In a very cerebral book I came across the "irresistible force paradox" (wiki: link) —okay, it was a Superman graphic novel, but still.
The paradox asks what would happen if an unstoppable force encounters an unmovable object.
Classically, the problem has no solution as the definition of each object violates the definition of the other.
Whereas, Kal-El's answer was they surrender, a rather witty, but nonsensical answer.
Another solution I can think up is that the unstoppable force are neutrinos, which don't interact much with matter, making them pretty unstoppable "force", but changing what the force is made of is cheating.
Maths has improved since classical times, we now have words for any big number (million, billion or even trimilliquinquigentisedecillion, i.e. 10^3519) and we now know that Euclid's did not get all his axioms right. One such mathematical improvement is transfinite numbers. The underlying concept of Cantor's transfinite numbers is pretty powerful, namely infinite values can come in different sizes, with some infinities bigger than others.
So the above problem in this light is obvious, namely that as no finite force can stop the unmovable object, whereas no finite force can move the unstoppable force: the one that will win is the bigger transfinite value. Those silly Greeks, ae?
