As I’ve already described, I’m worried about the oncoming MOOC revolution and its effect on math research. To say it plainly, I think there will be major cuts in professional math jobs starting very soon, and I’ve even started to discourage young people from their plans to become math professors.

I’d like to start up a conversation – with the public, but starting in the mathematical community – about mathematics research funding and why it’s important.

I’d like to argue for math research as a public good which deserves to be publicly funded. But although I’m sure that we need to make that case, the more I think about it the less sure I am how to make that case. I’d like your help.

So remember, we’re making the case that continuing math research is a good idea for our society, and we should put up some money towards it, even though we have competing needs to fund other stuff too.

So it’s not enough to talk about how arithmetic helps people balance their checkbooks, say, since arithmetic is already widely known and not a topic of research.

And it’s also a different question from “Why should I study math?” which is a reasonable question from a student (with a very reasonable answer found for example here) but also not what I’m asking.

Just to be clear, let’s start our answers with “Continuing math research is important because…”.

Here’s what I got so far and also why I find the individual reasons less than compelling:

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1) Continuing math research is important because incredibly useful concepts like cryptography and calculus and image and signal processing have and continue to come from mathematics and are helping people solve real-world problems.

This “math as tool” is absolutely true and probably the easiest way to go about making the case for math research. It’s a long-term project, we don’t know exactly what will come out next, or when, but if we follow the trend of “useful tools,” we trust that math will continue to produce for society.

After all, there’s a reason so many students take calculus and linear algebra for their majors. We could probably even put a dollar value on the knowledge they gain in such a class, which is more than one could probably say about classes in many other fields.

Perhaps we should go further – mathematics is omnipresent in the exact science. And although much of that math is basic stuff that’s been known for decades or centuries, there are probably many examples of techniques being used that would benefit from recent updates.

The problem I have with this answer is that no mathematician ever goes into math research because someday it might be useful for the real world. At least no mathematician I know. And although that wasn’t a requirement for my answers, it still strikes me as odd.

In other words, it’s an answer that, although utterly true, and one we should definitely use to make our case, will actually leave the math research community itself cold.

So where does that leave us? At least for me straight to the next reason:

2) Continuing math research is important because it is beautiful. It is an art form, and more than that, an ancient and collaborative art form, performed by an entire community. Seen in this light it is one of the crowning achievements of our civilization.

This answer allows us to compare math research directly with some other fields like philosophy or even writing or music, and we can feel like artisans, or at least craftspeople, and we can in some sense expect to be supported for the very reason they are, that our existence informs us on the most basic questions surrounding what it means to be human.

The problem I have with this is that, although it’s very true, and it’s what attracted me to math in the first place, it feels too elitist, in the following sense. If we mathematicians are performing a kind of art, like an enormous musical piece, then arguably it’s a musical piece that only we can hear.

Because let’s face it, most mathematics research – and I mean current math research, not stuff the Greeks did – is totally inaccessible to the average person. And so it’s kind of a stretch to be asking the public for support on something that they can’t appreciate directly.

3) Continuing math research is important because it trains people to think abstractly and to have a skeptical mindset.

I’ve said it before, and I’ll say it again: one of the most amazing things about mathematicians versus anyone else is that mathematicians – and other kinds of scientists – are trained to admit they’re wrong. This is just so freaking rare in the real world.

And I don’t mean they change their arguments slightly to acknowledge inconvenient truths. I mean that mathematicians, properly trained, are psyched to hear a mistake pointed out in their argument because it signifies progress. There’s no shame in being wrong – it’s an inevitable part of the process of learning.

I really love this answer but I’ll admit that there may be other ways to achieve this kind of abstract and principled mindset without having a fleet of thousands of math researchers. It’s perhaps too indirect as an answer.

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So that’s what I’ve got. Please chime in if I’ve missed something, or if you have more to add to one of these.