When giving a talk or writing a paper intended for non-specialist (i.e., mathematicians not specializing in the topic being discussed), the question inevitably occurs of what one can assume to be "common knowledge". Rather than trying to guess (e.g., I *assume* that almost all mathematicians know what a vector space over a field and what the Lebesgue measure are), it would probably be better to determine this experimentally. Have any surveys been conducted in order to answer this question?

Roughly which set of mathematical definitions and facts are known to a proportion at least $p$ of working mathematicians?

(Here, $\frac{1}{2}\leq p<1$ is some fixed but specified quantity. Of course, a survey like this would in fact measure how well-known various notions and theorems are, so would give results for a variety of different $p$. Also of course, this depends on some definition of what a "working mathematician" is, I'm assuming self-reporting as such, but I don't think the details are too important; even a survey limited to a particular country or membership to a particular mathematical society would be something.)

It seems to me that this would be interesting both mathematically (see above) and sociologically. More refined results indicating how results vary per country, per age group, or per specialty, would of course be of value, but any survey along these lines would interest me.

I tried Googling various terms to no avail, so I'm inclined to think that no such survey was ever conducted, but maybe I missed something.

even outside their field, beyond what they are taught in University. (To give a specific example, I suspect that many mathematicians know what the Banach-Tarski paradox is, because it's so fun and surprising, but I gather very few students are actuallytaughtabout it.) $\endgroup$ – Gro-Tsen Jan 20 at 18:08