Words or phrases that describe a person who knows the answer to a problem but is not believed

Question

I'm trying to find either a word or a phrase that describes a person who knows the answer to a problem or problems but is never believed, even though the person is actually correct.
The nearest I can come up with is maybe the story of Cassandra, but that is about knowing the future but never being believed.
The word or a phrase may indicate they are simply ignored, but I am more interested in answers indicating the person suffers negative consequences such as being ridiculed or even persecuted for their correct solution. Maybe think of people such as Galileo
I stumbled across this excellent visualisation of people whose ideas were rejected and were treated as pariahs for them but were later proven to be correct. These are exactly the kind of people I am looking for words or phrases to describe.

KRyan · Accepted Answer

I would argue that Cassandra does work here: the name is often used metaphorically, in a variety of fields. For example,

achieving a clear, shared vision in an organization is often difficult due to a lack of commitment to the new vision by some individuals in the organization, because it does not match reality as they see it. Those who support the new vision are termed ‘Cassandras’ – able to see what is going to happen, but not believed.

(same Wikipedia source linked above)

While Cassandra does have connotations of having to do with the future, any solution to a present problem is, by definition, a future thing. Someone who posits a solution is predicting that their solution will solve the problem. And failure to agree with a solution (that, we stipulate, would turn out to solve the problem) is most likely due to a failure of perception: either the perception that the person offering the solution isn’t worth listening to, or that the problem and/or its solution would work out differently than they will.

NVZ · Answer

Diamond in the rough or rough diamond — TFD

someone or something whose good qualities are hidden.
"This film is one of those diamonds in the rough, a wonderful gem that almost no one has noticed."

It may be applied to people too.
Ahead of one's time — TFD

Fig. having ideas or attitudes that are too advanced to be acceptable in the present. (*Typically: be ~; think ~.)
"Sue's grandmother was ahead of her time in wanting to study medicine."

One great example would be Nikola Tesla. Here's why: "Why was Nikola Tesla the greatest geek who ever lived" by Oatmeal. Here's a Quora discussion on "Who was most ahead of their time?"
Single words useful here are:
Underestimated — M-W

to think of (someone or something) as being lower in ability, influence, or value than that person or thing actually is

synonyms: underrate, undervalue, sell short
Or, perhaps visionary — M-W

having or showing clear ideas about what should happen or be done in the future
"She is known as a visionary leader."

But this doesn't necessarily mean that their people didn't believe in them.

DavidR · Answer

Not strictly a description of the person, but...

Falling on deaf ears

if a request or advice falls on deaf ears, people ignore it.
  
  Warnings that sunbathing can lead to skin cancer have largely fallen on deaf ears in Britain.

Link

Spagirl · Answer

Consider 'a voice in the wilderness' Different sources give slightly different nuance, 
Meaning: You're a voice in the wilderness, or a voice crying in the wilderness, if you're expressing an unpopular opinion or insight.

Meaning: You're a voice in the wilderness, or a voice crying in the
  wilderness, if you're expressing an unpopular opinion or insight.
  
  For example:
  
  When Galileo stated that the sun was the centre of the solar system,
  he was a voice crying in the wilderness. Most people thought he was
  crazy or evil, or possibly both.

Greg · Answer

I cannot think of a colloquialism or literary phrase, but I can think of a few descriptions:
Her correct answer did not satiate their hungry ears.
He poured his solution into the discussion where it quietly drained, as if through a sieve, unnoticed and leaving no trace.

Her illuminating solution was snuffed out

in the bluster of hot air from the crowd

by the snorts of their derision

by the winds of dissent

His helpful response was met with stolid bovine indifference.

Joce · Answer

An unrecognised genius if s/he's truly gifted, or maybe you can swap some weaker term for genius, such as expert.

Skilful yet unrecognised could also serve as an epithet.

andrew oxenburgh · Answer

Also, 'Pearls before Swine', which means to show valuable things to people who disregard them.

It's pretty negative, but it's usually used in a light hearted way. In a pub quiz, you might suggest an answer and have it dismissed. You would say 'Pearls before Swine', implying that you words are pearls, and the people you are playing with are too obtuse to see it.

user176105 · Answer

Although it doesn't describe the person, the phrase "casting pearls before swine" might apply to the situation.  It's originally from the Bible (Matthew 7:6: "Do not give dogs what is holy; do not throw your pearls before swine. If you do, they may trample them under their feet, and then turn and tear you to pieces.").

From the Cambridge dictionary:

cast pearls before swine - to offer something valuable or good to someone who does not know its value.

I'm afraid you're casting pearls before swine with your good advice - he won't listen.

gbh · Answer

Heresy: opinion profoundly at odds with what is generally accepted.

Heretic: a person holding an opinion at odds with what is generally accepted.

Words or phrases that describe a person who knows the answer to a problem but is not believed

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