I was finally able to sneak it in at the end of summer (while floating in my pool of course). I'm glad I did. It's a wonderful and inspiring read. At one time in my life (high school) I enjoyed math and was pretty good at it. College cured me of that. However, this book helped rekindle the joy I used to feel playing with numbers and unlocking their secrets.
Su begins the book with a correspondence from a prison inmate, Christopher Jackson, who has discovered a love of mathematics. He reached out to Su to gain insight and share in their mutual love of mathematics. The conceit works as Su repeatedly returns to the letters and we are updated with the prisoner's progress, both legally and mathematically.
Su also intersperses small math puzzles. This call for a pause now and again to really get down to the business of thinking and pondering patterns. Between the letters, the puzzles, and Su's conversational tone, the book is actually light and easy, and wonderfully refreshing despite it's intimidating subject matter. It reminds me a bit of Auguste Gusteau, the renowned and extremely talented chef from the movie Ratatouille, who wrote the bestseller "Anyone Can Cook". Su believes anyone can love mathematics.
The beauty of Su's book begins in the table of contents. Each chapter is dedicated to a virtue embodied in the study of mathematics: "flourishing," "exploration," "meaning," "play," "beauty," "permanence," "truth," "struggle," "power," "justice," "freedom," "community," and, of course, "love."
In "flourishing," Su begins with the proposition that, "Every being cries out silently to be read differently." (p.2) By this he means that humans want to be understood and "read." Seen. Appreciated. Su makes the radical claim the mathematics leads to the flourishing necessary for humans to be truly understood. "Human flourishing refers to a wholeness—of being and doing, of realizing one's potential and helping others do the same, of acting with honor and treating others with dignity, of living with integrity even in challenging circumstances...The well-lived life is a life of human flourishing." (p. 10) Su believes that math can build aspects of our character and habits of mind that allow us to live lives as fully-formed humans, truly enjoying what life has to offer.
Chapter 2, "exploration," describes "mathematical exploration [as] very much like space exploration, but of a different kind of space—a space of ideas." (p. 22) Like exploring the physical world, mathematicians don't know where they will end up when they start out. They test theories, become "captivated by mystery, motivated by questions, undeterred by setbacks." (p. 23) Exploration further cultivates imagination and the "expectation of enchantment." (p. 29) Su reminds us that anyone "born with the human capacities to inquire and to reason" can be an explorer. (p. 31) He urges the reader to dream, knowing "imaginative, creative, and unexpected enchantments await." (p. 31)
Next Su describes the way in which mathematics inculcates "meaning." Just as words develop over time and gain an inherent richness, number, which are very abstract, can grow richer with use. Searching for meaning in any context builds other virtues: story-telling, thinking abstractly, persistence, and contemplation. Su summarizes the main idea of the chapter with, "Mathematics is the science of patterns and the art of engaging the meaning of those patterns." (p. 44)
In chapter 4, "play," Su does the seeming impossible and seeks to describe math as a playground. His lighthearted and optimistic tone to this part makes a chapter called, "play" seem almost credulous. Su describes "play" as fun, voluntary, meaningful, structured freedom, exploration, and imagination. For Su, mathematics, done properly, can embody all these characteristics. "Play" in math begins with pattern exploration and used inductive reasoning in reaching conclusions. But math requires the student to then move into deductive reasoning, which can include proof by contradiction or proof by induction. Which should, ideally, lead to more questions to explore. Math play can lead to virtues like hopefulness, curiosity, and concentration, as well as confidence.
Su moves on to describe the "beauty" found in math. Mathematical beauty manifests itself in four ways. The first is sensory beauty. This is the kind of beautiful patterns that can been experienced with the senses like ripples in the sand or fractal patterns in nature. The second kind is wondrous beauty. This is the awe felt at the idea expressed within mathematics, like E = mc2. Even the idea of mathematical constants, like the speed of light, can inspire this kind of wondrous awe. Next is insightful beauty. This involves communication and refers to simple, insightful proofs that are simply beautiful to hear and read. Finally, there is transcendent beauty. "Transcendent beauty arises when one moves from the beauty of a specific object, idea, or reasoning to a greater truth of some kind—perhaps an insight that reveals its deep significance, or a deep connection to there known ideas." (p. 79) This kind of beauty sees math as speaking directly into what it means to be human.
Math also teaches "permanence." Humans naturally seek the permanent things, and math, by its very nature involves permanence. Whether it is in constants, or invariants, math continuously reminds us that some things never change. Math gives humans fixed points. Humans "seek permanence because it is a refuge, a yardstick, and a foothold. But that does not fully capture why this is such a deeply embedded human longing." (p. 97) Su believes all of this is actually a desire to answer the question, "Who can I trust?" "Trust is at the heart of a desire for permanence." (p. 97)
One of the deepest desires humans have is for "truth." In fact, only oppressive societies seek to suppress the truth. It is necessary for human flourishing. Su defines truth as a statement that aligns with reality. He sidesteps all the philosophical questions about "reality" and sticks to a common sense definition. Math completely fails if its answers are not true. In fact, the common refrain, "Check your work." is a bane too many a student. But if we are taught to appreciate the beauty of truth and therefore the beauty of deeply questioning mathematical solutions to discover if they do, in fact, comport with reality, we can learn to appreciate the truth embodied in mathematics. As mathematicians engage in "the quest for deep knowledge and deep investigation," other virtues are built, among them the thirst for knowledge and circumspection, and intellectual humility.
Anyone who has ever studied math knows it also invariably involves "struggle." However, struggles are a necessary component of what it means to be human. We struggle through suffering, to achieve, and to grow. And if humans are to flourish, we must grow, therefore we must struggle. Su makes the point that while many may be tempted to cheat and bypass the struggle, working through a difficult problem can have fantastic ramifications for human flourishing.
Math gives students a sense of power as they learn "unlock and expand" the innate capacity for reason (p. 129). We gain power over things, power to direct or influence, power to make stuff, and power to make sense. While power can be used for ill, math opens up the possibilities of "creative power" which can amplify the power to do good. We can amplify others' ability to make more stuff and make more sense. Creative power leads to a "humble, sacrificial, encouraging character with a heart of service and a resolve to unleash creativity in others." (p. 143) All from diving deeply into mathematics.
Justice is better served with a study of mathematics. Su describes two kinds of justice: primary justice and rectifying justice. The first seeks to make right relationships. The second is needed when the first fails. "Rectifying justice is spotting something wrong and trying to make it right." (p. 150) This is right up the alley of a mathematician. Unfortunately Su describes myriad ways that the study of math has been unjust. Often people are thought incapable of succeeding because they do not meet a predetermined stereotype of someone who is "good at math." The field is ripe for rectifying justice.
One of humanity's core values is freedom. According to Su, math provides five essential freedoms: the freedom of knowledge, the freedom to explore, the freedom of understanding, the freedom to imagine, and the freedom of welcome. (p. 167) The freedom of knowledge is best illustrated when a student realizes multiple ways of attacking a problem. Previously he knew only one way and didn't know what he didn't know. Math gave him freedom of knowledge. Freedom to explore occurs when a student realizes that he can play with numbers. That numbers can be relational and tell stories. Freedom of understanding means your mind is freed up for higher level thinking. Once you understand the basics, you can move on to weightier topics. Freedom of imagination is offered when students are exposed to wonderful and beautiful possibilities like fractals. Finally freedom of welcome is on offer when a students sees himself as part of a group of similar explorers. He can speak the language and enter the conversation.
Another value supported by mathematics is community. For those that love math, that find joy in all things relating to math, the study and serious pursuit of mathematics forms a community of like-minded people. Contrary to the stereotype of the lone math geek, math is highly collaborative. However, by its very nature, even math communities can be harsh and competitive environments. Su envisions a hospitable math community, welcoming all comers, rejecting stereotypes and a narrow focus on achievement. He sees it as being made up of people like himself, who love math and just want to share that joy with other.
Finally, math can be a vehicle for the highest value of all, love. While mathematics can be a beautiful thing, it is not the ultimate thing. Su found himself struggling when he encountered a setback studying for his doctorate. Discouraged, he couldn't even muster up a desire to continue to pursue math. But in the meantime, he was tutoring undergraduates in math. This brought him back to the core, to the most important value, love. Not love of mathematics, or the use of mathematics to study love, but love for his fellow humans being expressed through and because of mathematics. "To love is to give the gift of play and exploration, to grow in a desire for truth and beauty, to bestow creative power on another human being by showing them mathematics. To love someone is to set them free, not just in their heart, soul, and strength, but also in their minds." (p. 206)
I would highly recommend this book. It was an easy and enjoyable read. The puzzles at the end and the stories of his correspondence with Christopher alone almost make it worth it. Francis Su is a wonderful story teller and he invites us to love what he loves for the sake of loving people. That is beautiful.
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