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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.

Background:

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 [1] for the presentation of this panel). I quote from the first paragraph of the introduction in [1]:

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 [2] 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.

References.

[1] E. Colli, F. R. Nemenzo, K. Polthier, C. Rousseau: Mathematics is everywhere, Proceedings of ICM 2014, Vol. 1, pp: 799-811.

[2] What students are saying about the value of Math, The New York Times, November 10, 2022.

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    $\begingroup$ I do not see a question here that we can answer. Please revise this to ask a question related to math education. $\endgroup$
    – Sue VanHattum ♦
    Mar 17 at 20:37
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    $\begingroup$ I think your question raises an important point and the discussion you would like to have would be interesting. However, Stack Exchange is not designed for questions whose main purpose is to start a discussion. For this reason, the help center says: If your motivation for asking the question is “I would like to participate in a discussion about ______”, then you should not be asking here. I am thus voting to close as off-topic. $\endgroup$
    – Jochen Glueck
    Mar 17 at 22:24
  • $\begingroup$ Maybe you should edit that into the question body. It's not generally a good idea to have the question only in the title. $\endgroup$
    – Isaiah
    Mar 18 at 2:37
  • $\begingroup$ "Have you ever heard anyone try to popularize music by saying music is everywhere?" Hum, yes, I have. Many times, in fact. And I wasn't surprised, because indeed: music is everywhere. Every culture in the world has developed music. There isn't a single day that I don't listen to music. Even on days when I don't actively try to listen to music, I hear music because other people in my entourage are listening to it. Even birds sing!! $\endgroup$
    – Stef
    Mar 20 at 8:53
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    $\begingroup$ After the edits I think the question is both on topic and a very good question. I thus voted to reopen (and upvoted the question). $\endgroup$
    – Jochen Glueck
    Mar 24 at 18:06

1 Answer 1

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The simple answer to your question is that math is everywhere because the universe in which we live is not a chaotic and unordered universe which is devoid of meaning. Rather, the universe in which we live speaks to the existence of an intelligence from which this order flows. As a Christian, we speak of the General Revelation of God, the fact that the universe itself testifies to His existence. The beauty and majesty of creation itself which includes mathematical and physical law in part testifies to the existence of creative agent which stands above the created order. Of course atheists are free to disagree, but that's how I see it.

There are those who believe in the multiverse and believe that our ability to see mathematics in everything is a quirk of our particular existence. In their view there are infinitely many other universes where it is not so. I don't have faith in the multiverse, so, I don't find such speculations particularly interesting or convincing.

Getting back to your question, if there is a question, yes I agree, we should not preach mathematics on the basis of its applicability. Surely it can be applied, but for many of us who love it most dearly, the application is of tertiary importance. The beauty and complexity of mathematics and the discovery of new structures in math, new levels of abstraction, the completion of classifications,... These vistas of undiscovered mathematics, these are what draw us in, we want to understand more. Looking backward to see how little our predecessors understood, it makes us question, are we the same ? At this point in history, the internet gives us a collective memory which was before unavailable except in limited form in libraries at universities. Now the internet is the library and universities are soon becoming irrelevant.

In any event, your question is doomed as you have not taken enough time to reformulate your argumentative essay into the form of a question which is acceptable discourse on this Q&A site.

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    $\begingroup$ The best models of physics are pretty close to something that one might call chaotic, or at least random at their very foundation. Also, who is "we" in your third sentence? $\endgroup$
    – Jasper
    Mar 18 at 10:28
  • $\begingroup$ @Jasper, yeah that "we" should be I. I stand corrected. I'll just have to agree to disagree about your assessment of the foundation of physics. $\endgroup$
    – James S. Cook
    Mar 19 at 2:14

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