1. What’s going on mathematically?
A non-mathematician asks me about math.
2. What is the emotional and logistical context?
For example, I’m on the bus or at a bar. I definitely don’t bring it up (and I’ve usually given up before I open my mouth). It’s sudden, and there’s not enough time. The context may be more or less conducive, we may be more or less willing and patient. This usually means I have between thirty seconds and three minutes before I lose their interest and attention.
3. What thoughts are there?
I have a few short prepared soundbites, that don’t take much thought (something about negative dimensions, or translating questions between algebra and topology, or looking for patterns…). I think to myself about sounding elitist and condescending, about the hopelessness of expressing any more than the briefest snapshot. I think about gracefully changing the subject.
But if the stranger and I are willing, I’ll try, until he or she loses interest. I’ll grasp for spontaneous metaphors, I’ll gesture a lot, I’ll come up with new soundbites. The more I know about my audience, the easier this is. I think about them, and what I know of them and their life experiences. Usually I can identify something and build a metaphor around it (“it’s like cooking, but with ideas”).
What people are mostly interested in is not the math, but what it’s like to do the math. This is easier, because math is just another human activity, and has the same emotions, stories, ups and downs, politics, tragedies, and jokes, as soccer or marketing.
4. What quality of awareness?
I’m aware of being vague and non-rigorous; the voice in my head keeps accusing me of lying. I’m aware of a disconnect between what I’m saying, what’s being heard, and what my stranger is thinking. You can really tell when you’ve lost someone, when they’re thinking about something else (any second they’re going to announce, “I always hated math” or ask, “Does this have something to do with string theory?”). Unless I’m really in the mood and the context is right, I’m also aware of not trying very hard, of having given up, of being shallow and distractible. On those rare occasions that we do connect, it is brilliant, inspired, freeing, expanding.
5. What emotions?
I feel proud to call myself a mathematician, proud to be cool, proud to dream the impossible dream. Wonder at the amazing thing that is math. Concern to not sound elitist or condescending. Sadness, frustration, and disappointment with the disconnect and failed attempts. That isolation used to make me feel special and feed my ego, but now it just makes me sad.
6. What does it resolve to, after how much time?
Six times out of ten it ends soon after the question, “Does this have anything to do with string theory/quantum physics?”, or we get snagged on questions about higher dimensions. If interest is lacking, usually I can redirect the conversation without too much permanent damage. Maybe once every ten times it ends up being really fun.
7. How frequent is this flavor?
Thirty second to three minute conversation: about three times a week.
Longer than three minute conversation: twice a month.
8. What are good/bad ways to change or follow it up?
I try to be willing, to have fun, be humble, and cherish the times that my stranger becomes my friend. Is it wrong to want to be understood? I don’t know, but I don’t think mathematicians should get their hopes too high.