I read a lot of books, both technical and not. Some I struggle through; some I enjoy in a forgettable sort of way; and some grab me and promise to stay with me. I recently finished Francis Su’s Mathematics for Human Flourishing, and to cut to the chase, you should read this book too. What’s that? You’re not a mathematician? Well, neither am I.
Actually, this book is only sort of about mathematics. First, as Su says in his opening paragraph,
This book is not about how great mathematics is, though it is, indeed, a glorious endeavor. Nor does it focus on what math can do, though it undeniably can do many things. Rather, this is a book that grounds mathematics in what it means to be a human being and to live a more fully human life.
That’s what Su means by “math for human flourishing” – the contribution that doing mathematics (at any level at all) can make to living a good and fully human life. (Su refers to an ancient Greek word, eudaimonia, which he suggests meant the highest possible good, “the good composed of all goods; an ability which suffices for living well”. So Su writes about how engaging with mathematics can help you find beauty and truth, and realize the value of struggle, and even think about, and find, justice and freedom. (Those are lofty claims, and of course Su approaches them with more nuance than my one sentence can represent.) These claims bring me to the second reason that I’d argue Su’s book is only “sort of” about mathematics: I think engaging with any of the sciences can bring the same benefits. It’s really about engaging with thinking. And yes, mathematics is mostly a system for thinking (“equipment for thinking”, in Su’s phrase).
But while you can extend all of Su’s arguments beyond math, you don’t have to. Su makes a compelling case that everyone – not just professional mathematicians – can engage with mathematics and benefit from doing so. As he puts it,
“To miss out on mathematics is to live without an opportunity to play with beautiful ideas and see the world in a new light. To grasp mathematical beauty is a unique and sublime experience that everyone should demand. All of us—no matter who you are or where you’re from—can cultivate mathematical affection.”
To demonstrate this, Su opens his book with two characters who aren’t professional mathematicians but who relate powerfully to math: the philosopher Simone Weil, and the penitentiary inmate Christopher Jackson. Each (especially Jackson) makes repeated appearances through the book, as we hear their stories of coming to math as outsiders. For readers in a similar position (of coming to math from the outside), Su sprinkles his book with mind-bending pieces of mathematics* and with little puzzles and games. The distinction between the “mind-bending math” and the “little puzzles and games” is blurry, and that’s very much Su’s point. There can be interesting math anywhere.
As an evolutionary biologist, I was particularly struck by Su’s discussion of math’s beauty. That’s because he recognizes four ways in which math can be beautiful; and the deepest is what he calls “transcendent beauty” – beauty that arises “when one moves from the beauty of a specific object, idea, or reasoning to a greater truth of some kind”. This is, of course, exactly the way in which biology is most beautiful: in the power of the very simple mechanism of natural selection to generate the astonishing diversity – but also unity – of all life. One could, of course, argue that natural selection is actually just math. One would be correct: it is**. In this we’re really seeing that math is just a system for thinking about the world around us – a world that includes natural selection, and quantum mechanics, and enzyme kinetics, and tectonic drift. There’s math under the hood of everything, and that means all of us can meet math on our own ground. But it’s exhilarating, nevertheless, to be shown Su’s vision of math seen more directly.
Su devotes a lot of attention to the ways that mathematics, and its human community, intersects with social-justice issues. This might surprise people who think of math as the purest and most above-human-problems of the sciences, but of course that view is naïve. All the sciences are embedded within human society, and all the sciences are inextricably interwoven with matters of history, human psychology, and social justice (something that emerged as an unexpected theme as I wrote my own recent book, Charles Darwin’s Barnacle and David Bowie’s Spider). Su makes one small but significant point by way of as simile, asking us to think about math not as a pole, which a vine can climb only one way, but as a trellis with many paths upward, none more valid than the others. This is a great way to think about science. Experiments, theory, observation; university, government, industry; professional, amateur; whatever. There are many ways to move science forward.
I could go on for a long time sharing pieces from Math for Human Flourishing that resonated with me. Su ranges from puzzles to injustice; from the gaps in Saturn’s rings to pedagogy; from geometry to love. I can’t do this book justice here – you should read it.
© Stephen Heard June 18, 2020
*^Like the Banach-Tarski Paradox: if you allow sufficiently complex cuts, you can cut a solid sphere into 5 pieces that can be reassembled to make TWO solid spheres of the same size as the original. I kid you not.
**^Which is one reason that it’s mind-blowingly silly for people to claim that evolution by natural selection hasn’t happened, or that it isn’t happening all around us. Given heritable variation and limits on population growth – and nothing more – it isn’t that evolution by natural selection can happen; it’s that evolution by natural selection has to happen. It’s mathematically inevitable. Creationists might as well argue that 1+1=7, because that’s just as sensible as denying the operation of natural selection.