In 1988, “Cecil” posted regarding this particular theological discussion. I thought to provide a further comment regarding his previous answer. On the one part, he was correct that the proper question was “how many could dance on the point of a needle”.
The debate was over the nature of angels and whether they had physical bodies. It was the position of Thomas Aquinas that they did and that therefore no two angels could occupy the same point in time and space. For Aquinas, the point of a needle represented the smallest “place” and so he used that for his point of reference that no two angels could be at that place at the same time. If he were speaking today, he might say “dance on an hydrogen atom” or a neutron … Others, typified by William of Ockham, believed that angels did not have a physical body and therefore, any number of them could exist in that point at any given moment of time.
Personally, I think that they are both wrong - I think that angels are spiritiual beings that can manifest themselves physically when they need to to discharge their duties. What little there is in the Bible regarding angels backs up the idea that they can have physical bodies. Nothing to lose sleep over though …
I forget where this was discussed by Ockham, but Aquinas dealt with this (from his view) in Summa Theological, somewhere around Q50 or so.