Read as much as you can. Read as little as you can.

In math, as in any subject, there is definitely an advantage to being widely and well read, so that every known fact about your topic of study is immediately available for recall. Thus, so long as the result of your reading is that you actually retain new and useful knowledge, the first sentence in the title is indeed sound advice. However, I have noticed that math students often find it very difficult to learn from reading. They spend time with their math book, but come away with…

Read More »

Mourning the Death of High-school Geometry

Don't get me wrong. I'm not some hide-bound traditionalist looking for a return of the "good old days." Just because our ancestors studied geometry in school doesn't mean we have to. Neither do I have any arguments to suggest that geometric knowledge is superior to other mathematical knowledge. In fact, in my life as a mathematician, the content of high-school geometry (for example, proving triangles are similar or congruent) doesn't come up all that often. So why this sense of loss? That will come later. First,…

Read More »