Jeremy Kun, a mathematician and programmer, writes about mathematical habits, applied math, and his book on math for programmers.
HN commenters cite his posts on how math education builds tolerance for being wrong and on practical uses of linear algebra.
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…
I think one non-obvious benefit of a good mathematics education is that you have little choice but to develop a tolerance for and understanding of being wrong. See Jeremy Kun's blog post [1] for more, but my own experience has been that in e.g. discussing different ways to solve a problem or prove something almost every person eventually has an "oh, no, I see, I'm wrong and you're right" moment. Not that every mathematician is necessarily a font of humility and grace, but I think math offers more regular and irrefutable demonstrations of your own fallibility than many other fields, and this is good.
[1] https://medium.com/@jeremyjkun/habits-of-highly-mathematical-people-b719df12d15e#.2ikc1ut7w
To reinforce this point: here's just a fraction of what you can do with linear algebra [1]
[1]: https://medium.com/@jeremyjkun/here-s-just-a-fraction-of-what-you-can-do-with-linear-algebra-633383d4153f
https://medium.com/@jeremyjkun/a-teary-goodbye-to-hagoromo-d29df12f3bce