[solomonb]

My experience talking with high level mathematicians is that they tend to know their subjects so well and are so excited to share it that they can and will scale their explanation to match their audience.

[_carbyau_]

I mean, they likely have practice!

Dating or maybe a significant other, parents, siblings, any BBQ event IE any social event outside academia where someone asks "So what do you do?"

[Turneyboy]

Not to forget mathematicians from other fields. They might be equally unfamiliar with most of our research topics.

Yes we do have plenty of practice adjusting our explanations to the audience.