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you 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
by cliveowen 13y ago
you 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.