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Comment by potbelly83 | Hacker News Reader

As a math PhD I have to say the only way you're going to learn mathematics is if you actually have a pressing need to do so. i.e. You have a project at work that needs some math, you have a hobby that needs some math. In this case you just learn what you need. Just learning math for its own sake outside of a University STEM track is just too hard (I wouldn't be able to do it and I've tried).

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I hesitate to contradict someone who has gone through the whole Math PhD process, but I have to say that the best mathematicians that I know treat the problems they're working on as games, or riddles to be solved... and they've taught their kids (and others) this same method of thinking about these problems. There's a huge mental tool set, and often a lot of grinding to get to a solution, but it's just a game (and there are often more elegant solutions)!

I enjoy provoking interest in complex numbers and exponentials among precocious teens, but I've never been more humbled than having a Galois theory joyously explained to me by an 11 year old. (p.s. I'm an engineer so I follow your technique).

To me the problem isn’t learning it, it’s retaining it.

I learned all kinds of quantitative analysis and statistics in the CFA program ten+ years ago.

I had daily sheets that I would solve equations and answer all kinds of questions. I knew them forwards and backwards. I just looked at one now on fixed income - not sure if could answer any of the questions today to save my life.

And I work in finance daily!!

I don't think you're contradicting the GP. Solving problems for fun still counts as "pressing need".

The alternative is something like "Oh, I should learn abstract algebra because it's a fundamental course in all curricula". You'll learn it, and then forget it.

Was programming a 3-axis machine in early college back in 90s. After a few months I was mostly re-inventing trigonometry. The I actually took trig later on. That would have been super handy at time.

I think the question needs to be asked, "What am I hoping to get from this?"

If its tools to help you solve some problem, great. If its because you find it fun, great.

But if its because you feel you want to 'better yourself' or perhaps feel like it would somehow prove your intellectual worth, you probably won't get a lot out of it.

This is true. When I started my first job, I tried casually learning more from where I stopped after I finished school. My motivation slowly waned as I realized I vastly preferred playing video games than watching lectures and trying to do some problem sets.

Correct me if I’m wrong, but I assume you’re looking at this through the wrong lens. As a PhD you’ve learnt something hard at a considerable depth but this isn’t what I, or most people, hope to achieve by learning maths themselves. It’s normally to a far lower depth that’s far more achievable like Calculus I or some aspects of number theory or knowing what all the funky symbols such as Summation mean.

I just want to do basic engineering and physics. Understand some of the higher level models we have to describe our world.

I experienced something like this recently. I struggled to grasp linear algebra when I took it in undergrad and as a result was always intimidated by the subject. Now, years later, I'm taking a course in graphics and naturally needing to relearn linear algebra and suddenly everything just clicks.

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