How to Read Mathematics

stonehill.edu

24 points·ulvund··2 comments

The idea of a reading protocol is a pretty essential concept. I appreciate the author carefully detailing such a protocol for Mathematics, and I imagine this exercise would be pretty simply done for code as well.

I'd vie that Mathematics is much more subtle, in general, than code: average reading speed something like 0-15 "concepts" (because we all know how terrible LOC is) in 30 minutes, depending, of course, on how subtle the code is, how skillful the reader, and how elegant the coder.

I agree. Math is extremely subtle. And despite its nature as the most exacting and rigorous of sciences, the notation used in mathematics is anything but. Each author uses their own conventions. Abuse of notation runs rampant.

Sometimes the difference between theta and phi is more than just alpha conversion... some authors use certain variable names to communicate important properties that must be satisfied in the premise of theorems -- but without making those premises explicit.

A derivative is a 'special form' in calculus when it is so cleanly expressed as a higher-order function. And indefinite integrals introduce a mysterious constant, C, when really, what you're talking about is a multivalued-function!

I think math is pretty much the coolest subject one could study, but in many of the books I've read, the difficulty in understanding is evenly divided between the concepts and the author himself.

Reply on news.ycombinator.com