Mathematical Thinking

The Lumonator has a recent post on the importance of mathematical thinking, and of teaching it.

He summarizes some of this in ten points, which I endorse, but I would like to add one more point which he doesn't quite state explicitly: mathematical thinking teaches disciplined methods of thought. I am reminded of the fact that Lincoln taught himself to prove all the theorems of Euclid's first six elements at sight not because he thought they would come up in his legal practice, but because he thought that would sharpen his logical and analytical skills. It also teaches a language for expressing analysis in a disciplined manner.

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