
How to Develop a Mindset for Math - nickb
http://betterexplained.com/articles/how-to-develop-a-mindset-for-math/
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jsomers
Yes, math -- like every other discipline that can take itself seriously -- is
about models and relationships. But given these models, we ought not
necessarily "apply them to real-world objects." Rigorous math is powerful
precisely because it is _abstract_.

One of this guy's prized "deep insights" is that negative numbers refer to
deficits of cows. Granted, that's a slick (if not wholly obvious) way to
represent an intuitively awkward concept, but it engenders a false confidence.
Negative numbers don't exist to represent bookkeeping deficits. They are there
because some formal mathematical argument grounded in pure logic _said_ they
had to be there. The fact that we use negatives to refer to cows reveals more
about primitive functions of the human brain (distinguishing among objects,
counting) than it does the deep algebraic structure of the numbers themselves.

I admire attempts to ground difficult abstractions in physical reality as much
as the next guy, but we shouldn't confuse these simplistic observations with
mathematical insight.

