In my experience, mathematicians will frequently argue (in general, not just in mathematics) by passing to an extreme case at the beginning. Non-mathematicians (again in my experience) sometimes object to such a mode of argument as invalid or irrelevant because such extreme hypotheticals are clearly unrealistic.
I think that the mathematical idea of first setting all the parameters to their maximal, or minimal, values, and understanding that case, before trying to tune them to a more realistic choice of values (and seeing how the solution/context changes with the parameters) can sometimes be valuable (even though it involves as a first step considering a situation that may be very unrealistic).
