Jeremy Kun (who is worth reading beyond this article) has a post with very useful insights: https://j2kun.svbtle.com/mathematicians-are-chronically-lost-and-co

Jeremy Kun (who is worth reading beyond this article) has a post with very useful insights: https://j2kun.svbtle.com/mathematicians-are-chronically-lost-and-confused https://j2kun.svbtle.com/mathematicians-are-chronically-lost... It begins (and there is far more of value in the post): Many people who are in this position, trying to learn mathematics on their own, have roughly two approaches. The first is to learn only the things that you need for the applications you’re interested in. There’s nothing wrong with it, but it’s akin to learning just enough vocabulary to fill out your tax forms. It’s often too specialized to give you a good understanding of how to apply the key ideas elsewhere. A common example is learning very specific linear algebra facts in order to understand a particular machine learning algorithm. It’s a commendable effort and undoubtedly useful, but in my experience this route makes you start from scratch in every new application. The second approach is to try to understand everything so thoroughly as to become a part of it. In technical terms, they try to grok mathematics. For example, I often hear of people going through some foundational (and truly good) mathematics textbook forcing themselves to solve every exercise and prove every claim “left for the reader” before moving on. This is again commendable, but it often results in insurmountable frustrations and quitting before the best part of the subject. And for all one’s desire to grok mathematics, mathematicians don’t work like this! The truth is that mathematicians are chronically lost and confused. It’s our natural state of being, and I mean that in a good way. ...