Book Description Review “Inspiring.”—Scott McLemee, Inside Higher Ed“The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them.”—Kevin Hartnett, Quanta Magazine “Please read this beautiful, compelling, galvanizing book if you care about mathematics, social justice, or humanity, which I hope is everyone.”—Eugenia Cheng, author of The Art of Logic in an Illogical World “The world desperately needs this all‑embracing and deeply human perspective on what mathematics is and why it matters. The key qualities developed by mathematical thinking are characteristics that we should all value and long for.”—Eddie Woo, author of It’s a Numberful World ʺI was mesmerized by this unusual, sublime book. Original insights and engaging puzzles made me feel young again, discovering a way to Zen and the Art of Mathematics.ʺ—Nalini Joshi, University of Sydney “Francis Su believes that math can make us better humans—and he leads by example. Every page is a work of generosity and compassion. Plus, the puzzles will haunt you for weeks.”—Ben Orlin, author of Math with Bad Drawings “A celebration of mathematics and the human spirit. Learning mathematics enriches our lives, and Su wants everyone to have a seat at the banquet.”—Edward Scheinerman, author of The Mathematics Lover’s Companion “A delightful mixture of philosophy, mathematical illustrations, and compassion.”—John Cook, Singular Value Consulting”Francis Su has written a lyrical meditation on the beauty of mathematics and how it connects to our common humanity.”—John Urschel, author of Mind and Matter: A Life in Math and Football “Su elegantly uncovers the beauty and power of mathematics as they relate to our desires to be loved, trusted, and accepted. A powerful narrative of mathematical beauty, this book is the antidote for a mathematically fixed mindset.”—Talithia Williams, author of Power in Numbers: The Rebel Women of Mathematics “This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart.”—James Tanton, Global Math Project Read more About the Author Francis Su is the Benediktsson‑Karwa Professor of Mathematics at Harvey Mudd College and the past president of the Mathematical Association of America. In 2013, he received the Haimo Award, a nationwide teaching prize for college math faculty, and in 2018 he won the Halmos-Ford writing award for the highly-acclaimed speech on which this book is based. His work has been featured in Quanta Magazine, Wired, and the New York Times. Read more Customers Review: It isn’t often I get chills while reading a book. This book is inspiring, empowering, and eye-opening.A quote I love from the first chapter: “Not tapping everyone’s potential is a loss for all of us and will limit he ability of future generations to solve the problems they will face”. Su views mathematical thinking as an essential component of becoming our best selves.I love this book and thank Francis Su for sharing his vision of a more inclusive flourishing world.
What a great subject for a book. Written with care and conviction, and with fun math puzzles to boot, this accessible discussion on how beautifully math can reflect the beauty of human kind is inspiring. I got a couple as gifts for people who teach in math.
This book was awesome, everyone needs to read this. It had so many profound and powerful ideas to enhance humans around the world. I could not put it down. I feel like a better person for reading this.
Awesome book :)Please read if you real want to learn about what actually mathematics is and what it can do for ALL of us.
Wanted to like it but did not. Material could have been presented in 2 pages.
I oversee the K-12 math program at a private school. I bought copies for all of our math faculty and we’ll be doing a book study in the spring, including parents and students. This book comes with a money-back guarantee. Not from the publisher or the author or Amazon, but from me. If this book doesn’t impact your understanding of what it means to be a “math person” then I will be happy to take your copy off your hands so that I can give them to my future students.
Why do mathematics?There are many possible answers to this question. For some, it is because mathematics is useful: with mathematics one can study mechanical engineering and build airplanes. For others, mathematics is a form of entertainment: a vast world of puzzles, as challenging as you can handle. For yet others, there is a social element: mathematics is a way to demonstrate how smart one is. The list goes on.Su’s answer to the question “Why do mathematics?” is this: Mathematics helps people flourish. Flourishing here is what the Greeks called /eudaimonia/ — the highest good, a sort of realization of human potential rooted in the exercise of virtue. Broadly speaking, the book is organized into chapters, each of which considers one basic desire linked to “human flourishing”. Each chapter considers this desire, with respect to its role within mathematical practice as well as in the virtues which this engenders. Here Su considers mathematical practice broadly speaking — not just in the context of “solving a math problem”, but also viewed through the lens of the classroom experience, of a research mathematician, or even society and culture at large.There is a lot in the book. Rather than discuss the breadth, I decided to consider a single chapter, chosen at random, in somewhat more detail.—Chapter 9: PowerPower, writes Su, is a universal human desire. The form of power of interest here is creative power: the ability to make, both to make “stuff” and to make “sense”. Mathematics is powerful.To lead into this, Su considers an extended example of card shuffling. Which number is bigger? i) the number of stars in the universe, ii) the number of seconds since the big bang, iii) the number of ways to order a deck of 52 cards?Su briefly works this out: astronomers believe there are roughly 10^23 stars, and that the universe is a bit less than 10^18 seconds old. On the other hand, the number of configurations of a deck of cards is 52! (approx. 10^68).This number, 10^68, is so large that each time one shuffles a deck the resulting configuration is unlikely to have ever occurred before. This segues into the mention of a classic result by Bayer and Diaconis on the mixing time of the Gilbert-Shannon-Reed model of shuffling, which informally says that seven shuffles suffice. Over the next few pages, Su sketches the general argument over.I am reminded of the quote of Carl Sagan, “If you wish to make an apple pie from scratch, you must first invent the universe.” Although the oft-quoted punchline of the Bayer-Diaconis theorem (“seven shuffles suffice”) is easy enough to state, to even sketch the argument Su must develop a whole body of ideas: probability distributions, total-variation distance, the GSR model of shuffling, rising sequences in permutations, etc. As I read this I wondered what a novice would think of it all. The treatment is necessarily informal, probably successful in conveying some of the ideas of the proof, but at the same time a bit dizzying and without an solid ground to stand on.In fitting with the theme of the chapter, as Su develops this extended example, he considers various “powers” of mathematics. I found the word “power” here to be a bit vacuous. To give an example, in the discussion of the Bayer-Diaconis theorem Su discusses distance by providing several notions of what “distance” means mathematically, and notes that to decide among them exercises the “power of strategization”. This is rather typical of the other sorts of power: pick a verb (to strategize), consider its noun form (strategization), and then add “power of” in front. Thus mathematics offers the power of “interpretation, definition, quantification, abstraction, visualization, imagination, creation, strategization, modeling, multiple representations, generalization, and structure identification.”These all fall broadly within Su’s heading of “creative power”. Su also considers a more sinister variant, “coercive power”. For Su, coercive power “disrupts other people’s capacity to exercise creative power”. Here is a discussion of Sofia Kovalevskaya, the first woman in the world to receive a doctorate in mathematics, although not without overcoming a substantial number of barriers. As a student, she was only permitted to attend courses unofficially. When she had done enough research for her doctoral dissertation, she had to search for a university that would give her a degree. And afterwards, she was unable to get a job in mathematics (despite her considerable talents). Ultimately, she left mathematics to write fiction and theater reviews.This discussion highlights that coercive power can (and to a large extent does) hide in social norms. This is not quite what I expect from the word “coerce” (to be a bit stubborn about language, I have in mind something like: Tony Soprano “coerces” an insurance executive with a gambling debt to engage in fraud). Still, the example of Sofia Kovalevskaya is compelling and undeniable, and it is nice to see it discussed.Each chapter links the desire (in this case, “power”) with virtues which its pursuit exercises. Creative power, says Su, is sacrificial, and when one pursues creative power, one also acquires the virtue of “having a humble, sacrificial, encouraging character” with a “heart of service” and a “resolve to unleash creativity in others”.Language subtleties aside, this is not true in any reasonable sense. It is almost a trope that many wielders of great creative power — artists, writers, musicians, and yes, even some mathematicians — are rude, vain, difficult people. There are also many, many creative people who are humble, kind, and serving. The fact seems to be that creative power can, and often does, live independently of humility and sacrifice.What are we to make of this meandering meditation on power? Ultimately, I think not much. The long-form example may be inspirational to some readers, and if this writing provokes them to learn more about it, that is worth something. As for “creative power”, I think it is useful to have a description of mathematical experience which highlights such things as visualization, strategy, modeling, and so forth, but Su’s tendency to keep a safe distance from the actual mathematics (you will not find formula, definition, theorems, or proofs here) leaves the reader without any real experience on which to pin Su’s breezy philosophizing.—-There is another thread running through this book.Christopher Jackson is an inmate, convicted of armed robbery, currently serving a 32 year sentence in federal prison. Jackson is also a man who found himself drawn towards mathematics. As an inmate, he began to study basic mathematics — algebra, trigonometry, and so on — and worked his way up to more advanced topics, such as linear algebra, topology, and number theory. During this time Jackson began a long-running correspondence with Su, discussing mathematics, learning, and life. At the end of each chapter, Su presents a letter from Jackson to himself, often related in some manner to the theme of the chapter or one of the mathematical examples contained within.I found these letters to be quite touching, and feel that this thread is a high-point of the book. For Jackson, learning mathematics elevates a life that is otherwise weighed down by its own sad history. Mathematics gives meaning and focus, in spite of the circumstances of prison and all that entails (at one point, there is a gap in Jackson’s letters as he is being held in solitary confinement). As the book progresses, we get to know more and more about Jackson and his mathematical development. At the end, we are given a brief retrospective interview between Su and Jackson.With this said, Jackson’s story is only one facet of a larger prism which begins to emerge. Early on we are also introduced to Simone Weil, the younger sister to the prolific mathematician Andre Weil. Simone was a deeply sensitive and intelligent woman, who was also drawn to mathematics. However, living in the shadow of her brother was in a sense a curse for her. She writes””” At fourteen I fell into one of those fits of bottomless despair that come with adolescence, and I seriously thought of dying because of the mediocrity of my natural faculties. The exceptional gifts of my brother, who had a childhood and youth comparable to those of Pascal, brought my own inferiority home to me. I did not mind having no visible successes, but what did grieve me was the idea of being excluded from the transcendent kingdom to which only the truly great have access and wherein truth abides. I preferred to die without that truth. “””Weil returns on a few occasions throughout the book, occasionally in the main text, and a few times in a chapter epigraph.Many mathematics books which discuss the human element of the subject do so by considering those great mathematicians of the past. “Mathematics for Human Flourishing” is /not/ such a book. Jackson and Weil are two of the most prominent characters, but there are a number of others, all of whom have a certain meekness to their relation to mathematics.And this is what the book is really about. As Su says, he writes for the “demoralized… the disenchanted… those who haven’t had the resources or the confidence to get a mathematical education… to the artist who never thought math was beautiful, to the social worker who never thought math was relational, and the mathematician who never thought math was accessible to anyone else.”Let us ask ourselves again: why do mathematics? In a sense, there are as many answers to this question as there are human beings: each must come to ones own personal relationship with the subject. What Su hopes to show us is that, although one may inherit certain stereotypes of what such a relationship looks like, the actual space of possibilities is infinitely broader and more varied than these stereotypes can span. We may all find the wonder, the power, and the joy of mathematics, if only we have the vision to seek it.
There are moments in one’s reading life where one come across an unexpected book which gives one pleasure in absorbing the text and revelation in ruminating about the message. This was my feeling after I finished Mathematics for Human Flourishing by Frances Su.This is a book that I discovered when I saw Thomas Lin, the editor of Quanta Magazine touting it on Twitter. Being curious and being as that the author gave me a code which gave me 25% off on the purchase of the book, I jumped at the chance.It was one the best chance that I have ever taken.Professor Su is a mathematician at Harvey Mudd College in California. He was also the President of the mathematical Association of America; this book came out of an address that he made in 2014 as the president of MAA. I have not read the address, but I have read the book and the book is an amazing amalgam of intellectual wonderings about life and what humans hold to be noble and mathematics of course. The author asks question, many questions. Illuminating questions that is much beyond quick and facile answers. He also lays himself out honestly and courageously, sharing with the readers his quest to becoming a mathematician, on his insecurities about growing up Asian in the United States, his feelings about being in an over achieving family culture, and working in an art form that America does not appreciate or value. He also introduces his friend Christopher Jackson, an inmate in the penal law system of Georgia. Chris had committed a crime when he was very young, aged 19, and he’s has been in the penal system for what he had done. While he was in prison he also started to dabble in mathematics, soon discovering that he a passion for mathematics and also that he was adept at mathematics, enough to be a researcher, per Prof. Su’s estimation. Prof. Su shared some of his correspondence with Chris Jackson. The correspondences were about math, but also about many things beyond math, which helped illustrate the main thesis of the exposition.Prof. Su chose thirteen concepts, words, and ideas to delineate his feelings about mathematics. He uses them to dive deeply into the ideas that mathematics enhances and improves, he uses these concepts to expound on what it means for him to be doing mathematics. The structure of the book is completely non-traditional, and it is breathtaking in its scope.The central tenet of the book of course is laid out in the title: Mathematics for Human Flourishing. The author’s thesis is that mathematics is the path towards making humans flourish in their reality, to give us humans a path towards reaching realms that are beyond our initially meager imaginations, that doing math is not just a task or chore or a talent but a necessary spiritual practice to advance our society, to feed our naturally fecund imaginations, to sate our very human yearning for meaning in this life and in this world.This thesis a giant leap for those who are math phobic, but it is a heroic declaration for those who are passionate about mathematics. Professor Su does yeoman’s work in using those concepts to illuminate his thesis: flourishing, exploration, meaning, play, beauty, permanence, truth, struggle, power, justice, freedom, community, and love to flesh out his argument that not only is mathematics a practical and beautiful practice, but it is also a critical necessity for human thriving in our internal lives. The doing of mathematics makes us better people, it makes us kinder, more patient, more cognizant of the world around us, it makes us more curious, it makes us learn that our world is more than just what we see in front of us.Ever the detailed technician, Prof. Su carefully lists the virtues that comes through each of the concepts he chose to highlight in each chapter. He assiduously frames his chapters to clearly illustrate each of the virtues and connects them to each of the words he used to name the chapters. He also lists them all at the end of the book, to make sure the readers understood his point.The completeness of his authorly duties does not end there, he provides discussion questions at the end, as well as hints and solutions to the puzzles he provides at the end of his chapters. He was very complete in pursuing his mission.Unlike many of the books regarding mathematics, this one goes into the reasons why mathematicians become mathematicians, more importantly, the book amply demonstrates the point that mathematics is not only a magnificent art to pursue, it is also one that is desirable one to pursuit. This book is enlightening, inspirational, and gives hope to everyone who is willing to read it. |
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