  Our digital technology depends on mathematics to compute current flow and
design its devices. Mathematics describes current flow by an idealization,
Kirchhoff's current law. All the electrons that flow into a node flow out. This
idealization describes real circuits only when stray capacitances are included
in the circuit design. Motivated by Maxwell's equations, we propose that
current in Kirchhoff's law be defined as \[{\varepsilon }_{\mathrm{0\ \
}}\frac{\mathrm{\partial }\boldsymbol{\mathrm{E}}}{\mathrm{\partial }t}\
\mathrm{+}\mathrm{\ }\mathrm{\ }\widetilde{\boldsymbol{\mathrm{J}}},\] the sum
of (1) displacement current (2) the flux of charge associated with mass. The
flux of charge associated with mass $\widetilde{\boldsymbol{\mathrm{J}}}$
includes, for example, the polarization of dielectrics as well as the movement
of electrons. Kirchhoff's law becomes exact and universal when current is
defined this way. This current is the source of the magnetic field; it is the
source of $\boldsymbol{\mathrm{curl}}\boldsymbol{\mathrm{\
}}\boldsymbol{\mathrm{B}}$ in Maxwell's equations. Kirchoff's laws and
Maxwell's equations can use the same definition of current.
