Mathematics for Human Flourishing
Notes from reading “Mathematics for Human Flourishing” by Francis Su
Mathematics for Human Flourishing
Preface
Book grew out of https://www.maa.org/news/francis-su-s-farewell-address-calls-for-math-for-everyone
Written for lay person.
flourishing
Into to Christopher Jackson, inmate with 32 year sentence. When you think “who does math?” do you think of Christopher?
Simone Weil: loved mathematics but lived in shadow of brother Andre. Only woman in Nicolas Bourbaki.
Author is enthusiast, teacher, researcher of math, and former president of MAA. Had some math opportunities as a kid, but not much except for older books from public library. Felt like Simone Weil when entering Harvard for PhD. One professor told him, “You don’t have what it takes”. Many question their capacity for math, others question the point, and others lack opportunities.
So much of society needs math now, but education isn’t as good as it should be. This is most devastating for poor and disadvantaged groups.
If you ever interact with kids, you are a teacher of math. Being afraid to help kids with their homework is teaching them an attitude about math. Parents pass on math anxiety to their children.
If you ask me “Why do mathematics?” I say “it helps people flourish.”
Idea of Eudaimonia, Shalom, Salaam
Aristotle though flourishing comes from exercise of virtue, which includes excellence of character, conduct.
Proper practice of math cultivates virtues.
If math is sailing, desires are the wind, virtues are the character traits sailing builds: mindfulness, attention, harmony with wind. Sailing is useful as transportation, but that’s not the only reason to sail. There are technical skills, but we don’t learn sailing by learning to tie knots.
People don’t mean “when am I going to use this?” They mean “when am I going to value this?”
Each chapter in this book is a human desire whose fulfillment is a sign of flourishing, and how math can meet the desire by building aspects of character and habits of mind like ability to think clearly and reason well.
I hope you can see yourself as an explorer.
Puzzles
- Brownie has one rectangular piece missing – any location, any orientation. Make one straight cut to cut the remaining brownie exactly in half.
- 100 lightbulbs each have a switch numbered 1–100. All lights off. Toggle all multiples of 1, then all multiples of 2, then all multiples of 3, etc, all the way to multiples of 100. What’s the remaining pattern?
exploration
Stories about Chris Jackson
I was excited about exploring space, as a kid. Math is in those worlds. Saturn’s rings look like annular bands, but they are moonlets that orbit due to gravity. All rocks at the same distance take the same time to do one orbit. Inner rings go faster.
Rocks that orbit exactly twice as frequently as a moon tend to get pulled by the moon at the same time every orbit and get pulled higher (resonance). This creates gaps. Cassini Division is due to 2-1 resonance with Mimas
Math exploration is like space exploration. You send probes to test theories. “captivated by mystery, motivated by questions, undeterred by setbacks”. Since it’s in the mind, it can be done anywhere by anone.
Example: Achi. Variants:
- What happens if no legal move?
- Are you forced to move if you can?
- What if each player had 3 pieces instead of 4?
- Can you create an interesting variant with different lines?
Math reasoning can decide which options make a more interesting game.
Every culture has strategy games. Strategic thinking is mathematical thinking. Math exploration begins with “Why?” and “How?” and “What happens if…?”
Fawn Nguyen: “Critique the effectiveness of [math lessons], not by what answers students give, but by what questions they ask.”
Exploration cultivates:
- imagination. “Maybe we can show X or Y.”
- creativity. moon program generated inventions. exploring primes led to cryptography. knot theory has applications in protein folding. Radon transforms led to CAT scans. Math with Bad Drawings: dull problem: “Find the area and perimeter of a rectangle with height 3 and width 11” exploratory problem: “Create two rectangles so the first has a bigger perimeter, and the second a bigger area.”
- expectation of enchantment. unfamiliar terrain, unexplored caves, deep sea creatures. e.g. space-filling curve, banach-tarski paradox: solid ball can be cut into 5 pieces and reassembled into two solid balls of the same size as original. Linda Furuto shows students linear functions modeling coral reefs being cleared of algae, matrices describing ocean debris collection, and quadratic equations involved in sustaining limited island resources.
Puzzles
From “Divides Sudoku” there’s a puzzle with normal sudoku rules, plus some constraints on neighbors that evenly divide others, and some “greater than” constraints