Have particle physicists really falsified set theory (and with it mathematics as a whole)?

Set theory took off when Georg Cantor distinguished “countable and uncountable infinity”.This distinction meant that we could finally understand the fundamental sets N, Z, Q and R consistently as constructs from N (the former three being countably infinite and the latter being uncountably infinite). This made possible a consistent set theory avoiding Russell’s paradox (ie, that no set can contain itself as set, but just as a subset).

However, about 80 years later the German Nazi entomologist Willi Hennig surprisingly claimed that it is high time for biological systematists to acknowledge that Russell’s paradox is real in the form of a “single true tree of life” (an approach that was later called “cladistics”). It was just as if consistent set theory hadn’t took off at all. Hennig was in any case obviously not aware of it.

Even more surprising, about at the same time some physicists (called particle physicists) began searching for Russell’s paradox empirically in the form of “Higgs particle” using the “Large Hadron Collider” at Cern in Switzerland, a search they recently claimed had been successful, or at least that they “as laymen can say that they think they have got it”.

Today, we can thus understand that if Willi Hennig and particle physicists are right, then set theory (and with it mathematics as a whole) is fundamentally wrong, whereas if set theory (and with it mathematics as a whole) is right, then Willi Hennig and particle physicists are wrong. So, which is it? Have particle physicists really falsified set theory (and with it mathematics as a whole) empirically? Have they really found the impossible “Higgs particle”?