"I have never had to do integrate the "arctan" function by hand in my entire career" arguments are not worth engaging with.
If people are happy with a job or a role that does not need math that' fine.
Familiarity with Maths let's you to rise to the occasion, to become more than a replaceable cog.
The thing is, unless you are trained in math you wouldn't even recognise the opportunity, that a certain kind Of Math could have been used here. In fact, even if you are trained in Math you may not see it till much later -- it needs a special eye and something in that moment.
Polyhedrons were looked at for centuries after centuries by top-notch mathematicians. All missed Euler's formula, except perhaps Descartes.
Often what happens is some nontrivial branch of mathematics suddenly finds a novel and impactful application. Then crowds jump in to learn that Math. But it's mostly already a little too late for them, they have missed this bus.
The best case is one already knows the Math beforehand and you don't know which part will be handy. It helps if you love the subject and can afford to invest time to learn it for the love of the subject. Once in a while you happen to find yourself in the right place and the right time and with the right tools you need.
> Often what happens is some nontrivial branch of mathematics suddenly finds a novel and impactful application. Then crowds jump in to learn that Math. But it's mostly already a little too late for them, they have missed this bus.
However, in the meantime, the experts in that math have "missed the bus" on whatever the application area is, that the math expert knows not enough about because they were studying math instead.
If people are happy with a job or a role that does not need math that' fine.
Familiarity with Maths let's you to rise to the occasion, to become more than a replaceable cog.
The thing is, unless you are trained in math you wouldn't even recognise the opportunity, that a certain kind Of Math could have been used here. In fact, even if you are trained in Math you may not see it till much later -- it needs a special eye and something in that moment.
Polyhedrons were looked at for centuries after centuries by top-notch mathematicians. All missed Euler's formula, except perhaps Descartes.
Often what happens is some nontrivial branch of mathematics suddenly finds a novel and impactful application. Then crowds jump in to learn that Math. But it's mostly already a little too late for them, they have missed this bus.
The best case is one already knows the Math beforehand and you don't know which part will be handy. It helps if you love the subject and can afford to invest time to learn it for the love of the subject. Once in a while you happen to find yourself in the right place and the right time and with the right tools you need.