Hadamard estimated that :
About 90% of mathematicians thinkvisually, 10% think formally.
Usually, they think in steps:
- Get the right idea, often think vaguely about structural issues, leading to some kind of strategic vision;
- Tactics to implement it;
- Rewrite everything in formal terms to present a clean, logical story. (Gauss’s removal of ‘scaffolding’ – middle working steps)
Source: [NLB #510.922]
Mathtuition88 