Try to be the less technical as you can.
Try to be less technical as you can means, for the ones who don't understand: "focus on the ideas, don't try to prove everything, try to make things the simplest you can to emphasize the main points without loosing your interlocutor into technical details that any mathematician knows very well"well, and non mathematician cannot appreciate". It is simple to make things look like complicated, it is more difficult to make complicate things simple, and it is much more appreciated.
In spite of the -1, I maintain my advice.
