Because I really don't think it can be both. I've heard people say that perhaps mathematical ability is in genetics. If that were true it would be highly disappointing. I'm a complete maths n00b at the age of 19. I've always considered maths to be a skill and that as you practice you'll become better. To what extent is this true?
Whether you have talent or not, you still need to practice. The only difference is the amount of practice you'll need to put in to become sufficient at it. I've also heard cases of "complete maths n00bs" becoming really good at it through hard effort and dedication. It's as if they had talent in their genes all along
Ah good. That's the sort of talk that makes me feel much better. I suppose it's many other factors too such as access to education. I used to think mathematics was too inaccessible for me. Then I brought a cheap 'for dummies' math book. From there I'm here.
I agree completely with the above statement. There are those that as in any subject have an affinity for the subject, "it comes easy". There are those that are at the Master level, the ones we envy all. They look at a flower and see the symmetry, the recurring formula that generated the petals, etc. Or they see an apple drop and create the law of gravity. That skill I think you are born with.
You might read "Talent Is Overrated" by Geoff Colvin. He tries to make the case that world class talent is not something you either have or you don't. He claims many people could have this if they have enormous energy, drive, focus and concentration and are willing to pay the price of giving up literally everything else in their life for perhaps ten years of extremely intense "directed practice" and usually requiring a skilled coach to observe your weak points and make you work very very hard to improve those. He does caution the reader to consider the price they will pay before attempting this. I don't believe he specifically addresses how to find a suitable coach in some particular field, like mathematics. I would be very interested in the answer to that question. Two related comments. You would not need to go to that extreme to be competent and even fairly skilled in a new field. I also tend to think that if anyone is skilled in some subject and wanders off into a completely different unrelated new subject that they will be perplexed and confused when they first arrive. It is my superstition, based on a number of experiences, that the people making up each subject have a different culture and even a very different way of thinking. I believe it is only after learning the new way of thinking that you can become competent and skilled in the new subject. Wander out of say ancient literature and over into molecular genetics or out of there into psychology or out of there into modern algebra. "Those people don't think the same way."
I should tell you that it's a skill in order to spur you onward to hours and hours and years and years of laborious practice. I hate to give anybody an excuse to slack off. However, I think the skill part mainly applies to parts of mathematics that have been refined and worked out. That's good enough to get you an A in most undergraduate courses. When it comes to advanced topics or developing new mathematics, I think it's definitely a talent. In particular, it's very hard to develop imagination (in math or anything else) by practicing things that are known.
Love of mathematics is a talent. Born of this talent is the skill of mathematics. ie. I am partially genetically predisposed to like maths so i do maths more often and do reasonably well (flawless end of year report for yr. 11 VCE mathematics whilst in yr. 10 *cough* who said that?). But jokes aside... Everyone can be skillful in maths but not everyone has the talent to want to do so.
Why would you think it couldn't be both? Just because it's a mental activity instead of a physical activity doesn't mean the same principals don't apply (including the fuzziness of defining 'talent'). A slow, short person can become very skilled at something like basketball through practice, but they probably won't challenge Michael Jordan's reputation. Of couse, there are ways to improve one's speed, but only to a certain extent, so speed is kind of a fuzzy talent. And there are players that improve their skill level to a point where they can do well even among the top talent in the NBA ("Spud" Webb comes to mind). Likewise, a person can improve their math skills, but I'm pretty sure a lot of people start with more math talent than the average person, even if math talent is a lot harder to define than physical talent. For example, intelligence level would be one relevant talent, but intelligence is pretty hard to define in itself. And even if you could define math talent, you'd have to be specific about what kind of talent. Being really good with mental calculations doesn't mean a person would be a good mathematician, nor does being able to really understand applied equations (such as physics equations) mean a person would be a good mathematician. Yet, either of those two talents would give you a reputation of being good at math (for whatever that's worth, which is probably worth about as much as my mother thinking my nice smile makes me a talented basketball player).
I don't think that math itself is a 'skill' but instead it's a body of knowledge used while applying different skills. Gaining mastery of math at a particular level is just proof that you know how to apply the gained knowledge using your personal skillset. Math is easier to learn using particular personal skillsets than others. For instance: most math requires good visualization and organizational skills. These are core skills that can be practiced in different ways. For instance - in my early childhood, I was taught to use models and diagrams to represent simple things. Rearranging a bedroom at age 4, for instance, was a task of creating a scale bedroom and creating manipulatable scale 'cutouts' of furniture. Both of my parents are civil engineers, so these were practiced and refined skills to them which they were passing along.
All of the views mentioned add to this discussion, they are all acceptable and don't seem to be to diametrically opposed. I think this discussion is heading in the same direction as "What is intelligence?" Is Mathematica the most intelligent mathematician on the planet or just a great "calculator". Its "skill" level is very high. People fit the same categories, great "calculator", great fountain of knowledge, and in my case a love and interest in the mysteries of the "numbers". Because of this, I seek more knowledge and delve into areas that interest me.
I think maths is a skill, but people often mistake it for a talent. Most people are scared of maths, and so they do allthat they can to avoid it. There are a few however who really enjoy maths, and therefore make the effort to learn it. As a maths tutor I often find people who don’t like maths often start to after they see how easy and useful it can become once you try.
Defining natural talent isn't that easy, and is not easy to separate from acquired skills. Early cognitive development due to environmental factors certainly can't be called natural talent, and having a beneficial genetic disposition wont get you anywhere unless you use your mind in the "right" way pretty early on.
For the purpose of this thread, I'll define natural talent/curiosity as the "stuff" that brings people to this forum. Barring homework help, of course. All of us here didn't look through a career book and picked mathematics. There is something we like abut the subject. We do not all have the same mathematical interests, I.E. number theory vs. calculus vs. geometry. The interest is there, and then we acquired the foundation/skill to pursue that interest.