I don't tend to do a lot of proofs anymore. When I think of math, I find it most important to be able to flip back and forth between symbol and referent freely - look at an equation and visualize the solutions, or (to take one example of the reverse) see a curve and think of ways of representing it as an equation. Since when visualizing numbers will often not be available, I tend to think of properties of a Taylor or Fourier series for that graph. I do a visual derivative and integral.

That way, the visual part tells me where to go with the symbolic part. Things grind to a halt when I have trouble piecing that visualization together.