This work analyzes the mathematical coherence of the electroweak theory.Quantum electrodynamics proves that the Dirac electron quantum function ψ has four degrees of freedom.This theory has solid experimental support.Furthermore, the rank of the matrix ( ) 5 1 γ ± is 2. Therefore, the electroweak theory that uses the product of this matrix and the Dirac electron function: ( ) 5 1 weak ψ γ ψ = ± has a mathematically erroneous structure because weak ψ assigns only two degrees of freedom to the function of the same elec-tron.An independent analysis supports this assertion because it shows a different argument that refutes the mathematical structure of the electroweak theory.