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#1 2006-10-25 01:14:30

Ultima Black Gate
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Registered: 2006-09-18
Posts: 14

Mathematical Intuition/Feeling ?

I was wondering if something like a math intuition exists, I mean something like having a feel that you are getting to the solution of a hard problem or when trying to solve a hard problem and you somehow "feel" when you are on the right track (or in a wrong one) and finally solve it.
It happens to me when writing in paper some math puzzles that I have in my mind.

I noticed that after practising mental maths skills and memorizing new formulas for known concepts (different ways of showing equivalences) this intuition seems to get more clear.

It kinda knowing in advance wether knowing an approach to the problem will work or not by checking different insights.

Have you ever experienced this?

Last edited by Ultima Black Gate (2006-10-25 01:15:34)

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#2 2006-10-25 02:32:16

Devantè
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Registered: 2006-07-14
Posts: 6,400

Re: Mathematical Intuition/Feeling ?

Yep, all the time. I get it when solving almost anything. And you feel really good inside.

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#3 2006-10-25 03:06:51

George,Y
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Registered: 2006-03-12
Posts: 1,306

Re: Mathematical Intuition/Feeling ?

Well, I think that may largely lies in transition of knowledge, that when you have a concept, it is similar to a concept you've learned. My instance: determining how many digits of a product in Help section, I unconciously borrow the sandwich theorem in calculus.

In common reasoning, one will think step by step, having little chance to get a leap of reasoning all of a sudden. And if so, I guess it will be sheer guess.

What about your experiences? May you analyze them, and see if my hypothesis stands.


X'(y-Xβ)=0

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#4 2006-10-25 09:43:57

MathsIsFun
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Registered: 2005-01-21
Posts: 7,529

Re: Mathematical Intuition/Feeling ?

Interesting points. Yes, I get a "feeling" that something is going in the right direction. But the feeling CAN be wrong. It is like I have a rough model of the problem in my mind, but actually working on the problem can change it.

And I think intuition plays a bigger role in mathematical discovery than people admit. I remember some mathematician said (something like): "the idea hit me when I was in the bus. It then took me months to make it look like I got there in logical steps."


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#5 2006-10-26 06:49:32

Patrick
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Registered: 2006-02-24
Posts: 1,005

Re: Mathematical Intuition/Feeling ?

MathsIsFunAnd wrote:

I think intuition plays a bigger role in mathematical discovery than people admit. I remember some mathematician said (something like): "the idea hit me when I was in the bus. It then took me months to make it look like I got there in logical steps."

Pioncaré maybe?

Before the age of 30 he developed the concept of automorphic functions which are functions of one complex variable invariant under a group of transformations characterised algebraically by ratios of linear terms ... The crucial idea came to him as he was about to get onto a bus, as he relates in Science and Method (1908)


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#6 2006-10-26 09:58:28

MathsIsFun
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Registered: 2005-01-21
Posts: 7,529

Re: Mathematical Intuition/Feeling ?

Ahhh ... perhaps!

Thank you.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#7 2006-12-19 13:20:26

Ultima Black Gate
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Registered: 2006-09-18
Posts: 14

Re: Mathematical Intuition/Feeling ?

MathsIsFun wrote:

Interesting points. Yes, I get a "feeling" that something is going in the right direction. But the feeling CAN be wrong. It is like I have a rough model of the problem in my mind, but actually working on the problem can change it.

And I think intuition plays a bigger role in mathematical discovery than people admit. I remember some mathematician said (something like): "the idea hit me when I was in the bus. It then took me months to make it look like I got there in logical steps."

Yes, same for me, sometimes the feeling is actually wrong, but it gives me a sense of control over the problem and motivation to solve it.

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#8 2006-12-27 13:52:10

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Mathematical Intuition/Feeling ?

In my opinion the intuition and the knowledge are the most important.
If you don't have intuition, it will be hard to develop alone.
If you don't have knowledges, you'll waste your time end intuition on subjects, already discovered, instead of learning them.

Last edited by krassi_holmz (2006-12-27 13:52:25)


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#9 2007-01-10 23:59:46

Anthony.R.Brown
Banned
Registered: 2006-11-16
Posts: 516

Re: Mathematical Intuition/Feeling ?

To Ultima Black Gate

Quote:
"I was wondering if something like a math intuition exists"

Yes!! for sure! Math and other things are solved in certain peoples minds,before they can actually explain How they have solved the problem!
Having forums like this! help a person to explain what they are trying to say,by the way other people question and answer.
There have been many examples where someone has said something! and everyone has disagreed with what that person is saying,then when its made clearer! everyone then says WOW!

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