomena. Once you have that right being slow or fast only makes a marginal difference.

Practice is important but for a different reason. It is not possible to grasp the relation between different ideas without thinking your way through many concrete instances. Also, every area of mathematics has certain tricks or idioms that are repeated again and again. You get a hang for them only through practice and exposure to good work done by others (good textbooks for beginners like me).

Unless you are being too modest and underplaying your effort, it is a very bad idea to "leisurely examine proofs and casually attempt a few exercises". Use pen and paper. Know the strategy of the proof well enough to be able to reproduce it on your own. Do at least 90% of the exercises.