The irrefutable proof of the incorrectness of the Korteweg—De Vries (KdV) equation is proposed. The correct methodological basis for the proof is the unity of formal logic and rational dialectics. The unity of formal logic and rational dialectics is the only correct criterion of truth. The proof leads to the following irrefutable statement: the Korteweg—De Vries (KdV) equation — a partial differential equation with respect to the dimensionless displacement as the function of the dimensionless coordinate and the dimensionless time — represents an incorrect equation in physics. The proof of this statement is based on the following irrefutable assertions: (1) the Korteweg-de Vries equation does not describe a physical phenomenon (process) because the dimensionless displacement, the dimensionless coordinate and the dimensionless time are non-physical quantities; (2) in the formal logical point of view, the physical (or geometric) interpretation of the equation and solutions of the equation are inadmissible; (3) comparison with experimental data (which have dimensions) is inadmissible (impossible).Consequently, the Korteweg-de Vries equation is a gross error in physics.