Definition:Argumentum ad Verecundiam

Definition
Argumentum ad verecundiam, or argument from authority, means arguing that something is true on the basis that a knowledgeable and well-reputed person has said it.

Argument from authority may be valid or invalid, depending on the circumstances.

If the trustworthy person is also an expert in the field, and is free to speak her mind about the matter, then the argument has some validity. Otherwise, it generally does not.

That said, argumentum ad verecundiam is never a valid mathematical argument.

Examples
If a well-reputed experimental physicist publishes a paper reporting results of an experiment,it is generally wise to trust that the experiment was performed competently and that the results were reported honestly.

However, if a well-known experimental physicist claims that certain plants are good for treating disease, one should not give much weight to the claims.