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No, but talent does matter a lot in the last mile. Barring any physical or mental handicaps, however, I'd say it matters very little in the first few miles. I
by jfarmer 13y ago
No, but talent does matter a lot in the last mile. Barring any physical or mental handicaps, however, I'd say it matters very little in the first few miles. I'd even go so far as to say this is true of almost any thing one might choose to get good at, not just mathematics.
To put on my logician's hat for a second, the great grandparent said, "You can't teach a person to paint, or to write, because you can't teach them talent, the same is true with math." The unstated assumption in this sentence is that one must be talented at, say, writing in order to learn how to write. Of course, this depends entirely on what one means by "writing", "talented," and "learning."
If "being able to write" means being able to write as well as the best writers do then, yes, I'd agree that takes talent. If "being able to write" means having a command of written language above the mere mechanical act of putting words on a page, e.g., humor, irony, structure, flow, etc., then no, I don't think that requires talent. It requires interest and deliberate practice, but I don't think it requires talent.
This word "talent" is kind of a boogey man, anyhow. On the one hand folks plenty of folks say I'm "talented" at math. On the other hand, there were years in college where I spent 40+ hours a week studying it.
I think anyone who chooses could become a decent at mathematics, swimming, playing the guitar, or baking pies if they really wanted to, regardless of talent.
- cliveowen 13y agoyou point is valid but there's a difference between writing and learning math: while you can't without a doubt learn the basics of putting words on a page, you can't just learn enough math to write/understand a proof. A proof is reasoning put into writing, there's no mathematical equivalent of "putting words on a page" that lets you come up/comprehend one.
- jfarmer 13y agoWell, perhaps we disagree, but I don't think mathematics is about "proofs". I think proofs are a by-product of folks doing mathematics. They're the output of a long chain of mathematical thinking and can take many forms. I would agree that being able to follow contemporary mathematical writing is important, but one should learn the formalisms after they have a grounding in mathematical thinking. The formalisms aren't the point. For example, I wouldn't stress out if a student couldn't follow Newton's * Principia Mathematica*. I've tried and I can't, really. This is why the way we introduce "proofs" in high school in the US (via tedious and seemingly arbitrary geometric arguments) is so destructive. It's all formalism and, honestly, very little mathematics. I can and have explained the Pythagorean theorem to folks with virtually no mathematical training. The only prerequisite is the ability to find the area of a rectangle and perhaps a little but of high school algebra. We're not talking about diagram chasing, here.