I believe magnetic monopoles do not exist. The reasoning is as follows:

Maxwell's equations in vacuum indeed possess an electric–magnetic dual symmetry (E → B, B → –E). However, once electric charges are introduced as sources, this symmetry is broken — unless magnetic charges are introduced at the same time.

Experiments have so far not observed any magnetic monopole, indicating that the electric–magnetic dual symmetry is broken in the actual world. This stands in evident conflict with the mathematical unity demanded by conservation laws. According to Noether's theorem, a continuous symmetry necessarily implies a conserved quantity. Yet here, a symmetry that "ought to" exist is excluded by experimental fact without any explanatory mechanism.

This is not a rigorous mathematical deduction, but a strong mathematical-physical inference based on symmetry structure and conservation laws, pointing to the incompleteness of current theory.