I've concluded that the way I was taught Math (waaay back when…) had a number of flaws:

1. It was purely formal: theorems and proofs ad nauseum. I recently took a graduate class where the instructor would explain a theorem intuitively ("what is this thing trying to do?", "What are the main pieces of the proof?") and also formally. This made a lot of sense to me.

2. Math is presented in terms of a series of results, and the history is left out of it. Very often something going on in the real world would spark the development of some area of math. And vice-versa at times. I remember learning that the invention of canons, which could batter down castle walls, led to the applied study of parabolas.

Likewise a number of mathematicians (Gauss was one example) would flip back and forth between abstract math and applied math. I guess Newton would be another example of this.

You sound like you're in the midst of some math-intensive areas of work. There's no time like the present to deepen your math skills. I would guess having some concrete areas of concern might serve to focus what you wanted to learn, if your brain works like mine.

]]>It turns out math actually can do really cool things, teachers just do a horrible job at making the material exciting.

I may not be a math buff, but I enjoyed your blog and encourage you to geek out as you wish.

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