The Mathematics of Flourishing

Scott McLemee reviews Francis Su's Mathematics for Human Flourishing.

January 3, 2020

In discussing the highest good for human beings -- the end toward which all other goods are the means -- Aristotle used the term eudaimonia, or (as spell-check absolutely insists) eudaemonia. Translators used to render this as “happiness,” which confuses things considerably. Whatever the highest human good might turn out to be, the heroin addict nodding off in ecstasy has not attained it.

Thinking of eudaemonia as “well-being” seems more to the point. It squares with the philosopher’s emphasis on balance, on determining the golden mean between extremes of appetite, emotion and habit. But another translation of eudaemonia has caught on in recent years: “human flourishing,” which is to say the full, vigorous exercise of our capacities and potentials as (in principle, anyway) rational organisms.

Happiness comes and goes, and well-being is contingent, when not downright precarious. To understand eudaemonia as human flourishing, by contrast, means seeing the highest good as dynamic, open-ended and resilient -- and something that can increase by being shared.

Three years ago this month, Francis Su gave a memorable speech on the occasion of his retirement as president of the Mathematical Association of America. Articles and blog commentary at the time reported that he received a standing ovation, as is confirmed by an audience member’s cellphone video of the event. In Mathematics for Human Flourishing, the much-expanded revision of his speech just published by Yale University Press, Su writes that some listeners approaching him afterward had tears in their eyes.

From another author that detail might come off as braggadocio, but Su (a professor of mathematics at Harvey Mudd College) treats it as evidence of “a need, even among those who do math for a living, to talk about our longings for the common good, and the need for us to be better human beings to one another.” The power and beauty of mathematics are commonly celebrated among its practitioners, who tend to have a preference for one or the other (as discussed here previously). The relevance of questions about human flourishing is much less well established.

To make the connection, Su draws on the work of neo-Aristotelian ethicist Alasdair MacIntyre by distinguishing between the external and the internal goods pursued in a given social practice. The latter refers, Su explains, to an “established cooperative human activity with standards of excellence appropriate to that activity” -- a category broad enough to take in the arts and sciences (math included) as well as, say, bricklaying or nursing or web design. An external good -- such as fame or money -- “come[s] about by engaging in the practice … [but] not inherently because of the activity,” since, by definition, the good can come from doing something else.

Conversely, internal goods “are bound up intrinsically with [a] practice” and “cannot be had apart from engaging in that or a similar practice.” MacIntyre gives the example of a child who is rewarded with candy for winning a chess game and thus has “every reason to cheat, provided he or she can do so successfully.” In the best case, the kid will instead discover and pursue the internal goods that come from playing the game itself -- including, as MacIntyre says, “a highly particular kind of analytic skill, strategic imagination and competitive intensity.” Also, presumably, confidence and self-respect, and a sense of flourishing.

Now, in recasting his thoughts to present them to a wider public, Su cannot really count on the reader grasping that internal goods may come from the practice of mathematics. Colleagues and nonacademic math nerds will have experienced it as a source of excitement, discovery, etc. But many readers Su hopes to reach will instead associate mathematics with pain: memories of frustration, confusion and boredom, possibly intensified by moments of embarrassment in front of a blackboard or an accountant.

Talk of mathematical elegance or creativity will leave such readers cold. At best, they recognize certain math skills as useful and (alas) necessary. In a surprising turn, Su acknowledges his own episodes of anxiety and humiliation as a math student -- experiences that he suggests may be more common among his peers than the norms of the profession tend to acknowledge. But through a series of short essays and puzzles, he tries to break through the mental blocks that prevent people from participating in -- or even imagining -- the pleasures of practicing mathematics at whatever level they can engage with it.

Each chapter includes a portion of the correspondence Su has received from Christopher Jackson, who is serving a 32-year term in the federal prison system for a number of armed robberies committed when he was a drug-addicted teenager. He acknowledges his crimes and makes no excuses, and in early letters he says he's worked his way through calculus but is having a hard time going any further. By the close of the book, he is keeping up with mathematical journals and teaching math classes, and he beats Su twice at chess during a visit. "Wrestling with a problem," Su writes, "persistently trying out various strategies, being unafraid of making mistakes, and progressing incrementally to understand the underlying ideas … produces a certain kind of endurance, which enables us to be comfortable with the struggle." I don't much like the word "inspiring," but damned if I can think of a more suitable word for this book.


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