True for a simple resistor, but not any circuit element. Not true of a varistor, for example.
Oops! Correct you are! I should have said any linear circuit element. What others besides varistors? Any semiconductor I suppose..
Other examples of non-linear resistors: light bulbs, heating elements, vacuum-tube cathode heaters. Actually, Ohm's law is approximate, but usually good enough for "normal" resistors. For two-terminal resistors, the equation we all learned is
V = I x R , where the voltage, current, and resistance are "scalars" and the resistance is constant. For a more general problem (such as a surface or bulk conductor) the linear equation is J = (sigma) x E , where the current density J (A/m
2) and electric field E (V/m) are vectors and the conductivity (sigma) (1/A m) is a constant. For more complicated cases, the conductivity can be a tensor (matrix) if the material is not isotropic (conduction depends on direction).
In non-linear resistor theory, a "resistor" is a device where the voltage across the device is a function of only the current through the device, while a "capacitor" is a device the voltage is a function of only the charge in the device, etc.
(PS: how does one insert symbols into these posts? I tried copy/paste from Word, but it didn't work.)