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# Nature of mathematical thought. watch

1. Anyway, I was going to write about maths in movies and how they normally show mathematician as crazy. Anyway, I was watching this clip http://www.youtube.com/watch?v=l0ywiYboCLk

I was wondering, can you write what your thinking when doing maths? as in whats your nature of thought when doing maths. This is sort of inspired by Borovik book http://micromath.wordpress.com/about/ the second one.

Anyway, sadly its not like Beautiful mind or Numb3rs.

My anwser;

I haven't got any visual pictures. I normally just read the question or vaguely stare into space. Suddenly, the problem or part of the problem sort of lights up and then a ha I got it. Alot, of my thought is algebraic as I mostly just do calculations and since I have done tons of them its pretty obvious if something is correct(when, its not correct then its painful) and if I finally can't do it as my last ditch attempt I will go backwards as most question depend on the previous question(AQA FP4 had a question where you had to go backwards to visualize you can use a matrix to find invariant points, luckly I got the anwsers by noticing that).

Sadly, I don't really think its mostly like you practice and it becomes obvious and so you can do it again. Most of the time I just come back to the problem a couple of days later and I can suddenly understand it.

Anyway, what do you think about when doing maths?

P.S. In movies or Numb3rs it makes maths seem cool and visual, however apart from sketching graphs most of my thought is algebraic.
P.P.P.S. On another topic, I hope I can get a girlfriend at uni as I don't really want to be ordering thai brides when I'm 30. Although, having asians kids and hot thai bride is not a bad option.:<
P.P.P.P.S. I wonder if a group of people have used Nash theory to get laid.
2. I say Descartes without that God bs!
3. I tend to go the other way and be quite visual - so I like problems where I have some way of picturing what I'm doing, and ideally have an opportunity to draw a diagram.

Usually when I'm thinking about a problem, I'll re-write everything I want to show in a way that I'm happy with, so that I get to introduce sensible notation and make sure I'm certain I understand everything and haven't missed any details.

Then I usually start thinking and writing down what's going on in my head, using the paper as an extended memory (else I quickly forget how I reached the point I'm at. Seeing my working makes me remember this). Usually I start with a good sense of direction and work in that direction, feeling my way as I go. When this runs into problems, I would either re-think my approach completely or tweak my starting point to fix the difficulties, depending on how serious the problem I've hit is.

In terms of what happens in my mind, I see nice pictures or have a general idea, and then write it down. Solving a problem could either be one big one of these (i.e. I see how to do it immediately), or I know a good way of getting going, and as I write that down, I see more of how to progress it.

Have I understood the question you asked correctly, or have I just answered something totally different?
4. (Original post by ImperceptibleNinja)
Have I understood the question you asked correctly, or have I just answered something totally different?
Yes, that was a really good anwser.

Its weird because I would never write down what I'm doing or even think about the big picture.

Even on M1 I would think thats a square or thats rectangle so whats the formula for it. Although, M1 was kind of sketch then the problem is solved.

But, yeah I sort of use intuition and that normally works. But, to have a plan or a image that just seems like going overboard.

(Original post by gammapulsar)
I say Descartes without that God bs!
Descartes seems like a pretty cool guy espically since he was a mercenary. Although, I do takes his advice to not wake up early in the mourning. But, that could be laziness.
5. I think it depends on the Maths I'm doing. When I'm doing Pure Maths, or the purer bits of Prob and Stats, I'll always be thinking 'Which theorem should I be using? Which definitions are relevant here?'. When I'm doing something that could in any way be visual, I'll probably think of it visually, as it really helps my understanding if I can understand both the Maths and a visual representation. And for stuff like integration, differentiation and algebraic manipulation, it's very visual (e.g. I see the exponent changing or dropping down, or I see algebra getting moved about the page) - I think because they become second nature by the time you've done a year or two of your degree, you start to go on 'auto-drive' for those sorts of things. For instance, I'd probably actually struggle for a few seconds to explain what, say, the chain rule is precisely, mostly because I just use it without even acknowledging it as the Chain rule! Ho hum...
6. A lot of what I do is purely mechanical nowadays. If I have a messy trigonometric expression, I'll automatically shove it into a nicer form that'll make the question more bearable. My basic thought pattern goes: a) what do I know? b) what do I want to know? c) what routes can I take to connect the two? d) what's already been proven? And after that, it's just trial and error.

I'm a big fan of solving individual questions in many ways to find the easiest way of doing it, or the way of doing it that makes the solution the most obvious. I like geometric interpretations; they don't always work, in fact they're often best avoided, but they can sometimes give you a picture of what's going on.
7. I should think of having a back up plan if everything goes wrong. But, read the question slower is probably okay.

I sort of think like Slyar when he gave Peter the watch and he was looking at it and then the watch started to move around intill it
wasen't broken.

(Original post by generalebriety)
A lot of what I do is purely mechanical nowadays. If I have a messy trigonometric expression, I'll automatically shove it into a nicer form that'll make the question more bearable. My basic thought pattern goes: a) what do I know? b) what do I want to know? c) what routes can I take to connect the two? d) what's already been proven? And after that, it's just trial and error.
Do you actually say that?

Hey wait a minute, have you said that before?

Purely mechanical? I was under the impression that as uni progresses you actually have to think more and be less mechanical.
8. (Original post by Simplicity)
Purely mechanical? I was under the impression that as uni progresses you actually have to think more and be less mechanical.
Sure, but it means there's a lot more stuff you just 'know' how to do automatically without thinking. When solving problems, you often find that spotting 'tricks', or finding "the right way" to solve a problem, while taking up 90% of your time, is actually only 10% of the calculation you need to do, and 90% of your calculations are fairly routine stuff.
9. I see everything in my head.

It seems I can never explain my thought processes to anybody. Well for simple exams at A level I dont need to do this, I just do the working. But for more complex problems I run into, if I ever get a solution its almost impossible to explain it to anybody because its all in my head. Even if its written on paper, it wont make any sense.

When I do maths I get a picture in my head and most of the time I can solve it from there. I see equations exactly as I see pictures and paintings, I remember them very well.

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