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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.

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@example, you've misread the question. The OP is not seeking authoritative sources that claim everything in mathematics is known, but that the layperson believes that everything in mathematics is known. – Kevin Carlson Sep 27 '12 at 22:18
I'm skeptical about your second sentence. Do you have any other reason, even anecdotal, to support your feeling that "the masses labor under that misconception"? I'd think that the masses have never even considered the statement, making the rest of your post moot, at best. – Rick Decker Sep 27 '12 at 23:51
Not only I think many believe all mathematics is known, they also believe each mathematician knows all of it. I recall: I was teaching some basic math (algebra-precalculus) to a relative that was beginning university. In a hiatus, a propos a book I had over the table, I told him that it was about a mathematical area I (engineer) knew almost nothing (analytic number-theory), and he was very surprised: "Wait... you mean you don't know ALL the math"? – leonbloy Sep 28 '12 at 0:12
Suppose we were to conduct a random poll of people to try to discover the answer to this question statistically. What question should we ask? The way questions are posed can skew the answers. – Kaz May 6 '13 at 23:44
@Stahl - I appreciate your response. Not all that many years ago, a student asked me what I did as a mathematician, differentiate more complicated functions, solve harder equations. Maybe one or more of the math organizations would fancy conducting a survey to discover the degree to which people actually believe that all math is known, and, perhaps, what math researchers actually do. – Chris Leary May 14 '13 at 20:05

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.)

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