No, definitely not, and I agree with the other sibling replies. I was more specifically responding to the part that was dismissive of the "so you should too" po

No, definitely not, and I agree with the other sibling replies. I was more specifically responding to the part that was dismissive of the "so you should too" point. Certainly, we can and do develop newer and simpler ways of understanding previous theories. And teaching the historical sequence of events can help with understanding; I myself experienced that with [1] for modern analysis. However, these understanding-aids don't teach you how to do mathematics, and only marginally improve your ability to apply those models and theories to existing real-world problems. To improve your ability to do mathematics, active exercises are necessary. Really, it's the same with many other fields, you don't get to be a good musician merely by reading about music and music theory. I assumed they used the term "struggle" poetically, it certainly doesn't have to be unpleasant. But you have to put in some active mental exploratory effort. I found this post [2] a good summary of the skill set. But it's very abstract and likely won't make much sense unless you've been through the experience yourself. These understanding-aids are also sometimes unnecessary. If you've done enough of the right kinds of exercises, they are of themselves an aid to understanding. For example, I could understand category theory better, not by learning about how this theory was developed historically, but by writing lots and lots of similar programs, and having a natural tendency to syntactically (and without much thought) refactor my code to be less repetitive, eventually leading me to various "category theory aimed at programmers" blog posts and papers. This one [3] of course deserves a mention, but there are many more. To further emphasise this point, very brilliant mathematicians can just "pick up" models and concepts and work creatively and productively on them, without needing these aids. My other point was that, the understanding-aids are very rarely what actually happened in the head of the people that developed a theory. Even historical narratives have distortions, and they are rarely detailed or precise enough to describe the rejected options, nor why they were options in the first place. (This fact, is also why they are not useful for teaching how to do mathematics.) There are exceptions, but reconstructing them is a boring process with little reward, especially since new developments 10 years later might explain it in even simpler terms. That said, I would disagree with this part (from the top answer to the OP): > a) The goal is to learn how to do mathematics, not to "know" it. Modern mathematics has so much damn material these days that it's impossible to learn everything you need in order to solve modern-level problems, merely by teaching yourself all models and all theories "the hard way". Understanding-aids are certainly needed, and I use them very often myself, and I certainly prefer resources that teach using good analogies, proper context, descriptions of the motivations behind a theory, step-by-step "n/n+1" exercises, and everything else that other people mentioned here. [1] "Who Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus" [2] https://medium.com/@jeremyjkun/habits-of-highly-mathematical-people-b719df12d15e https://medium.com/@jeremyjkun/habits-of-highly-mathematical... (discussed on HN here https://news.ycombinator.com/item?id=12187469 https://news.ycombinator.com/item?id=12187469) [3] https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/ https://bartoszmilewski.com/2014/10/28/category-theory-for-p...