#and I used sohcahtoa to figure out pre-existing distances

[hose270]

I remember the exact moment math clicked for me, not in a “I understand it” sense, but in an “I understand why this is meaningful” sense.

I was in calculus, and we were using integrals to calculate the area under a curve. The teacher showed us how to use that process to derive the formula for the volume of a cone—a formula I’d had to memorize five years before in geometry class. My mind was blown, not only because there was logic behind that seemingly arbitrary formula, but because I understood that logic.

It wasn’t the first time I’d understood something, but never before had something so incomprehensible been so quickly transformed into something so rational, and that moment of understanding still stands out in my memory six years later. It taught me that, with enough study and research, almost anything can be understood. Now, I haven’t used the formula for the volume of a cube in years, let alone to calculus necessary for deriving it, but I have used that principle of study and research, and that’s something that math taught me.

Are you willing to make a long personal post about how Math should be presented in an educational environment or in general conversation trying to convince the other participants about its daily usage. How it can advance a person’s problem-solving skills and approach in life.

I’m really good in Mathematics. I’ve given help for my classmates and friends about Math when they are having trouble or ask for it. But I have never been convinced of its importance outside of the classroom, outside of the test papers that gives me the variables to substitute in the given equation of that test of the day.

How can Math and it’s many properties relate back to everyday life in a casual manner?

Hm. Well, as someone who hasn't had to solve an antiderivative in years, my perspective on this is that the most important and widely-applicable skill math can teach you is the stuff behind the math - mostly the muscle-memory you get from proofs.

Math is, at its core, puzzles and logic and pattern-recognition. You learn a set of tools, you practice those tools on a set of simple problems until you get a feel for them, you are presented with a bigger problem, you recall which tools best applied to problems that are shaped like this, you break the problem down using your tools and eventually reduce it to something you know how to solve.

The fact of the matter is, the tools that are specific to branches of math don't really have much widespread use outside pure mathematics, and unless you go out of your way to keep using them you're likely to lose track of them. Studying math is not going to turn you into a super-calculator-wizard who can bounce stuff off the walls at perfect angles and do six-figure arithmetic in seconds, and I think some people feel overwhelmed at the assumption that that's what's expected of them if they learn math, and some other people feel cheated when they learn that that's absolutely not going to happen, because most writers don't know math and when they tell stories with math in them their best guess is it makes you a wizard.

I think the most advanced math I've used lately was trigonometry, and that was just because I was curious about how fast my plane was traveling relative to the sun's apparent movement at my latitude. We were flying back to the US from Iceland and we'd taken off at sunset, and we had been in that sunset for at least an hour by the time I got curious how the math worked out and started estimating our latitude, the circumference of the slice of the earth at that latitude, and correspondingly how fast we were flying vs how fast it was spinning to complete a full rotation in 24 hours. But even if the math involved didn't tap into any of the higher-level stuff I'd learned post-trig, those years doing proofs and figuring out which tools applied to which geometry meant that I could use the tools and my training applying those tools to calculate what I wanted to know, and confirm that our plane was actually outflying the sun when we were at iceland latitude, but as we curved south the sun's apparent relative movement (aka the rotational speed of that latitude of the earth) slowly accelerated until we were falling behind, landing right as the sun finally set. The math involved was high school level, but if I'd been given that problem in high school it would've taken more work and more stress to figure out how the tools I had needed to be applied to the problem I was facing. The years of practice I had tackling much more complicated proofs made the diagnostic process much faster.

I saw someone once analogize studying math to lifting weights. Where am I going to use this in real life? How often will I really be faced with two dumbbells that need to be lifted in three sets of twenty? Where am I going to apply the skill of holding a heavy thing straight out to one side of my body?

You don't lift weights because lifting weights is such a valuable and widely-applicable skillset, you do it because lifting weights makes you better at lifting everything.

You don't study math because math is going to fill your daily life with concepts that you need to prove true for 1 and for n+1 given true for n, or complex solids that you need to sum an approximate volume for, or a surplus of sunset plane flights that demand you calculate a bunch of cosines. You study math because it is the skillset of making things make sense. It trains you to break a huge, incomprehensible problem down into a series of small problems you already know how to solve. It lets you reach true and correct conclusions by starting from facts and transforming them through operations that preserve truth, and correspondingly that if you reach a false conclusion from these methods, then either the methods are flawed or the initial assumption is not as true as you believed. It teaches you to put two and two together and be confident, once you've double-checked your work, that you can say four.

This is stuff I use all the time in both my video research and my freeform writing. Building out a slow picture of how a story was told or changed over time involves finding the context it was created in, and reverse-engineering what parts of that context could have produced what standout portions of the story - what authorial or cultural bias results in this standout story element. Worldbuilding where I take two wildly disparate parts of the world, put them together and see what web of implications springs out of combining them, following the threads to new and interesting concepts that follow from what I've already established. Building a character arc by breaking down exactly what events are happening to them and what transformation each component will apply to the underlying character. If I want the story to go in a certain direction, what transformations do I need to apply to make that happen while still preserving truth? If I'm faced with a seemingly insurmountable problem, what methods can I use to break it down into bite-sized pieces?

This isn't something I think about most of the time. It's just how my brain works at this point, and I can't promise it'd work for anyone else. But thanks to all my years of hard work and training, my brain has been buff enough to solve every problem I've tangled with since graduation, and that feels pretty good.