Answer:
Although present standard theory does not appear to forbid them, no magnetic monopoles have as yet been observed.
Explanation:
Additional notes:
At the theoretcial level, my understanding* is that their existence predicted by most (possibly all) extensions of the standard model. It has been suggested that this might imply that magnetic monopoles existed in the early universe but that monopole symmetry was not broken in the same way that charge symmetry was broken - in which case the monopole pairs would have mutually anihilated leaving a near undetectably low number in today’s universe.
Non-detection at CERN may imply that their masses are outside the range of energies so far available, or it may be that there is some as yet unidentified mechanism that inhibits production from “ordinary” energetic matter (all speculation, of course).
