User Reviews
Rating: really liked it
A while back, my sister gifted me a calendar, each page of which features a different comic about anthropomorphic animals by the cartoonist Liz Climo. My favorite page is June 5, a two-panel comic: in the first panel, a pair of dolphins offer a wine-bottle cork to a narwhal, saying, "Larry, we got you a present." The narwhal, puzzled, asks, "A cork? What's that for?" In the second panel, which has no words in it, the narwhal is wearing the cork on the tip of his tusk-like tooth, thereby blunting its dangerous sharpness, and he is joyfully playing water polo with the two dolphins. Because of the cork, the narwhal is no longer hindered from joining in the game by his fear of puncturing the ball with his tooth. All three animals are smiling.
Mathematics for Human Flourishing, a book developed from Harvey Mudd professor Francis Su's phenomenally popular 2017 Mathematical Association of America speech, is kind of a pop-math-book analogue of this comic. Unlike other books that have attempted to answer the question "Why would anyone want to do math?" -- say, the G.H. Hardy classic
A Mathematician's Apology -- Su's book takes a humanistic, social-justice-conscious approach to the question: de-emphasizing thorny concepts like talent, genius, and achievement, Su instead focuses on how the practice of math can help all people flourish as human beings regardless of their background or skillset, enabling them to access joys and develop virtues by whose aid they can experience human life more fully. As a corollary, Su argues that efforts must be made to make mathematical communities more welcoming to people from historically underrepresented demographics, such as women and people of color, and he gives concrete examples of ways that this can be done. I thought this was a good companion read to Catherine Chung's novel about a woman mathematician,
The Tenth Muse , which moved me when I read it last month. Regardless of how much or how little mathematical background we have, all of us have the opportunity to embody one of the two dolphins in the comic and give the gift of a fuller life through mathematics to a narwhal we know.
Rating: really liked it
To try to help my father understand why I decided to go to graduate school in mathematics, I gave him a copy of A Mathematician's Apology. It was not perfect for the task, and I have many issues with that book, but my father understood me and the idea of a pure symbolism that drew me to the subject as he explained it to his sister.
I think if I am ever in a similar circumstance of trying to explain my love of mathematics, I would give this book instead.
Professor Francis Su has a emphatic voice that combats the cold austere stereotype of mathematicians. The human element of mathematics is explained wonderfully in this book to the extent that I think this is an excellent book for both those who don't know much about mathematics and for any mathematician to remind them of their human soul. While the farewell address that this book is based, serves as a good summary of the ideas, I don't feel like this book is padded out to just fill out the book.
Rating: really liked it
ARC provided by Yale University Press and Francis Su. All opinions are mine and freely given.
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09-21: I don't know what drew me to 'Mathematics for Human Flourishing' by Francis Su. If I'm being completely honest, I think I found the title intriguingly unusual. Without actually paying attention at the time to who the author might be, the cadence of the title had a very eastern feel to it.. and being of mixed Asian and Native Hawaiian descent.. sometimes my eye has a tendency toward those fluid sort of word dances.
Perhaps, not so ironically.. in hindsight, as a student I was incredibly bored by mathematics and science. Not initially of course, in grade school instructors often seem to have a different approach to learning than in later grades. Not simply because the age of the students is younger, but in my experience most of them seemed to be in it for the kids and often genuinely liked them. As an adult, I know several people who teach junior high or high schoolers and none of them like their students as a rule.
Likewise, I didn't much care for the instructors who wanted me to fit in a convenient box. And if I didn't like them, I didn't work well for them.. add to that.. the curriculum of math and science in traditional schools.. and I didn't even want to be there. Amusingly enough, I understood it fine. I could teach others, even those in college classes above me. Though I was a student who strongly disliked those classes, as an adult.. some of my favorite casual reads are books on quantum physics and quantum mechanics (science).. and what must you have for those? Mathematics. There's the irony for you.
It probably seems as if I'm off on a tangent here and not reviewing the book, but bear with me.. my apparent tangent relates. What I expected from the book was for it to be heavily focused on mathematical theory and possibly full of formulas and problem solving.. the latter of which I love.. with a few anecdotes which might be interesting.
Don't get me wrong. Sprinkled throughout the book there is some of that, but it's much more than it might seem.
Su actually spends much of his time discussing the ripple effects that mathematics and the attitudes we're unintentionally groomed to have towards them have on our lives. He talks about how differently we might take to the topic if the focus was on learning and exploring, rather than ultimately on the grade and the correct solutions. The experience of exploration in mathematics leading students to find it more fun.. more engaging.. rather than turning away from it because it's shoved at them with a set of hard rules and expectations for results.
There's some discussion on the fact mathematics are used more frequently in our every day lives than we understand. That there are algorithms choosing what we'll see, what opportunities we'll get, who or what we might make contact with and how a deeper understanding of all that might benefit us.
He talks a great deal about spotting patterns (which are my go-to in just about every setting), and how our unknown inherent biases affect our decision making. There was a story in fact.. about restaurants with different menus that was surprising to me at first.. but when I got to thinking about what lead them to this method.. I began to see how it might happen more regularly than people realized.
Certainly, there are assumptions made upon every interaction.. be it personal or professional. We judge, if not by race or common stereotype, at least by our own experiences. And that can lead us to approaching the same situation in an entirely different way, simply because we perceive a certain level of understanding within the other person. It's fascinating really.
In addition to the things I mentioned, I genuinely enjoyed his reflection on letters sent to him by Christopher Jackson.. a man who discovered mathematics as an inmate in a federal prison. Christopher shares some truly introspective self-assessment with the author during the exchanges and the two seem to have forged quite a friendship over the years.
The author touches on a lot of topics that are afflicting us currently and I highly suggest giving this book a try. I think you'll be pleasantly surprised by the content and his insight.
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Rating: really liked it
Summary: An argument for the value of mathematics in all of our lives through meeting our deep desires and cultivating virtues helping us and others to flourish.I have to admit approaching this book with both fascination, and a bit of trepidation. I was curious for how the author would demonstrate that math fosters human flourishing. And I was afraid that the book would reveal the deficit in my rusty math skills, that it would be a discussion of inside baseball, with me on the outside, as it were.
Francis Su sets us at ease from the earliest pages. He introduces us to a correspondent friend, Christopher Jackson and to Simone Weil. Jackson is in prison for armed robbery, connected with drug addiction, who won't be released until 2033 at the earliest. Simone Weil was the younger sister of famed number theorist, André Weil. Simone Weil once said "Every being cries out to be read differently." As it turns out, Jackson runs circles around most of us in his knowledge of advanced subjects in mathematics, and Weil loved mathematics, and more than held her own with her brother's circle of friends.
Su's appeal in this book is that we read others, and perhaps ourselves differently when we think of mathematics. For too long, he contends, we have left math to the whiz kids who can solve problems quickly and the eccentrics. For many of us, math is either irrelevant or a memory of shame. He contends we are all mathematicians, and all teachers of math and invites us to read ourselves, others, and the practice of mathematics differently.
His contention is that mathematics fosters human flourishing. We flourish as we develop certain virtues, and our pursuit of virtues is aroused by basic desires or longings. Longings like that of exploration, such as how to explain the gaps in the rings of Saturn. Or the longing for meaning, such as the stories we may use to make sense of the Pythagorean theorem. There is play, particularly as we explore the interesting patterns we find in math, engaging in inductive inquiry, and deductive reasoning to explain what we find. We come up with shortcuts, and try to figure out why they work. We long for beauty, and discover it in the sensory beauty of a fractal, the wondrous beauty of an elegant equation, the insightful beauty of the dualities in math (multiplication and division, sine and cosine), and the transcendent beauty when we realize that math can explain the world. We long for permanence and truth and find these in mathematical ideas that do not change.
Math cultivates virtue as we struggle. Su gives the lie to the whiz kid who comes up with the quick solution. Real creativity in math involves struggle, the failed solutions that lead to a novel way of seeing the problem that yields the solution. Math's power may be coercive or creative. The creative use of power multiplies math's power in the lives of others rather than showing oneself to be powerful. Math can be used to include or exclude and may be a source of either justice or injustice. Math can be a source of freedom--particularly if it is coupled with justice and extend welcome to all. When this happens, mathematics creates good communities, not ones that exclude those who don't "measure up." Math sees everyone as capable of discovery in math. Suddenly, you have a group of people engaged in joyous discovery.
Above all, Su believes that love is the ultimate virtue in math as in all things. This is not merely the love of math, but the love of people that believes "that you and every person in your life can flourish in mathematics." One of the beauties of this book is that Su models this in the respectful way he engages Christopher's questions and desire to learn math. It is evident that he sought Christopher's advice on the book, and includes in each chapter one of Christopher's reflections. At the end of the epilogue, an interaction between the author and Christopher, Su mentions that Christopher will share in the book's royalties.
When you read this book, I suspect you will agree that Francis Su is the math teacher we all wish we had. He reminded me of one high school teacher, Mr. Erickson, who made math fun, and was not above engaging in dialogues with his invisible friend Harvey during class. Su helps us to discover the fun in math by including math puzzles in each chapter. He offers hints or solutions to each in the back, but I was reminded of the math puzzles I used to delight solving in Mr. Erickson's class, and as a kid. I found myself wanting to find some math books and brush up my math. He got me curious about the mathematical realities I could do well to pay more attention to, like trying to make sense out of the analytics on a website and what the patterns mean, or the correlation between voting percentages and incarceration patterns.
I wonder if others will have this reaction and if in fact that is the author's intent. Even teachers can lose their "first love" of math, and lose touch with the desires that math aroused in their lives. Might renewal come with remembering, remembering ourselves as we consider the student before us, allowing that remembering to shape how we teach? Su does us a valuable service in awakening us to the ways we flourish through math, motivating us to share with others the abundance we have discovered, even as Christopher now teaches other inmates the math he has learned, flourishing even more as he does so.
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Disclosure of Material Connection: I received a complimentary review copy of this book from the publisher. The opinions I have expressed are my own.
Rating: really liked it
“No—I’m not saying that math gives you greater claim to worthiness or human dignity. I’m saying that the pursuit of math can, if grounded in human desires, build aspects of character and habits of mind that will allow you to live a more fully human life and experience the best of what life has to offer. None of us is wholly virtuous; we all are works in progress with room to grow. And there are many ways to grow in virtue, not just in mathematics. But does the proper practice of mathematics build particular virtues, like the ability to think clearly and to reason well? Unequivocally yes, and it may do so in a distinctive way.”
Rating: really liked 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.
Rating: really liked it
I discovered professor Su through his lecture series on YouTube on analysis. They're based on Rudin, which really isn't an easy read, but he teaches the material in such a rigorous yet intuitive way that it's impossible not to develop an interest in the subject. He was "promoting" this book on his website, so I decided to check it out.
Parts of his writing, especially his chapter on love, made me feel like I was about to receive the Eucharist. Yes, we should be talking about love, justice, community (these are all section names), etc. etc., but I really wanted nothing more than some professional perspectives on what it means to study math, and world peace - though beautiful - is just not an answer I felt happy about.
That said, "Mathematics for Human Flourishing" also made me think. Professor Su called G.H. Hardy out for claiming that math is an elite field reserved for the truly gifted in "A Mathematician's apology." Su believes instead that everyone who nurtures a passion and welcomes a struggle can succeed. Although I agree that Hardy put too much emphasis on the value of natural abilities, I seriously doubt that a pile of participation awards equates to a Fields Medal. On the other hand, deluding students into thinking they have "immeasurable" mathematical potential is much more of a sport today than in Hardy's era, but at the same time, a healthy amount of confidence, maybe bordering on the delusional, might sometimes be the missing ingredient for bringing about a significant breakthrough. Given the latter, professor Su probably has a point.
My favorite chapters in "Mathematics for Human Flourishing" were "beauty" and "struggle." Professor Su distinguishes between 4 types of beauty in math:
* Sensory beauty: the beauty of patterned objects that we experience with our senses, such as can be found in Escher's artwork, for example.
* Wondrous beauty: the sense of awe we feel when confronted with, say, a curious conjecture.
* Insightful beauty: the beauty we experience when we truly get to understand something, e.g. when we come up with an elegant proof for a theorem.
* Transcendent beauty: a greater truth of some kind, the beauty hidden in deeper insights that connect known ideas.
Although I've only caught glimpses of the "sensory," "wondrous," and "insightful" beauty of math in the past, which can be pretty mind-blowing in their own right, I can only imagine what it's like to know "transcendent" beauty. Since math is so intense and difficult, I don't know why some people are so unshakeable in their belief that it's worth it to find out, and maybe it's not. But there must be something about the exclusive nature of true mathematical beauty, i.e. it's only accessible to people who truly "struggle" to find it, that elevates it above the beauty of music, literature, or art (in a way). Still, I'd gladly exchange some of my willingness to "struggle" for beautiful solutions for a greater aptitude for the subject any time. One day, I hope to understand it enough to be able to convince myself that I truly do appreciate it. This book strengthened that hope.
Also, hats off to Christopher Jackson (and thanks to professor Su for including his story in this book). The most inspiring person I've read about all year.
Rating: really liked it
Mathematics is often seen as cold and logical science. If the layman should be interested in mathematics, it is because it is so darn useful. Su holds a powerful appeal to appreciate the warm and human side of [[mathematics]]. The book is not primarily aimed towards mathematical professionals but rather towards any person who can understand the beauty in numbers or enjoys thinking about a puzzle. Though the chapters of this book, Su explores how mathematical thinking relates to various human [[virtues]], such as exploring, beauty, struggle, sense of community and, most of all, [[love]]. As a particular striking narrative device, Su uses his correspondence with Christopher, a young convict who studies advanced mathematics as a way to better himself. I think the content of this book will stay in my mind for a while.
Rating: really liked it
Beautiful book, beautiful problems, a bit preachy at times.
Rating: really liked it
A society without mathematical affection is like a city without concerts, parks, or museums.
Something went wrong, that I don't love this book. I think the technical is essential for real intellectual work; normal mind-numbing maths education put me off for years; I thirst for meaning; it's by a teacher at one of the best maths schools in the world (actual best, not just Fancy). But it's essentially a hippie self-help book which got into a university press. I'm surprised it doesn't open by saying namaste to me.
People often think of abstraction as stripping away meaning. But in fact, abstraction does the opposite—it enriches meaning. When you see that two things have similar structures or behavior, then those similarities create a connection, a new meaning for you that wasn’t there before. Poincaré famously said that “mathematics is the art of giving the same name to different things".
“make your daughter practice math. She’ll thank you later.”13 The op-ed never asked the question of how to teach math so she’ll thank you now.
The list of values at the back is shockingly poorly conceptualised. But Su is a powerful analyst - just one rule for abstractions and another for humans. (
All I want is humanism without sentimental overreach. It's unclear whether I can have this.)
One problem: he is too nice for me. (
“Let me start by thanking you, the reader, for taking the time to sit with this book and these ideas. Simone Weil said, “Attention is the rarest and purest form of generosity”) It's a very Christian book. Not in its metaphysics: in its intentional naivety, piety, humility, and cuddliness (though Weil and Buber and MacIntyre come up). He is credulous about the findings of educational psychology, including the absurd Pygmalion effect size. Every chapter includes a letter from a maths student in prison, the book ends with a long awkward interview with him, and Su gave some fraction of the royalties to him. One exception: chapter 9, a laudation for power. A huge number of smart people talk as if coercive power was the only sort. They are poisoned by paying too much attention to society.
Years of study have still not given me the virtues Su rightly names - persistence, patience, disposition towards abstract beauty, gaman. Ain't giving up though.
Maryam Mirzakhani... once said: “The beauty of mathematics only shows itself to more patient followers."
I know.
At my local hiking club, there’s bonding over a shared love of hiking. When it’s time to go, we split into different skill levels to do the hike at various speeds. I have no trouble admitting that I’m a slow hiker” By contrast, in mathematics the joy often requires the skill.
Borcherds made me laugh:
“I was over the moon when I proved the moonshine conjecture. If I get a good result I spend several days feeling really happy about it.
Days!
The puzzles are all nice and can be solved in your head, a good property. But read Rota, Hersch, Taleb, Lockhart, Gardner, Byers for the meat.
Rating: really liked it
As I study math in college, I frequently get sidetracked into thinking about the "external goods" that math can help me achieve, whether it be prestige, reputation, respect from others, an ego boost, or a stable career. Focused on completing assignments and doing well on tests, I too often lose touch with math's inherent value.
This book is a gentle yet passionate reminder of why learning and doing math is so important. Rather than focusing on beautiful theorems and theories or all of math's cool applications in the real world, it focuses 12 human virtues that math builds. Each chapter is devoted to a single virtue; they begin with a few thought-provoking quotes, followed by an explanation of how math builds the given virtue and the importance of the virtue for human flourishing.
Prof. Su and Mr. Jackson convey their thoughts on math and their experiences with it with beautiful simplicity. The chapters and Jackson's letters are caringly arranged; I appreciate how they come together to form an overarching story. A number of interesting math puzzles are speckled in for good measure (I've yet to give any of them much thought). What an awesome, encouraging book!
Rating: really liked it
This is a book about math. And a book about being human. And a book about the connections between those two. Francis Su has a lot to say and every teacher, student, parent, or person (no, these categories are not mutually exclusive) should read this book.
Rating: really liked it
This book was excellent. It counts now among my favorite books of all time. I will return to the book later to finish working the puzzles and also write a more extensive review here.
---- Update 2021 ----
I will still return to finish more puzzles but here is the first edition of the "more extensive review":
------------------
I came to this work from a recommendation following the horrific events of 2020. Like the author, I find great joy in the study and practice of mathematics. I recognize that such intellectual freedom is a privilege that is unfortunately not afforded to as many as it should be.
Is mathematics created or discovered? That well worn question, like most questions that incite unresolvable debates, is missing the point entirely. The uncontroversial fact is that Mathematics is a human activity. It is only because of this that we can even talk about aspects such as innovation and beauty with respect to mathematics.
This book addresses an uncomfortable truth head on. Unfortunately, like many other human activities, Mathematics has been tainted by mankind's propensity for evil against itself.
Mathematics, like most human endeavors, operates by analogy. Also key to mathematics is the interplay of the specific and the general, each informing the other.
In engaging, lucid text, this book takes the specific tale of one poignant piece of injustice to a mathematically motivated individual and weaves it together with general mathematical principles, ideas, and values.
By analogy, the author then projects these mathematical desiderata onto the larger societal context this showing that mathematics teaches values that can be harnessed for the benefit of all.
As a few posters that I saw while growing up state: "Math is Power." It's not an accident that one of the core principles of the ancient Pythagorean order was secrecy. Millennia later, access to powerful ideas are still threatening to some whose interest is not in Human Flourishing but only the amplification of their own short-term gains.
This is the world we live in but it helps no one to just resign ourselves to say, "It is what it is" (one of my least favorite pop phrases right behind "very unique") This book takes the bold step of not just telling it like it is, but imploring us all that it does not HAVE to be this way. We have the power to change this.
I hope this book inspires even the slightest bit of such change. My fear is that the people who need to read this book will never see it. However, it is great that this effort is being promoted as part of social justice initiatives.
Dr. Su is continuing to fight the good fight. This book is an existence proof that like-minded people are out there, and are willing to do something to advance humanity. I won't give up just yet on the better angels of our nature.
Rating: really liked it
I got Francis Su's book because of his essay on grace in teaching, and partway through the first chapter I am already smitten.
This book makes me smile.
Rating: really liked it
A beautiful book, born out of a speech Francis Su gave to a gathering of mathematicians about 3 years ago. While reading it, I could not help but hear Francis’s exceedingly kind voice on every page. As a math professor, this book came across as a gentle, lovingly written admonition to practice what I preach. If I agree with Francis, that “To miss out on mathematics is to live without an opportunity to play with beautiful ideas and see the world in a new light,” then what am I doing to ensure that those I have influence with don’t have to miss out? And yet the book is not aimed at teachers of mathematics, the book is aimed at humans . . . Humans who have relationships to each other and to mathematics and who need to realize that the two need not be separate.
I have had many of my students read the speech from 2017, and I discovered that the real people introduced there (namely Christopher & Simone) had the biggest impact on my students. So it is terrific to see these two people (and more) play a still prominent role in the book, Christopher so much that his name is on the cover and is earning a portion of the book’s royalties.
I believe this book is a gift to the mathematical community, both present and future. I’m sure I will loan it out to colleagues and students, but I will always request it’s return. I will need to reread it from time to time.
