It's very similar to how most anyone can catch a ball, but it takes way more to catch the ball on paper.
It's very similar to how most anyone can catch a ball, but it takes way more to catch the ball on paper.
Math education could be so much better, when you compare school to self-directed learning with knowledgeable peers. I went to a good high school by U.S. standards, and tested into the advanced freshman math class at Caltech, and still had to ask if the roots of a polynomial with real coefficients came in complex-conjugate pairs -- I wasn't sure. (Maybe nowadays with math circles and the web, the frosh are a lot better prepared?)
I think there's also a problem with the culture of math writing undervaluing things like examples and motivating background.
http://worrydream.com/KillMath/ talks about going beyond the limits of paper for media for doing math.
Then when it's time to do math you can use your techniques so avoid letting small details trip you up and let you focus on the bigger picture.