I’ve checked carefully, and nowhere is it necessary to add ‘condom’ to the Peano axioms in order to prove that 1+1=2.
Perhaps the writer intended to use a different two-variable function than additon, like ‘fucking?’ 1 fucking 1 = 3? Nonetheless 1 fucking 1 is actually a probability distribution over the natural numbers.
The best way to understand magnets is to study Maxwell’s equations for electromagnetic fields.
Magnets themselves either work by having a system of dipoles linked together. Each dipole is the result of quantum-mechanical spin. Electromagnets work by running a changing current, inducing a magnetic field (the opposite method works as well; in fact the voltage of house current is dropped from its high level in the wires to the 120/240V level by transformers which are just two electromagnets next to one another; one of them produces a magnetic field, and the other picks up a current from being placed in the field).
The magnetic field has, so far as is known, no monopoles.