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Ff = μN

can also be defined as

Ff = μ.m.g

One of my friend say that mathematically, that equation tell us that when there is a gravity force, Ff can't be zero assuming that there is no zero μ

Is that true? While on static condition I will say that even when there's a gravity force, the friction force is zero. But he said then if it is in static condition, then the formula would be

Fmax = μ.m.g

which mean when there is a gravity force, Fmax can't be zero.

Can physics really defined just by formula mathematically?