May 26, 2020

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An Inclusive Vision of Math

I spent last weekend the way I spend a lot of weekends: singing Protestant hymns at the top of my lungs with friends from around the country. Sacred Harp singing is an a cappella hymn tradition that has a long history in New England and the rural south and is now sung all over the US and in several other countries. The powerful harmonies gripped me the moment I walked into my first singing 16 years ago. Sacred Harp is one of the great joys in my life. I started singing simply because it made me happy, but as my relationship with this music and the community of people who make it deepens, I often find myself thinking about what people find in Sacred Harp and how it helps us grow as human beings.

Most humans desire to know and be known by others. I believe Sacred Harp singing can help us fulfill those desires. Singing together is an intimate act. Many of us feel self-conscious about our voices and worry that we will be ridiculed if we sing in front of other people. Many of our musical experiences today are mediated by recordings, where every sour note and missed entrance has been corrected. We are constantly listening to perfect performances, and it is no wonder we are afraid to open our mouths lest we make a mistake. In Sacred Harp singing, every voice is welcome, whether trained or untrained, raspy or mellifluous. We embrace the vulnerability of singing together, sharing our voices with each other, warts and all. Through this vulnerable act, we know each other and are known. We also honor each other’s vulnerability by being gentle with each other. We may laugh together over a mistake we made, but it would be considered inappropriate to criticize someone else’s voice.

At a Sacred Harp singing, everyone who wants to has an opportunity to choose a song and lead it. Singers sit facing into a square, and each leader in turn comes to the center and beats time in a simple pattern while the group (referred to as a class) sings together. The leader chooses the tempo and which verses they want to sing and may make other choices about how the song is sung. We know and are known through our song choices and how we choose to lead each song. We honor and respect each other’s choices by singing songs the way the leader asks us to. When the class is following me well and singing my song the way I want it to be sung, I feel known. When I am paying attention to the leader and singing their song the way they are leading it, I feel like I am knowing and honoring them.

This practice cultivates the virtue of sympathetic joy, finding joy in the happiness of others. (I first encountered the concept of sympathetic joy through Buddhism, but I am not a Buddhist, and I do not claim I am using the term in exactly the same way Buddhists do.) There are songs I have sung so many times that I am tired of them, and there are songs that never did much for me in the first place, but when one of my fellow singers calls a song, my goal is to sing it with an enthusiasm that honors their choice. Whether or not I’m in the mood for their song, I sing it for them as well as I can because I know them, and I know that this song means something to them. Over time, songs I didn’t used to appreciate have started to become meaningful to me. I sing song number 232 in fond memory of my friend Barbara, and 41 makes me smile and think about my friend Jim. After singing with people around the world for 16 years, my tunebook is a cloud of memories. I know my community through singing these songs.

The preceding paragraphs are an unconventional way to start a review of a math book, but Mathematics for Human Flourishing by Francis Su of Harvey Mudd College is an unconventional math book. I happened to be reading it while I was on a singing trip, and it got me thinking about the way Sacred Harp singing fulfills some of the same desires and allows us to develop some of the same virtues that mathematics does.

Mathematics for Human Flourishing is at once an invitation and a manifesto. Su’s thesis is one that I share: engaging with mathematics is an activity that enriches human lives, and everyone should feel welcome to participate in that activity. He organizes the book by what he labels as human desires—exploration, meaning, and play are a few. Each chapter explores the way the practice of mathematics can help fulfill one of these desires, along with the related virtues mathematics cultivates and the things that can get in the way of fulfilling those desires. He starts chapters with epigraphs from a diverse collection of mathematicians and other thinkers and ends most of them with a puzzle or two. (A warning: I estimate that publication of this review was substantially delayed by the pentomino sudoku puzzle at the end of chapter 8, which Su takes from Double Trouble Sudoku by Philip Riley and Laura Taalman.)

Su’s first chapter, “Flourishing,” begins with an epigraph by Simone Weil, “Every being cries out silently to be read differently,” a line Su also ruminated on in the address he gave at the end of his tenure as president of the Mathematical Association of America, from which the book grew. (The book expands and deepens the address significantly, so those who enjoyed the address should know that they have not seen it all already.) That line and Su’s ruminations have stuck with me ever since reading the address a few years ago and has shaped how I think about mathematics, belonging, community, and our human desires to know and be known.

Su is vulnerable with his readers, sharing stories of his feelings of isolation and inadequacy as an adopted Chinese-American kid growing up in a predominantly white and Latinx town. In the chapter on justice, he writes about the fact that he is often not offered the “secret menu” at Chinese restaurants. To whom do we deny the mathematical “secret menu” because we assume that because of their gender, race, or past grades they are not cut out for advanced mathematics? (He wrote about this idea in MAA Focus magazine a few years ago as well.) In the chapter on truth, he connects his history as an adoptee to the way mathematics helps us seek deep knowledge and truth.

Su incorporates reflections from an unlikely contributor into the book. Christopher Jackson is an inmate at a federal prison who first wrote to Su several years ago because he had been studying mathematics in prison and wanted to find more resources as he continued learning new mathematics. (For his contributions to the book, Jackson receives a portion of the royalties.) Su’s relationship with Jackson has clearly shaped his way of thinking about mathematics and education as tools for social justice. Su shows that mathematics can enrich one’s life in both small and large ways. It can help us find the personal contentment of solving a tricky puzzle and give us tools to understand and combat systemic oppression.

Reflecting on the book, I see another important similarity between mathematics and singing in the unfortunate fact that many people have been traumatized by their past experiences in math and music. As a mathematician, I often hear from people whose mathematics education made them believe they were not “math people” and that they are incapable of making sense of the world using mathematics. As a singer, people tell me, “You wouldn’t want to hear me sing.” Perhaps someone laughed at them when they sang, or a teacher told them to mouth the words in the school program instead of singing them out loud, or someone scowled at them in the church pew during a hymn. They believe they are not capable of interacting with others or expressing themselves through song. I believe that Su’s vision for mathematics education and the ethos of Sacred Harp singing can both be antidotes for these damaging beliefs people have about themselves. I hope inclusive, joyful approaches like Su’s will help more humans access meaningful mathematical and musical experiences. I hope Mathematics for Human Flourishing is widely read by the mathematics educators who mediate many of our mathematical experiences and anyone who wants to access the joy and power of mathematics.