"Classical Mechanics is a well known field of Mathematics." Do you even listen to yourself...? – Najib Idrissi 19 hours ago
The user "Najib Idrissi" asks the author of the sentence Classical Mechanics is a well known field of Mathematics. to read that statement for themselves. Najib makes sure that the author will realize the scientific mistake in that sentence and, in short, "will come to their senses."
It's like your friend has told you something very oddly wrong, and you didn't expect him to say so. You tell him/her to listen to himself/herself, so that s/he will realize the mistake they've made. In this case, it seems very rudimentary to the mathematicians that "classical mechanics" are a physics' subject, and hardly related to math. So, "well known", as it means that "many are familiar with it being a part of mathematics" seems a very idiotic expression to them, as if the author didn't know what they were typing, or simply, talking about.
If you ask me, there is a bit of negative connotation in this sentence, but it wouldn't be considered as offensive. (As "offensive" is too strong for it)
In fact, the expression "listen to yourself" is commonly used in the area of philosophy when there's a speak of art of communicating between humans.
philosophy reference 1
philosophy reference 2
The third
And this is a nice example of a similar usage. (Though it contains the expression and not the exact question)
in Google books
Best Answer
Yes, this is something native speakers say. It's not an especially common expression, but I don't see anything wrong with it. You can find some examples if you search online. When I did, I found this quote by the comedian A. Whitney Brown:
To me the phrase sounds somewhat informal.