Mathematical Moments
I feel lucky that no one in my life ever told me I was bad at math. Likely I am good at math because of the very opposite: even when I struggled, I was encouraged. When I was young, I imagined that someday I would be a professor of mathematics. And while that wasn’t my career path, what I know about how I learn and problem-solve parallels how I learned (or locked horns with) mathematics.
I was uninspired through three years of the algebras. Math felt abstract and like a pile of random strings to cram before the next test. And while it was fine and my grades were good, it was certainly not fun. Side note, later chemistry was infinitely easier for me because those same abstract skills got put to use again - balancing equations became a puzzle that had to be figured out in order not to defy the Law of Conservation of Mass. That theme—concreteness and storytelling and context—carries through all of the following anecdotes.
Geometry - Burden of Proof
It was in my sophomore year of high school that math opened up to me. In itself, geometry was awesome because its very identity was physical. Math became REAL. It was a way of describing the world.
Even more wondrously, everything I learned about a circle’s radius or the relationships of angles on parallel lines cut by a transversal became an arrow in my quiver for proving something entirely different (and bigger!) later. I could reason it out. I could break it down. There were multiple paths to arrive at a conclusion. You could follow a trail of statements and arrive somewhere new. It wasn’t rote memorization of formulae. And it had a secret code of triangles and dots and symbols.
I LOVED that class.
This experience repeated itself when I spent my freshman year in college with Euclid, going through each proposition on a blackboard. It was illuminating. Instead of trusting an authority figure that A squared plus B squared equals C squared, I had access to the origin story. It felt like reading a great mystery, enjoying how all the pieces click together. It is the difference between eating something because it’s delicious and eating something because your mother insisted.
Calculus - The Limitless Heavens
In high school, calculus made sense. It didn’t hurt that I was taking physics at the same time and there was overlap. But, in college, reading Newton’s Principia, it became something else. Calculus became very tangible. Newton was practical AF! He stuck a needle in his eye to see all the pretty lights when he was codifying his color theory. Dude was hands-on!
So it’s probably not such a surprise that when the math didn’t exist to solve the problem he was contemplating, he just invented the whole dang thing. Studying calculus from the original text contextualizes it as a model that can describe gravity and the orbits of the planets. It is physical and builds on geometry. It blew my mind to see that the area under a curve was approximated by stuffing in more and more rectangles. Making magical, mystical stuff accessible and intelligible? That is cool!
Lobachevsky’s Geometry - So Hyperbolic
A guy was so bothered by the parallel postulate that he wrote an alternate geometry that matched Euclid’s except for that one assumption. Having had geometry as a bedrock for how I thought about math, this rocked me. It made me question the limits of math and science in describing actual truths. And I wondered if one could just use math to say or prove ANYTHING.
But, surprisingly, it did not feel like a crisis of faith, it felt like reading a page-turner fantasy novel where everything makes sense and is just off from our own world in a small detail that has big ramifications. It was hilarious to me in a way. And it helped me move from rigidity to equifinality. There can both be a truth AND multiple models, stories, and approaches that fit it.
Statistics - Door Number Three
I came to statistics late, not until I took a summer class to prep for my MBA program. Stats felt like sand through my fingers. Yes, 50/50 coin flips, but then, gotcha, that isn’t what you should expect in reality. It would be explained to me and I would have a little aha moment. And then I wouldn’t be able to explain it to myself again later. It was slippery.
An example? The Monty Hall problem. How can you change the probability when there are still two donkeys and one Oldsmobile behind three doors? I finally recognized that my mental hangup was the phrasing of the scenario. Like one of those lateral thinking puzzles, it was mostly trick wording. You weren’t overriding the initial 2:1 bad to good ratio and mysteriously giving yourself better chances. Rather, there is one set of odds before the first door is opened, when there are three variables, then another set of odds when there are only two unknowns.
In the middle of the magic trick, Monty opens one of the doors you didn’t pick, always revealing a donkey. Now it is down to one burro and one automobile, raising your chances to 50/50 for your next guess. It makes sense but only if, when describing the game to yourself, you accurately describe the problem and givens.
I like understanding the rules, how something works, and why things are ordered in the way that they are. When I began learning JavaScript, I was frustrated that it was impenetrable to me; it seemed arbitrary. So I made up stories about each command being an ant, that I taught a job to. The ants had to work together to make something happen on my webpage. I had to train each one correctly. Seeing them as little creatures I could deploy helped me tell the story to myself about what I was doing and made it grokable. And it made me smile to be reminded of Richard Feynman’s ants.
Admittedly, I do like math because it is useful. I’m comfortable in the formula bar of Excel. I can calculate a sale price. I can scale up or down recipes when cooking. I really dig using analytics at my job. But math is also beauty and truth. Mathematics sings to me when applied (from a physics problem to working out a metalworking design) to explain, interpret, or do something in the world. An equation is handy. But immeasurably better is being able to explain the why, to see how the equation is shorthand for a rule about nature.
Fundamentally, I approach the unknown through a loop of analysis and synthesis. That is how I teach myself and others: bite-sized pieces within a system. Even watercolor painting works this way. I know truths about the behaviors of a plethora of individual pigments, papers, brushes, and water, and I can leverage and combine each of those bits of knowledge to do all sorts of new things.