> Society thinks of math as technical and functional, rather than beautiful.
The math people suck at is the technical and functional part, just as much as the beautiful parts. I'd frame the issue like this: there's the journey of arriving at the result, there's wielding the result, and then there's applying it to a very particular problem.
Schools are teaching mostly the last part - applying a^2+b^2=c^2 to a set of contrived problems that are meant to exercise your ability in arithmetic, variable substitution, and simple symbolic transformation. They do not teach people how to wield the formula - as in, how can you realize on your own that any particular real-life challenge calls for application of that tool (or of mathematics in general). That's the middle part that's directly valuable, in the immediate term. That's the difference between a carpenter, and a person who figured out how to use a hammer to drive a nail into a wall.
The beauty and journey part? That's study of history and art of inventing new types of hammers and other impactors, and perhaps inventing your own. Even further upstream of the "knowing how to use it to build something" part, but neither is taught in schools.
> Society thinks of math as technical and functional, rather than beautiful.
The math people suck at is the technical and functional part, just as much as the beautiful parts. I'd frame the issue like this: there's the journey of arriving at the result, there's wielding the result, and then there's applying it to a very particular problem.
Schools are teaching mostly the last part - applying a^2+b^2=c^2 to a set of contrived problems that are meant to exercise your ability in arithmetic, variable substitution, and simple symbolic transformation. They do not teach people how to wield the formula - as in, how can you realize on your own that any particular real-life challenge calls for application of that tool (or of mathematics in general). That's the middle part that's directly valuable, in the immediate term. That's the difference between a carpenter, and a person who figured out how to use a hammer to drive a nail into a wall.
The beauty and journey part? That's study of history and art of inventing new types of hammers and other impactors, and perhaps inventing your own. Even further upstream of the "knowing how to use it to build something" part, but neither is taught in schools.