[faktorialas]

I don't know about willingness. There's one way to back up your point though. Philosophers learn to apply rigor in very broad situations, getting used to usisng it everywhere.

Mathematicians apply it very rigorously, but mostly in math. Applying that to other areas without specific training is difficult. For this reason, academic philosophy makes a person more rigorous in life generally.

Until you meet a math problem, of course.

Not that learning anything as rigorous and precise as math won't teach you clearer thinking - of course it will.