If you look at the output of mathematicians and their biggest discoveries it suggests that it is similarly limited for mental tasks.

Probably this category of mental tasks. For politicians it's the other way around. Prolly you need to have some 'elder statesman' skills as well as wisdom to achieve greatness. Deng Xiaoping (https://en.wikipedia.org/wiki/Deng_Xiaoping) started changing China at the venerable age of 70+ moving forward until his death almost two decades later.

Do not underestimate wisdom as a cognitive skill, even if in today's world we tend to discredit it because of agism.