Allison wrote:

> Do you have a similar metaphor for _reading_ mathematics?

Reading mathematics is a complicated business. I read mathematics in different ways for different purposes.

[That handout]( does an excellent job of explaining how to read mathematics when you 1) don't yet understand it but 2) want to understand it very well. That _does_ take an awful lot of time! It's the complete opposite of passive reading: you have work through all the concepts, see how they interact with the concepts you already understand, let them fight it out, ask yourself lots of questions, answer those questions - sometimes by doing calculations - and go through the reading over and over until the impenetrable murk turns into crystal clarity.

Maybe an appropriate metaphor is hiking into the jungle, setting up a network of trails and camps, and exploring deeper and deeper until you know the territory by heart and aren't scared of it anymore.

But I can read math much faster when I already roughly understand what's going on. Since I've been thinking about math for 40 years, that's often the case. For example: I'm writing a paper, I need something Theorem X and I feel it should be true, I look for papers that seem to state a theorem like this, I find one, but I notice it's stating Theorem X' - something a bit than I want. So I need to figure out if Theorem X' implies Theorem X - or perhaps I was confused and Theorem X is false and Theorem X' is the best substitute that's actually true. Here I usually dive straight into the middle of a paper, where I see Theorem X', and then work backwards to make sure I understand the definitions, and dip into the proof of Theorem X' just enough to get a sense of what's going on.

I guess the appropriate metaphor is parachuting into the jungle, in the midst of enemy territory, to save a hostage. Get in and out as fast as possible: just get the job done with minimum damage.

I can also read math quickly if I just want to get a flavor of what's going on, not a deep understanding. Here the metaphor might be a riverboat cruise where you sail past the jungle and admire it, but don't get off the boat.