To me what makes mathematical discovery really hard is the pressure to get to a point of no error. That pressure to be perfect is so daunting but so absolute! As with a single error an entire framework of thought can collapse.

Pursuing perfection defines mathematical discovery unlike any other human endeavor, except I guess logic, because there are so few areas where a perfect argument can be known!

For other areas there is an approximation, or finding of things that work where it may not be clear why.

But in mathematics for a mathematical proof every single connecting element must be known, and every single one must be absolutely perfect. And every single piece of the mathematical argument must be absolutely correct.

Or you have nothing.

James Harris