What Math Values?
By David Neel
So, what am I doing here? It’s a good question. I haven’t been the most regular MAA dues-payer, I haven’t preserved my mathematical network anywhere near as well as many of my colleagues. (I do miss you all, friends, and hope to reconnect.) But that’s also part of the answer: a friend, Kira, asked me to be here, take on this role as an editorial board member. But as I began to reckon with the role, it began to make some good sense in other ways too.
Start with the title of the blog: “Math Values.” The actual listed values up there at the top of the blog: Community, Inclusivity, Communication, Teaching & Learning. Yes, all excellent, and very important. But let’s riff on the title, enjoy how it can be read as multivalent when we allow ourselves to punctuate or extend it variously.
Version 1: “Math-values.” Math is used to value almost everything now. All of reality, each human person, temperature, wave, infection, demographic, cough, pet preference, everything else rendered into bits, bytes, and math-values. Or at any rate, the world system is attempting this. So, in this math-valued world our (approach to) math then values mightily. All reality is being subsumed into number, with all the distortions and lies that become baked into this! What is most easily measurable is all too quickly and invisibly converted into that which matters. We lose what we actually value in the tide of what is measurable with the same old tools. What is easily mathematically evaluated for its value ends up mattering. Cathy O’Neil has written well on this in Weapons of Math Destruction, a title I thought at first to be a little overwrought, despite her careful description of the ways various mathematical tools like credit scores and “big data” and AI have baked in all the old racist/sexist/etc biases ahead of time. But that was before recent reports of AI use in the targeting of US-funded ordinance during urban bombing campaigns and the associated 10,000 dead children and 7000 dead women (and counting). Weapons of math destruction, indeed. We have to trouble the current form of math-values, and also we have 17,000 lost universes to mourn.
Version 2: “Math instills values.” In a different vein, Francis Su has done a beautiful job of directing us towards the values that might emerge or develop naturally in the practice of mathematics. I’m sympathetic to his argument and share it with my students. I also worry at times it might be utopian. We can see the ways that mathematics has helped each of us to improve as a person, but this is of course far from a representative sample. (Indeed, nor is it an unbiased sample of mathematicians that even bother with MAA or read this blog.) And we all have crossed paths with the counterexamples, the leering old Big Names that send woman colleagues ducking for cover at the conference and/or who use their elder-statesman (gendered language intended) clout to scoop the research of younger scholars asking for advice. We know that mathematical achievement can yet leave the soul well begrimed.
Version 3: “Math (pl. n.) values (v.).” But it is also true that that first word, “math”, that is all of us. The collection of our work and practices, our theorems and proofs, our conjectures and homework and counterexamples and lessons, our histories and memories, the group work and exams, papers and abandoned drafts, and all that we create and contend with in our minds. So we can struggle for it, then, our real nature as math, can actively define what it, or rather what we value moving forward. I dream it could be more than it has been, more than just the next thing to prove or the next counterexample. I dream it could be the new metrics or models or structures or statistics that reveal more clearly the shortcomings of our current ways of being, render obvious the inequities and damage and exploitation, and then chart paths to something better. Chart paths to a future where more of humanity can choose to become math with us, join this process. Can you imagine what insights we’ve lost by foreclosing that possibility from so many kinds of people for so long? Should we not mourn those who’ve lost the chance to share those insights?
Version 4: “Everything is math values?” For over a decade now I’ve been digging into Alain Badiou’s philosophy. A bracing thinker, he’s produced three major works (Being & Event, The Logics of Worlds, The Immanence of Truths) over 40 years that engage, rather deeply it turns out, with various mathematical ideas, including set theory and forcing, Heyting algebras, category theory, and the higher infinities. It’s wild and provocative stuff, but he takes the math seriously. Part of what I find thrilling about it is that he’s deploying mathematics not as mere description or metaphorical crutch, but with an assumption, declared at the outset, that we mathematicians have been doing ontology, unknowingly, since at least Cantor. If nothing else, it’s a gleefully wild solution to Eugene Wigner’s question about why mathematics are so unreasonably effective in the natural sciences: it is because we’ve been exploring the very nature of Being in all its radically multiple possibility!
What excites me about that idea is that it challenges us, we accidental ontologists, to make the same shift in mathematics that Marx so famously suggested for philosophy. If mathematics has turned out to be the very science of possibly existent reality, then what an opportunity to dream new ways of organizing life, especially in the face of the dire, nonlinear, and accelerating environmental collapse (among many other crises) that we have made for ourselves and these next generations.
In short, we should embrace and adapt Marx’s final thesis: mathematicians have hitherto only interpreted the world, in various ways; the point is to change it.
I am excited to seek out the mathematical thinkers committed to creating this changed world and, hopefully, convince them to write about what they’re doing, here. Please contact me at blogs@maa.org if you have an idea of how you or someone you know might be able to write for us in this way.
David Neel is a new Math Values editorial board member. He loves cats and books, works at Seattle University, and gets to the forest or mountain when he can.