Question: What are some arguments for and against telling the public that Mathematics is everywhere? I would like to know if there is any evidence that telling the public Mathematics is everywhere generates some interest in mathematics, as opposed to perhaps only making people respect mathematics, without necessarily changing their feelings toward it?
Note: I am not asking whether mathematics is everywhere or not.
You have probably heard that Mathematics is everywhere. It is used to popularize mathematics. In fact, Mathematics is everywhere has even found its way to the International Congress of Mathematicians (ICM). For instance, in ICM 2014 there was a "Mathematics is everywhere" panel (see  for the presentation of this panel). I quote from the first paragraph of the introduction in :
Suppose you are a mathematician and you are put in front of this statement [Mathematics is everywhere]. Are you convinced? If you are in front of your classroom, are you able to explain the statement? And if you are in front of the public, or of a journalist, what examples will you choose to illustrate the statement? We, the panelists, have the impression that many of our mathematician colleagues are convinced. Yet, many of us lack good examples to pass the message.
The last sentence: "Yet, many of us lack good examples to pass the message" is notable, as it implies that many of our mathematician colleagues were not attracted to mathematics because mathematics is everywhere, otherwise, you would expect them to know a few good examples of where mathematics is. So then why should one attempt to popularize mathematics in this way?
Perhaps a more prevalent reason for why some people become mathematicians is that they find mathematics enjoyable, but does telling the public Mathematics is everywhere convey this message? In November 2022 there was a piece  in the New York Times that reflected high-school students' opinion about the value of learning mathematics. Reading through these opinions, one will quickly realize that almost all of them assess the value of learning mathematics based on its possible applications rather than being an enjoyable activity. Interestingly, there were some students who "admitted" mathematics is very important because it is everywhere, but still said they detested it. By contrast, one can speculate that if these students were asked about the value of learning music, many of them would talk about how much they enjoy music.
 E. Colli, F. R. Nemenzo, K. Polthier, C. Rousseau: Mathematics is everywhere, Proceedings of ICM 2014, Vol. 1, pp: 799-811.
 What students are saying about the value of Math, The New York Times, November 10, 2022.