Q: How many mathematicians/physicists does it take to screw in a light bulb?

Mathematician:Theorem (Bulb Screwing)It only takes one mathematician to screw in a light bulb. Proof: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. 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. So far, it looks like physicists can’t pick up light bulbs, but two physicists can break a bulb between them.