Ask HN: "Math is hard!" - The limits of individiual mathematical ability | Hacker News Reader

Ask HN: "Math is hard!" - The limits of individiual mathematical ability

12 pointsbiznerd9 comments

I got a head start in math because when I was young my parents signed me up for Kumon, the Japanese math tutoring service. In high school, I was definitely ahead of the vast majority of people.

However, Physics did not come naturally to me like other math classes. On the first test (speed/velocity), the teacher told me I got the highest grade out of all his students. It got progressively worse as the material got more difficult. Combined with the fact that it was almost senior year, I almost failed a semester or two.

In college, I was absolutely awful with math proofs. Awful. Like I would stare at the sheet of paper and not even know where to start. I took one class involving them (inear algebra) and decided this was way too hard to continue my Math career. A really hard statistics class was similarly very hard (a regular stats class was quite easy.) Not sure if that was because the textbook and teacher were hard to understand.

I'm revisiting many things though. I did very poorly in high school for english and now I have writing clients on odesk. So it makes me think - what are my true abilities with math?

Math is partially IQ related. That cannot be denied.

"Art is hard!"

It is common knowledge that math is hard. But it's not common knowledge that art is just as hard. Did you ever try to compose a song like Beethoven, to paint a picture like Van Gogh or to rap like eminem? Probably you did, but did you succeed? If you don't have affinity with a task, you will find it hard to invest your capacities to finally get a good result. It's the same with mathematics.

So why do people see mathematics as special? It is not because it is exceptionally hard. It is because of two reason.

1. We can determine the correctness of a piece of mathematical work.

2. Society forces everybody to learn mathematics to a much higher degree than art.

So what can we do about these points? In regard to the first, I'd say that it's an advantage of mathematics and other areas should take it as an ideal.

The second reason is a consequence of the unreasonable effectiveness of mathematics to predict nature. There is nothing I can say about this besides observing it.

IQ measures how well you do on IQ tests.

Math is many things. Math is arithmetic. Math is geometry. Math is algebra. Math is topology. Math research is proofs. Math calculation is quite different.

Physics uses math, but physics has is own set of concepts. Solid state physics uses different concepts than particle physics, and both are different than astrophysics or biophysics. A lot of learning physics is to understand those models, and only part of that is to understand the math used to make the models.

That you could calculate math doesn't mean that you could do proofs, or think like a physicist. I say the last with experience - I found as a physics graduate student that my math undergrad meant I could follow the math, but I had problems with the intent.

"what are my true abilities with math?" - My belief is that if you believe there are 'true abilities' then the first time you stumble you will start to believe that you don't have those abilities, and that will keep you from going further, when the more likely answer is that you need to practice more, and learn more, and ask for help in understanding.

Mind you, there's plenty of other things in the world besides learning math. You may decide to take up watercolors. Or waltz. Or study history.

Different math is also hard in different ways.

I knew physics students who found calculus infinitely easier than doing trigonometry proofs. But there's others for whom the very idea of calculus is horrifying, and statistics and calculus were literally different tracks entirely when I was in school because it was pretty common for people to utterly fail to get one even if they could ace the other.

math IS hard. i didn't learn this until recently. i never met a practicing mathematician before a few years ago, and when i did they told me that they struggle to get stuff. that was a HUGE relief. if you enjoy it, then maybe you can apply yourself to it for the hours it may take to understand something - a book, a topic, a paper, etc.

i think a lot of what it comes down to for me - and maybe you - is mental discipline (staying focused for more than an hour without straying), knowing that it is very common for it to be tough, and learning how to play with math and explore it. i was never taught those things (or at least i never learned them), and so i have had to learn them the hard way. maybe you suffer from some of the same hurdles? try and overcome them, it's worth it.

as for writing proofs, one of those mathematicians got me interested in this book:

http://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0...

You have latent mathematical abilities that only hard, long, difficult labor will unlock. You will revisit topics that used to be impossibly hard, and without your noticing the change, they will be trivial; you'll know them effortlessly, fluently. Meanwhile, the next ridge will beckon.

It is not. Nothing is hard if you are interested i.e. have fun out of it. It is about personal preferences, what you enjoy and what you don't. That's it.

What makes you say this? Is it based on personal experience, definitions, or some consensus? I have definitely known people who found things interesting but still thought they were hard. I have friends who find math fun and engaging, but also find it hard and (seemingly rightfully so) don't think they're very good at it.

Yes, personal experience and watching other people around me as well. Mostly, hard is boring, i.e. when you don't have enough interest to pursue it. As for math - it is not just about being good, but also the process itself - of becoming good, i.e. learning. When this process seems interesting and fun, I doubt someone will say it is hard.

E.g. for many people, literature classes or some other humanities stuff is hard.

>when this process seems interesting and fun, I doubt someone will say it is hard

That doesn't mesh with my personal experience. I know some very, very smart people, who have found the process itself interesting and fun, but who still find it hard and also don't think they're that good at it. Perhaps your personal experience is difference, but I've seen that interesting and fun does not preclude subjective feelings of hardness.

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