Why is it that some of us will study math textbooks for hours and barely grasp what is going on, while other people will grasp these same concepts while only skimming the textbook? To what extent are you born with mathematical ability? How much does your environment affect the development of your mathematical ability?

And most importantly, what exactly is mathematical ability?

I have a friend whose dad owns a construction business, and they built their own house together. As a result, my friend is naturally inclined to build and fix all sorts of things whether they are mechanical, electrical, or structural. It seems this natural inclination has translated into an insane ability to grasp and understand mathematical concepts almost instantly. I had several math classes with him, and he rarely did his homework and was mostly indifferent about how he did in school... yet he got an A in every math class he took. But again I wonder, is there really a correlation, or is it just a coincidence?

I have another friend who also has a tremendous ability to build and fix all sorts of things; he is a self-taught electrical engineer, computer scientist, and botanist, among other things. However, he had a complete and utter disregard for his schoolwork, and never got an A in a math class. In fact, he struggled with math in school even more than I did. Is it possible he has mathematical ability, but it failed to show in school because of how much he despised schoolwork?

My parents insisted I had tremendous mathematical ability and pushed me and pushed me to excel in math. They put me in a supplemental school for several years so I could learn more advanced mathematical concepts when I was younger, and get ahead of everyone at school. I never had much trouble with math as a result, but I never thought it was because I was good at math. However, due to excessive pushing, by high school I hated doing math, and this inhibited my ability to learn new mathematical concepts. I struggled through several years of high school and college math, despising every minute of it, always only doing the minimum amount of work required to get a decent grade.

After middle school I never got an A in an advanced math class, and I wonder, is it because I don't have the mathematical ability, or because of the utter lack of desire to do anything math related?

The only way I can answer the above questions is by finding what mathematical ability is, and where it comes from. So what exactly is mathematical ability?

Based on my experiences I believe it consists of several major factors.
1) Internal motivation to figure out problems
2) Desire to know how things work
3) The ability to think logically
4) The ability to focus on one thing for extended periods of time

Where does mathematical ability come from?
1) Natural talent- Some people are simply born with a superior grasp of logic and mathematics. I can't explain why except maybe through genetics.
2) Parental influence- If parents guide their kids in the right way they can maximize their kids' mathematical ability.
3) Education- Math classes build up one's mathematical ability by training kids how to think logically.
4) Motivation- The desire to be good at math and logic can go a long ways.
5) Environment- People that are less social have less distractions and may find it easier to find their internal motivation, and are better able to focus on one thing for extended periods of time.

What you described is exactly the way it worked for me. I got straight A's in math without trying. When i got my first tricycle i took it apart to see how it worked. My first watch, took it apart and put it back together, it worked. Our new color TV? I took it apart to see how it worked. My parents bought me a 1000 piece robot that you had to build. It was full of gears and wound up to work. I simply have to know how everything works and i have always been that way. Math, algebra, geometry, trigonometry, binary, have always been easy pretty much. When i went to school we were not allowed to use calculators either. I know i was born that way because as soon as i was able to use my hands i was taking things apart. So, I would have to assume it is not learned, you either have it or you don't.
Everyone has something that they excel at though.

I was a math-o-phobe until I learned to program, when using math was required to get my answer. The way particulalry advanced math is taught precludes that because it's taught as a pure theory rather than something that can be used to solve problems. I now know there's nothing "wrong" with me in terms of being able to understand math. It's just that I wasn't interested enough to pay enough attention when they zapped algebra on me in 8th grade.

But there's a larger issue here. If we play catch and I throw the ball to you, you can catch it. That's pure trignometry. Not only can you do it, so can your dog. Indeed, he may be better at it than you. The point is that our bodies perform perfect mathematical functions all the time. We don't use formulas. Just a little eye-hand coordination and we're there. It's just that this does not always translate well to "intellectual" study.

Musical ability has been tied to mathmatical ability, but there is a twist I believe. People who play by ear. Chris Isaak is one artist who can't read a lick of music. My son is the same way. He writes amazing music, but struggled with math in school. He read at age four, and is extremely gifted with language and writing, but struggles with math the way it is taught. I think some people see math differently.

How to maximize mathematical ability:

Be exposed to it, and use it at an early age. Using my builder-fixer friend who is not good at math as an example, he has a tremendous aptitude for dealing with physical systems, but not with abstract equations. This is because he was exposed to the physical systems before he was exposed to the abstract mathematical concepts. As a result, he does not do well in school but excels with practical application. But the confusing thing is, can we call his ability "mathematical ability" then? Because he is not actually good at math, just the practical application of it. When you say "mathematical ability" I think of the ability to manipulate and understand abstract mathematical concepts in one's mind, and then apply it. My friend here does not seem to have that ability... so I would argue he has a "practical mind" and not a "mathematical mind."

Me, on the other hand, am neither. I had minimal exposure to physical systems, and forced exposure to math, and now am not too good at either. If I put my mind to it I can understand most physical systems and mathematical concepts, but it is only through tremendous effort; it does not seem to come naturally.

On the other hand, reading, writing, learning new languages, and thinking comes naturally to me. However, I don't know if I developed a creative aptitude as an escape from the terror doing math for hours on end, or if I really am a more creative person.

I don't see myself as naturally creative, however. I see myself as more of a mixture of a mathematical and creative mind... I'd like to call it an "analytic" or "philosophical" mind.

Now that I've thrown all these terms out there, "mathematical mind," "creative mind," "analytic mind," and "philosophical mind," I wonder if these are all separate talents or if they are all somehow interconnected...

Anyways, getting back to the main point of this post, how to maximize mathematical ability. Exposure, but non-forced exposure. Someone who is mathematically gifted has to find it on his own. He may not find it through math class in school... he may struggle in math class even with tremendous mathematical ability. But he may find it through music, logic, engineering, among other things.

This is the reason why I am a philosophy major. I was not born better at reading and writing than I was at math. Up until high school everyone knew me as the guy who was good at math, while I actually enjoyed reading and writing more, even though I was not as good at it. I tried harder in those subjects, and through initiative and self motivation I like to think I've developed a decent analytic and philosophical mind. And I firmly believe I was only able to do this because no one EVER told me to go do my English homework, or go read a book, or go write, or go get into advanced english class. I did that all on my own, so now I can take pride in what I've done.