Joel Liu's List: Joel's hobby in math

• By the way, the Rule of 72 applies to anything that grows, including population. Can you see why a population growth rate of 3% vs 2% could be a huge problem for planning? Instead of needing to double your capacity in 36 years, you only have 24. Twelve years were shaved off your schedule with one percentage point.

  • hi, this is my private highlight

• Elegant, “a ha!” insights should be our focus, but we leave that for  students to randomly stumble upon themselves. I hit an “a ha” moment after  a hellish cram session in college; since then, I’ve wanted to find and share  those epiphanies to spare others the same pain.

• A reading protocol is a set of strategies that a reader must use in order to benefit fully from reading the text. Poetry calls for a different set of strategies than fiction, and fiction a different set than non-fiction. It would be ridiculous to read fiction and ask oneself what is the author's source for the assertion that the hero is blond and tanned; it would be wrong to read non-fiction and not ask such a question.  This reading protocol extends to a viewing or listening protocol in art and music. Indeed, much of the introductory course material in literature, music and art is spent teaching these protocols.
• The beauty in a novel is in the aesthetic way it uses language to evoke emotions and present themes which defy precise definition. The beauty in a mathematics article is in the elegant efficient way it concisely describes precise ideas of great complexity.
• Don't assume that understanding each phrase, will enable you to understand the whole idea. This is like trying to see a painting by staring at each square inch of it from the distance of your nose. You will get the detail, texture and style but miss the picture completely. A math article has a story!  Try to see what the story is before you delve into the details. You can go in for a closer look once you have a framework to fill with details, just as you might reread a novel.
• The best way to understand what you are reading is to make the idea your own.  This means following the idea back to its origin, and rediscovering it for  yourself. Mathematicians often say that to understand something you must first  read it, then write it down in your own words, then teach it to someone  else. Everyone has a different set of tools and a different level of “chunking  up” complicated ideas. Make the idea fit in with your own perspective and  experience.
• Most math books are written with assumptions about the audience: that they know certain things, that they have a certain level of "mathematical maturity", etc. Before you start to read, make sure you know what the author expects you to know.

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