Do lay persons really believe that all of mathematics is known? I once found a professor of medicine to be under the impression that everything in mathematics is already known.
It's probably commonplace to hear that the masses labor under that misconception.
In some contexts, one is expected to cite authoritative sources to support factual statements.  If one asserts that the belief that everything in mathematics is already known is widespread among the general population, are there authoritative sources one could cite to support that?
It seems to me that if one were taking a poll, it might be difficult to phrase a suitable question in a way that doesn't give away hints.
 A: It is a common misconception in regard to math, but this kind of misconception is common everywhere.
It's caused by the recursive properties of knowledge. The more you learn, the more you realize how little you know.; i.e:
Since it is known that less informed individuals see fields as more finite than informed individuals; While laymen may relate to the field of Carpentry as "If someone is skilled in carpentry; Then that someone builds houses," while a carpenter may relate to the field as such: "Carpentry is a complex occupational field which includes, but is not limited to:  Formwork carpentry, framing, coopering, and cabinetmakers."
I think the lack of authoritative sources on the misconception that everything in mathematics is already known, simply is a result of the fact that this is true for any topic, profession, occupation, ect.
I haven't come across any sources which provides specifically what you've requested, but there are studies supporting what I am describing. (I'll append a link to a paper if I can find it again.)
