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"There are a lot of hard problems out there, sometimes they are toys like the Rubik's Cube and sometimes its quantum physics. I work on the math that let's people solve them."

Every software developer has had this conversation themselves.

The problem with toy-based analogies is that people then think the math is a toy. "Who cares if you can solve a Rubik's cube faster?"

Telling them what it can do or what it is used for is almost always the best way to talk about something you do with the totally uninitiated.

Make sure it's something they've heard of before, e.g. the Rubik's cube example.

>"Telling them what it can do or what it is used for is almost always the best way to talk about something you do with the totally uninitiated."

Although I'd guess for most researchers in Maths what it can be used for is many years away (if it actually has a "practical use") and what it can do is far too esoteric for the layman.