Where did the rule of "You should never blindly accept a rule given by authority" come from? What does it mean geometrically?

Starboy

Does every rule always have some geometrical meanings?

dchen2

Isn't mathematics just assuming a bunch of axioms true then deriving whatever theorems you can from them? So in that sense, don't we have to blindly accept the axioms? I know trying to understand the intuition behind them helps with applying the theorems or deriving more, but in the end, they are still rules given to us that we must accept.

Where did the rule of "You should never blindly accept a rule given by authority" come from? What does it mean geometrically?

Does every rule always have some geometrical meanings?

Isn't mathematics just assuming a bunch of axioms true then deriving whatever theorems you can from them? So in that sense, don't we have to blindly accept the axioms? I know trying to understand the intuition behind them helps with applying the theorems or deriving more, but in the end, they are still rules given to us that we must accept.