One of our favorite ways to avoid work is to browse the articles at 3quarksdaily. They post essays about politics, science, art, music, literature, history, and everything else you can think of. Sometimes even math!
They’ve posted some great essays, and we want to point out a couple to you. The first is Mathematical learning (and math as a hobby) by Rishidev Chaudhuri. Many of the people who read 3QD are more into art and such, and don’t have a proper appreciation of how much fun math can be. This essay is to convince them to change their minds:
…proving a mathematical statement or solving a problem is an unfolding of false sallies and blind alleys, of ideas that seem to work but fail in very particular ways, of realizing that you don’t understand a problem or a concept as well as you thought. And again, these are not wasted. In almost every case, if someone were to just give you a proof or a solution and you didn’t either try to come up with it first or actively interrogate it once you had it (which is almost the same thing), you’d learn that the statement was true, but learn very little about why it was true or what it meant for that statement to be true. And much of the learning in a math class happens not in the lectures but afterwards, in the time spent on problem sets (and, if you had a choice between attending the lectures and doing the problem sets, you should always pick the latter).
Unfortunately, most people make it through a high school mathematical education without being taught this. This has unfortunate consequences and makes mathematical learning exceedingly vulnerable to expectation and self-belief, so that it is often seen as something you either can or can’t do, and many people see the struggle as a sign of a lack of ability rather than as an intrinsic part of the learning….
One of the inevitable tragedies of specialization is that most people don’t take classes in most areas after college or high school. For some this is compensated by an amateur interest in history, say, or philosophy. But for the variety of reasons I mentioned, the reasons that make students think that mathematics proficiency is an extreme example of a natural talent and that it is hopeless to do math without this essential ability, few people seem to maintain an amateur interest in mathematics or study mathematics recreationally.
If it isn’t clear already, I think this is a huge pity, especially because it is often motivated by a false assessment of one’s mathematical ability. And it is also a pity because most people stop doing math just at the point when the fun stuff starts, just when they’ve worked through most of the tedious arithmetic and are finally ready to embark on sweeping journeys of abstraction. It’s like taking dance classes but never going dancing.
— From the 3QD essay
In the same spirit (and linked to in the comments to the above article) is Monday Musing: Aptitude Schmaptitude! by Abbas Raza:
…there are those who feel that it is no great loss to be innumerate. In that case, I’m sorry, but you don’t know what you are missing. Some of the most profoundly beautiful ideas produced in the last few thousand years are beyond you, as is the serious study of about 80% of what is taught in modern universities. Even the social sciences cannot exist without math anymore, and you cannot have any deep sense of political and economic issues if you are completely innumerate.
— from the other 3QD essay