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I recently had, for various reasons, improve my math skills. I was surprised at how difficult I found math. Now, I was never really great at math; logic and ca

I recently had, for various reasons, improve my math skills. I was surprised at how difficult I found math. Now, I was never really great at math; logic and calculation in the head I could do fairly well (above average), but just foundational knowledge was hard and mathematical theory even harder. But now I even had trouble with integration and differentiation and even with understanding a problem to put it down into a formula. I am far from being the youngest anymore, but I was surprised at how shockingly bad I have become in the last some +25 years. So I decided to change this in the coming months. I think in a way computers actually made our brains worse; many problems can be auto-solved (python numpy, sympy etc...) and the computers work better than hand-held calculators, but math is actually surprisingly difficult without a computer. (Here I also include algorithms by the way, or rather, the theory behind algorithms. And of course I also forgot a lot of the mathematical notation - somehow programming is a lot easier than higher math.)

commandlinefan 10mo ago
I started going down that road decades ago myself. I had a degree in computer science already, but I'd only learned just enough math to graduate and then forgotten everything, deliberately. Years after I graduated, I was browsing comp.lang.java (I think it was) and somebody asked for help developing an applet that could draw a 3-D arrow that could orient itself in any direction. For some reason, that sounded interesting to me, so I started trying to work on it and I realized I needed to go back and re-learn all of that "point-slope" stuff that I'd made a point of learning just enough of to squeak through college. That sent me down the path of re-learning all the things I now wish I'd put more effort into learning when I was a teenager. I ended up working through my old undergraduate calculus textbook a few times and I understand undergraduate calculus _really_ well now. I was able to coach both of my kids through high school calculus and they both remarked that none of their friends parents were able to help them beyond algebra. It makes me wonder how many people are great (or even adequate) at math and how many are just faking it - as interesting as I now find it, math skills aren't actually very practically useful.
taeric 10mo ago
I've grown to see math as far more pattern matching than I remember it as a kid. I think that explains why "rote memorization" works more than folks want to admit for it.
- jaccola 10mo ago
  This doesn't end at kid level maths either, I have seen people get bachelors and masters in maths without understanding much of it intuitively or being able to apply it. Mostly because they have rote memorised it (and partly because much of the education system is a game to be played e.g. speaking with professors during office hours can give very strong hints to exams).
  - taeric 10mo ago
    Right, I've also seen people that couldn't get some higher math items because they haven't learned to recognize some things on sight. Curves are a good example. You should be able to roughly sight identify basic curves. Or distributions based on their shape. With obvious caveats. I suspect this is a lot like being able to recognize a piece of art to the artist by sight. Strictly, not required. But a lot of great artists can do it. For real fun, I saw an interview with Magnus Carlsen where someone was quizzing him on famous games. He was able to say the match on the first 2-3 moves a remarkable number of times.
  - nomel 10mo ago
    My professor said this was an inevitability that holds people back who don't understand it is. After a certain point, you can't understand it all, because actually understanding it requires understanding the 1000 page proof. After a certain point, in maths, you must rote memorize the tools, add them to your belt, and trust the centuries of work before you, so you can apply them to your problems. It serves no purpose to "understand" them, many cannot be put into an intuitive framework, and attempting to make "understanding" a prerequisite to your progress will mean you will eventually fail out of the program.
    - mcmoor 10mo ago
quantum_state 10mo ago
If I may share, the stuff occurring in a computer would not be qualified as math … math is more about intuition and the sense of describing things in quantitative languages …
dsjoerg 10mo ago
I wish this interesting story was related to the article.
2snakes 10mo ago
Neuroscience suggests global connectivity changes after 40 instead of specialized areas. Overall declines do not start until late 40s though.

commandlinefan 10mo ago

I started going down that road decades ago myself. I had a degree in computer science already, but I'd only learned just enough math to graduate and then forgotten everything, deliberately. Years after I graduated, I was browsing comp.lang.java (I think it was) and somebody asked for help developing an applet that could draw a 3-D arrow that could orient itself in any direction. For some reason, that sounded interesting to me, so I started trying to work on it and I realized I needed to go back and re-learn all of that "point-slope" stuff that I'd made a point of learning just enough of to squeak through college. That sent me down the path of re-learning all the things I now wish I'd put more effort into learning when I was a teenager. I ended up working through my old undergraduate calculus textbook a few times and I understand undergraduate calculus _really_ well now. I was able to coach both of my kids through high school calculus and they both remarked that none of their friends parents were able to help them beyond algebra. It makes me wonder how many people are great (or even adequate) at math and how many are just faking it - as interesting as I now find it, math skills aren't actually very practically useful.

taeric 10mo ago

I've grown to see math as far more pattern matching than I remember it as a kid. I think that explains why "rote memorization" works more than folks want to admit for it.

jaccola 10mo ago
This doesn't end at kid level maths either, I have seen people get bachelors and masters in maths without understanding much of it intuitively or being able to apply it. Mostly because they have rote memorised it (and partly because much of the education system is a game to be played e.g. speaking with professors during office hours can give very strong hints to exams).
- taeric 10mo ago
  Right, I've also seen people that couldn't get some higher math items because they haven't learned to recognize some things on sight. Curves are a good example. You should be able to roughly sight identify basic curves. Or distributions based on their shape. With obvious caveats. I suspect this is a lot like being able to recognize a piece of art to the artist by sight. Strictly, not required. But a lot of great artists can do it. For real fun, I saw an interview with Magnus Carlsen where someone was quizzing him on famous games. He was able to say the match on the first 2-3 moves a remarkable number of times.
- nomel 10mo ago
  My professor said this was an inevitability that holds people back who don't understand it is. After a certain point, you can't understand it all, because actually understanding it requires understanding the 1000 page proof. After a certain point, in maths, you must rote memorize the tools, add them to your belt, and trust the centuries of work before you, so you can apply them to your problems. It serves no purpose to "understand" them, many cannot be put into an intuitive framework, and attempting to make "understanding" a prerequisite to your progress will mean you will eventually fail out of the program.
  - mcmoor 10mo ago

quantum_state 10mo ago

If I may share, the stuff occurring in a computer would not be qualified as math … math is more about intuition and the sense of describing things in quantitative languages …

dsjoerg 10mo ago

I wish this interesting story was related to the article.

2snakes 10mo ago

Neuroscience suggests global connectivity changes after 40 instead of specialized areas. Overall declines do not start until late 40s though.