Asserting you are a mathematician without immediately volunteering further details is just a bad thing. It's very closed.
The principle is simple: As soon as you mark yourself as part of a world that people are not part of and don't understand, you alienate them. Unless you give them something that relates to their own experience, you are going to have a hard time.
Consider this conversation:
— Yeah, I'm a school teacher.
— Cool, do you teach little ones or big ones?
— Little ones, they're constantly surprising...
— Yeah, I've got two kids about to go to school.
It's OK for a teacher, because everyone knows what a teacher does, roughly. Even if they don't really understand what a teacher does day to day, they know why they do what they do.
— Yeah, I'm a mathematician.
— ... (blank look as they realize they know nothing about what a professional mathematician does) ... Yeah, I was bad at maths at school. (nothing else to say)
[Awkward silence ensues]
In this case they have nothing to work with. With something like maths, you have to give them something extra to relate to, or they will just jump to their only experience of mathematics: school, where more than likely they were not working at the standard of a profession mathematician.
It is easy to find yourself in the Ivory Tower. People responding in this way should be taken as an indication that your work has become very detached from social reality — although some mathematicians think this is a virtue, it really is not, it's more like laziness.
Things you could say instead of "I'm a mathematician":
- "I investigate the properties of prime numbers."
- "I look at how fluids move."
- "I'm interested in symmetry."
- "Do you know X? Well, I do something like X."
- "I try to find out why Y."
Just give a more open answer that give people a chance to grasp what you do. Do not require them to be part of your world to understand it. If you do this you will find people will suddenly become quite good at maths.