I announced a series on math and democracy back in October.
It will deal with a lot of concrete areas. Last time I talked about a case that is before the Supreme Court and will influence voting law throughout the land. In the future I’ll be talking about voting, political participation, technology and who has a say over its development, and of course the classroom.
But I want to properly kick things off with a post that is essentially philosophical. I am here to assert the following proposition:
Math is democracy!
What do I mean?
Democracy — from Greek — literally, “rule by the people.” I am referring to the ideal itself, not any particular system of government. Throughout the world we have various systems attempting to implement this ideal. One can ask questions about the degree of success of these attempts, but that’s not what this post is about. I’m just isolating the ideal — democracy — rule by the people.
Mathematics — from Greek — literally, “learning.” Of all the domains of human inquiry, math occupies a privileged place in terms of our confidence in its conclusions. It is the only field where practitioners regularly express unqualified certainty about its results. We sometimes discuss the wisdom it gives us as some sort of celestial gift (as in Wigner’s classic essay on its applicability to the sciences).
I am about to draw a connection. I expect it is still opaque at this point, but hang on.
If math is a miracle, then there is a second miracle: the divine gift was implanted in each of us, since it springs solely from the universal human capacity for rational thought. The wisdom of mathematics was not given us by way of Mt. Sinai, handed down from on high by somebody with privileged access to The Boss. Although many people think back to childhood and recall inscrutable formulas dispensed by a teacher who mysteriously knew the answer (how did they know??), this memory conceals the real truth, which is that the only place mathematical knowledge comes from is a community of peers reaching some kind of consensus after a period of engaged discussion. Furthermore, at least in principle (if not always in practice), anybody in this community has the right at any time to raise good-faith questions about the logic underlying any of our mathematical knowledge, and the matter is not really settled unless these questions have a good answer.
Thus, the only true source of mathematical authority is the consensus of a community of equals.
The principle of democracy is that this is also the only true source of legitimate political authority.
Broadening further, I offer that the principle of democracy holds that the only source of authority (of any kind) over a community is consensus of that community. So math is literally democracy.
This is edited from the version I posted yesterday, where I used the phrase “functional consensus” instead of “consensus.” This was to acknowledge that in a large-scale community such as a nation, or the international community of mathematics researchers, true consensus is not a viable goal. That said, the “functional” didn’t sit well with me overnight, because I thought it could be taken to suggest some sort of majoritarian principle. To me, majoritarianism is a fatal compromise of the principle of democracy articulated here, and it defeats the purpose of the analogy with math.
The thing about math is that, in principle, if an objection is raised to what is regarded as established fact, then that objection needs to be dealt with. Maybe something was overlooked! In actual practice, it may or may not be, because the question of whether you can get people to pay attention to your objection depends on things like if you’re famous, if you’re well-connected, how much work other people have to do to understand it, etc. But mathematicians’ collective understanding of what we’re doing holds that if somebody raises a new objection to something thought to be well-established, we have to answer it, not ignore it, in order to hold onto the established knowledge. This ideal isn’t attained, but it is still how we think about it.
By the same token, it seems to me that the democratic ideal insists that a minority view has the right to be processed rigorously by the community. I am making a high-level analogy so I’m not getting into what that processing might look like. But the failure of a community to take into account minority constituencies in some way is a failure of democracy.
I want to acknowledge some intellectual debt!
In 2008, I went to the Creating Balance in an Unjust World conference and saw a presentation by Sarah Bertucci, Jason Cushner, and several of their current and former students, entitled Consensus is the Answer Key: Empowerment in the Math Classroom. The presentation was on using consensus as the source of mathematical knowledge in the classroom. Later (in 2009?), I visited the school in Vermont where Jason and Sarah were then teaching, and saw Jason’s class. (Random aside: I also met Jasmine Walker!) The ideas have shaped how I saw both mathematics and the classroom ever since. You can see their clear imprint above (and in many of the things I’ve written on this blog over the years).
In about 2010, I was having a conversation with Jay Gillen of the Baltimore Algebra Project. At the time, I was preparing to apply to graduate school in math. Jay asked me many questions about how I thought about the math classroom and the subject itself. At some point he paused and said, “Everything you love about math is what free people love about democracy.” This comment has been continuously blowing my mind for 8 years, and again you can see its clear imprint in the above.