> So this guys method is exactly what other mathematicians warn against? Trying to understand? No, I don't think so. The "there's no intuition" advice is real

> So this guys method is exactly what other mathematicians warn against? Trying to understand? No, I don't think so. The "there's no intuition" advice is really good advice for undergraduates or lay people first encountering abstract concepts in pure mathematics. In fact there is an intuition, but the intuition is usually sort of on its own terms -- not so much grounded in physical life experiences. In other words, you will get an intuitive grasp on the ideas but that intuition will probably not be an analogy to your previous experiences in everyday life. When mathematicians say "there's no intuition" they usually mean "there's no physical experience that corresponds to the underlying intuition, and it's not really like anything you've seen before. It's a new experience and you need to experience it on its own terms. Stop trying to ground yourself in classical mechanics or whatever." But that's quite the mouthful, so better to just say "there's no intuition; just focus on working with the objects and you'll eventually get comfortable". This quote from the article captures it well, I think: > "Now I find real numbers much, much more confusing than p-adic numbers. I’ve gotten so used to them that now real numbers feel very strange."