There was one encounter recently where I was asked a question and gave the usual socially appropriate concise answer, until, after being pressed, I gave the "Here's what's really going on." The other person (I had not understood this) was a specialist enough to want the "Here's what's really going on" answer. But I was right to give the brief, simplified "general public" answer until I was prompted otherwise
"Just give me the time, don't build me a ____ing watch!"
That's a label and a reaction you don't want.
"So, what do you teach?" is a standard, socially appropriate question. Respond with a standard, socially appropriate answer (i.e. "Chemistry. What's your line of work?"). Be ready to needlessly have people be alienated if you take this as justification to invade and straighten out their ideas of what a professor is.
(I remember one math Ph.D. student saying, "How I envy people in particle physics! They can explain to other people what they do for work.")
If you're a mathematician, you might be interested in Theoni Pappas's The Magic of Mathematics: Discovering the Spell of Mathematics; I read an earlier title of his and found it, bar none, the most effective explanation of what exactly mathematicians do for readers who may or may not have scientific background. However, I would discourage you from adding a heavy reading assignment to help other people understand what life is like as a mathematician. Polite social conversationsconversation needs no footnotes, nor is adding footnotes an improvement.
Just give the polite answer and recognize that deepening the conversation is usually not helpful, for your reputation or for your listener's experience in meeting you.