Theorem (Bulb Screwing)
It only takes one mathematician to screw in a light bulb.
Let the “bulb screwing number” of a profession , be the minimum number of people of profession that must be assembled to screw in a light bulb. For any pair of professions and with and finite, there exists a “hiring” operation such that any one person of profession can hire a collection of size of appropriate people of profession such that the collection of such people can screw in a light bulb. By the transitive property of light bulb screwing with respect to hiring, a single member of profession can screw in a light bulb by hiring people of profession and therefore, so long as there exists a profession with finite bulb screwing number, the existence of this hiring operation implies that the bulb screwing number of is at most 1. But, since we know there exists at least one light bulb that has been screwed in by at least one person of some non-mathematician profession, and there has only ever been a finite number of people, there must exist some other profession with finite bulb screwing number, so the bulb screwing number for mathematicians is 1. QED
Physicist: The computers capable of accurately doing this simulation haven’t been invented (yet). So we’ve fallen back on some reasonable approximations, like massless light bulbs and spherical physicists.
So far, it looks like physicists can’t pick up light bulbs, but two physicists can break a bulb between them.
This is probably an NP problem or something, which means that the only remaining option is empirical research. So, once the NSF frees up the funding for us to hire a team of experimental physicists (to experiment on), build a lab, and buy a light bulb, we’ll have something to publish in a year or two.