Is problem solving a inborn skill or a skill which takes lots of hard work and lots of paper ?
I asked this because I find myself in situations which trouble me deeply. I solve a deep interesting problem, I learn a new concept, its good but a single question which I'm not able to do, leaves me depressed, sometimes I can't just understand whether I CAN or CANNOT apply a concept to solve a problem , even though I may have practiced on it. Seeing solutions to some problems I'm like "Hey I knew this concept, but why didn't I apply it, don't I have that much common sense to apply a concept which I have learned :-( ". So I just wanted to know, won't I ever get any more good, and seeing all the smaller kids doing these problems makes me kind of even more sad about myself, so I wanted to ask you guys, is it a inborn skill ? I just feel like it is so. Please help
Note by
Lord Aejeth
7 years, 8 months ago
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
*italics*or_italics_**bold**or__bold__paragraph 1
paragraph 2
[example link](https://brilliant.org)> This is a quote# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"\(...\)or\[...\]to ensure proper formatting.2 \times 32^{34}a_{i-1}\frac{2}{3}\sqrt{2}\sum_{i=1}^3\sin \theta\boxed{123}Comments
I think
Intelligence=[(Inborn Skill)*(Hardwork)]
As far as inborn mathematical skill, I believe humans have specialized brain regions to handle simple counting tasks, but that's it. Some people suffer from a disorder known as dyscalculia, which prevents them from doing things like, say, looking at a table full of 10 apples and 5 oranges and immediately knowing there are more apples. That's something most of us take for granted, but it actually takes a specialized brain region to do it!
In fact, it's been demonstrated in experiments that most humans are absolutely terrible at solving abstract logic problems, but when the exact same problems are couched as social problems, folks are suddenly much better at solving them. Humans are better general problem solvers than other animals, but we're still pretty specialized in what we're naturally good at.
The point of all that is, I don't believe mathematics to generally be a natural pursuit for humans. That is, our brains aren't specialized for it. In fact, solving math problems to me often feels like trying to squish my oblong brain into a cube.
So, how do we explain freaks of nature like Gauss, Euler, and Ramanujan? I don't know. Here's one idea:
Humans are generally terrible at remembering long lists of uninteresting or pointless data (like, say, the order of a shuffled deck of playing cards). However, humans tend to be really good at remembering sequences of novel or zany spatial data. There's a whole subculture devoted to plying the latter skill towards accomplishing the former task, which you can read about in the entertaining book Moonwalking with Einstein.
It's possible that the giants of mathematics independently and unbeknownst even to themselves discovered similar tricks for plying areas of human specialization in non-mathematical tasks towards solving math problems.
What might those tricks be? I wish I knew! Unfortunately, by the time the tricks are acquired, they're already subconscious and the person using them can't tell you what they are, either! So, minus some self-observant person who notices when they're making such a skill crossover and documents it, we're more or less waiting for brain imaging technology to get way more sophisticated so we can basically mindread the folks who are doing it to figure it out.
(Also, the giants of mathematics tended to be obsessed with mathematics from a young age, so put in tons of practice.)
Log in to reply
I think sir it's ultimately practice that matters leaving some exceptional cases. Prodigies like Ramanujan, Gauss are rare and what's more history has shown that only few of them survived in the Big race. While people with mediocre mind have defeated them, a good example here to give is of Einstein. It's how hard you push yourself each & everyday that matters. And sometimes we confuse ourselves in thinking a normal person to be a genius or something while the truth is that when in childhood you were watching Mr Bean, that person was busy struggling in the messy formulas. So now what you think to be Genius is actually an offspring of the tons of hours of hardwork.
Well, it's both. You may be a born genius, but without practice, you'll never get anywhere. As to applying yourself in new ways, well, that's harder to classify. You need to think unusual thoughts. Go wild. If you go by, "this is the conventional method, so I'll follow it", well, you won't break free of your on self imposed restrictions. Think of a crazy thing, then apply the maths to it. Right now, I'm writing a fantasy novel, but I decided to make a functioning physics system, and it's really cool to see the implications of adjusting gravity, mass of planets etc. Try it.
I myself sometimes feel the same. Watching the kids of age group 12-15, the age when I used to solve basic linear equations, doing level 5 problems make me feel I missed my chance. Time gone is gone forever but you can still learn. There is no age limit to it. :)
Log in to reply
Same here!
No, Not at all. But it depends on the way you think. How smart you are. Also, one can improve these skills by learning new problems, asking questions to teachers or make a discussion in brilliant and many more. Don't worry. A small 4 year old kid can't solve an algebra problem but when he studies in high school, he might be the brightest student, assuming only. Also you, if interested deeply, without you being aware, will get the solution. That's what happened to me when I tried to find what is logarithm. I just bought a calculator and played with it. That's all.
I dont know, I myself am too bad in maths I guess, even though I do very well at school level maths, I really suck when it gets to the math problem in which you really cannot use a built in template to solve it.
Problem solving is mainly hard-work and dedication. Looking back in 5th grade, my mathematical abilities were terrible. I wasn't exposed to any difficult problems; I only went along with the public school system in the US: solving simple equations such as x+3=7, arithmetic, and basic probability.
In 6th grade, I was exposed to competition math; I took an AMC 8 test and I got a 10/25!
That really motivated me to do better, so I,even to this day, strive to do my best. I put in hours upon hours of work to achieve the best I can. And it really pays off. I mean 25 on AMC 8's, 110+ on AMC 10's, etc. (and my Brilliant levels :)) is quite an accomplishment in a brief two years time.
So the moral of the story: Problem solving can definitely be learned.
both.
I think it's ultimately practice that matters leaving some exceptional cases. Prodigies like Ramanujan, Gauss are rare and what's more history has shown that only few of them survived in the Big race. While people with mediocre mind have defeated them, a good example here to give is of Einstein. It's how hard you push yourself each & everyday that matters. And sometimes we confuse ourselves in thinking a normal person to be a genius or something while the truth is that when in childhood you were watching Mr Bean, that person was busy struggling in the messy formulas. So now what you think to be Genius is actually an offspring of the tons of hours of hardwork. So don't be delusional & keep going, giving your absolute best everyday.
I think you have to be a bit crazy.
I had(have) the same problem. Problem solving skill is all about how you could get your thoughts coherently at the right time, in born skill constitutes a very tiny part. Think of it like this........... If RAMANUJAN had not got the trigonometry book, how could he even get started! the more experience you gain in matching the problem with the relevancy of your thought stream, the better you become, only possible by loads of DIVERSE practice. All the 12-15 age guys you see have had such diverse experience and help from their teachers( important! ) ............ CHILL :-p :-)