Mathematicians like to develop new math right at the boundary of what is known. Physicists don’t have that luxury because they have to describe/model/build/etc things that correlate to what is actually going on in the world.
The mathematician of this joke would scan the edge of the light, finding nothing. Then he would keep lighting little lanterns at the perimeter to make the lighted area larger until finally his keys were within sight.
The physicist in this joke would presumably root around in the dark where she thinks her keys actually were. Upon finding them through brute force and luck, she might think “wow maybe one day this place will be illuminated so I can tell wtf I just did”
It is a common (but not universal[0]) practice in English writing to use either "he" or "she" as a pronoun for a person of unspecified gender to avoid the awkwardness of "they" or "one" or constructions like "he or she". No gender has been specified here, this is a neutral use of "she".
[0] Very few practices in English writing are universal.
I think your entire reasoning is in reverse. Using "she" where no gender needs to be specified is the awkward thing to do, and it's not neutral, it's explicitly designating a female gender. Using "they/them" is far less awkward, the reader doesn't have to have any kind of opinion about the text based on gender associations, making it less awkward.
Occasionally, they/them can get more confusing, especially in a story involving multiple people. It can become unclear if you're referring to just one of the people using singular they, or if you are in fact returning to more people using plural they.
The mathematician of this joke would scan the edge of the light, finding nothing. Then he would keep lighting little lanterns at the perimeter to make the lighted area larger until finally his keys were within sight.
The physicist in this joke would presumably root around in the dark where she thinks her keys actually were. Upon finding them through brute force and luck, she might think “wow maybe one day this place will be illuminated so I can tell wtf I just did”