Interesting thread. I have spent a lifetime as a practicing mathematician/ statistician. I have a two observations/thoughts:
- I think being good in math is a function (no pun intended) of three things:
- Desire/Attitude/Belief
- Education/experience/exposure/repletion
- You have to see a benefit or reward
(I think this is true for any skill – piano, tennis, singing, swimming, woodworking, welding etc)
If you have no desire to do math or no belief in yourself to do math or have a bad attitude – you are NEVER going to be good at math. Parents, friends and society in general send strong signals about what you can/can’t should/shouldn’t do.
It was not cool to be good at math when I was growing up in the 70’s and 80’s. TV/movies mostly had cops, lawyers and dr’s. The first mathematician character I can remember was on “A Different World" in the early 90’s. Today, math is more mainstream (Numb3rs, big bang theory, etc).
Math builds on itself – the more “tricks” you see the more math you can do. Being exposed to lots of problems and techniques for solving problems goes a long way to being good.
I’m not sure “natural ability” plays much of a role. I think people use this as an excuse to not engage (ie "I have no natural ability to do math - so that’s why I’m bad at math)
Growing up I was encouraged to do math and exposed to it. It was “normal”. My grandmother was a “computer” (not the electronic one we have today). She could add a column or 25, 8 digit numbers as fast as she could read them (about 10 seconds). It was a highly desirable skill when she was growing up. My mother was an actuary and my dad was a CPA. (I know I was adopted because I have a personality).
The rewards for being good at math are considerable. It has been my experience that all other things being equal – a person with significant math skills makes considerably more than a person without (at least on average). I had to find a job in the depths of three recessions (82, 91, 01) and had no problem.
- When people ask me “what can you do with a math degree (other than teach)?”. I respond It’s a lot shorter conversation to give you a list of what you can’t do with a math degree because math is everywhere (like it or not). Every career/job category has a mathematical end. For example:
Insurance (actuary)
Medicine (boiostatistics, epidemiology, …)
Oil exploration (geophysics, reservoir engineering…)
Logging (how to cut a log to get the most value out of it)
Flying (scheduling planes/crews)
Sanitation services (shortest path through a town to collect all the garbage)
Acting (predicting the success of movies, animation)
I have never been stumped. But I will admit there may not be a lot of mathematicians scheduling sanitation workers.
Be good at math, combine it with something else that the world wants and you will have a long and successful career.