Lucas Wilkins over on the blog Jellymatter writes an article which starts from a grand old point: being annoyed by something on Wikipedia. In this case, it’s Wikipedia’s entry on the axioms of probability, which, like many Wikipedia entries on mathematical subjects is precise, correct, and useless.
Why useless? Because while the entry does draw from a nice, logically rigorous introduction to the way probability is defined, it’s done by way of measure theory, a mildly exotic field of mathematics — I didn’t get my toes wet in it until my senior year as a math major, and didn’t do any serious work with it until grad school — for a subject, probability, that an eight-year-old could reasonably be expected to study. (Measure theory gets called in for a number of tasks; in my grad school career, its biggest job was rebuilding integral calculus, compared to what I’d learned in high school and as an undergraduate, for greater analytic power. So, yes, calculus can be done harder.)
Wilkins goes on to explain the same topic but in plain English, to what seems to me great effect, including an introduction to measure theory that won’t make Wikipedia’s precise-but-curt definition make sense, but will leave someone better-prepared to read it.