There are "Levels" to Understanding Mathematics

The way it was described to me when I was in high school was in terms of 'levels'. Sometimes, in your mathematics career, you find that your slow progress, and careful accumulation of tools and ideas, has suddenly allowed you to do a bunch of new things that you couldn't possibly do before. Even though you were learning things that were useless by themselves, when they've all become second nature, a whole new world of possibility appears. You have "leveled up", if you will. Something clicks,...

 Aliens to Humans as Humans to Chimpanzees

know what you're thinking: we're smarter than bacteria. No doubt about it, we're smarter than every other living creature that ever walked, crawled, or slithered on Earth. But how smart is that? We cook our food. We compose poetry and music. We do art and science. We're good at math. Even if you're bad at math, you're probably much better at it than the smartest chimpanzee, whose genetic identity varies in only trifling ways from ours. Try as they might, primatologists will never get a chim...