Right now I am 18 and I should not have to worry, but how would I come up with an "original idea" as put by Mr. Nash in A Beautiful Mind? The field is mathjematics. I am curious because if I can somehow get an idea now, I have years to work on it. I have looked online for creativity techniques but none of them really seem to work. Maybe I missed some? James Sibley

Well you've answered your own question! You're a expert in the field of 'mathjematics'. Good luck!Please Register or Log in to view the hidden image! But seriously. Probably one of the best pieces of advice would be observation. Look at the unsolved problems out there how and start there. Can you make a contribution that is key to solving the given problems? I don't think an idea has to be 'original' to be the best idea.

I would suggest that you stop trying. No kidding, trying focuses all your mental energy into efficient paths of thought -- that you're already familiar with. You need to let your mind wander off in unexplored directions. Creativity happens, you don't "do" it. Yes I'm exaggerating. Many writers, in particular, make writing a regular day job and they just sit there 8-5 M-F and create words. But if you were that kind of person you'd probably know it by now. And just because "your field" is mathematics (not proofreading as Blackie so kindly pointed out), Please Register or Log in to view the hidden image! that doesn't mean that your brilliant ideas will occur in that discipline. It's quite possible that the parts of your mind that are not so well developed and organized and compartmentalized will give rise to some creative thoughts for the very reason that chaos and free association may act as a catalyst. Lots of people are really good at one thing and make a nice living at it, but when they go home at night they play the clarinet or do embroidery or invent tools. For many people, the reward of creativity is the satisfaction of having done whatever you did, not necessarily the recognition by others or (you know what I'm going to say next don't you) money. As for "creativity techniques," I would concentrate on more general mind-stretching exercises. You're at a perfect age to take up TM (transcendental meditation) or whatever kind of mediation appeals to you. Most of us math nerds could stand to completely clear our minds for a little while every day or two. Your brain is like a muscle, it needs to relax. I have a friend who took up TM as an adult, then suddenly when he was in his 50s he was struck with inspiration, sat down, and wrote a really good novel. If meditation just doesn't appeal to you, spend time listening to instrumental music, hanging with your pets, or doing something that takes your attention away from your mind so that it can go off on its own adventures unencumbered by your detailed directions. This is one of those things where you have to put up with some really paradoxical advice: Don't try so hard! Good luck. Oh, and don't forget that Prof. Nash was certifiably nuts. That's a heavy price to pay for creativity, and it's not guaranteed to work!

Read a few really interseting and innovative books on the subject non-stop for about a week. Then hit a LOT of real quality :m: and think on it. (I know it sounds like a joke, but I am serious)

I forgot to add... Do it with a tape recorder and pad and pen. Try to record as much of what you think as possible.

I think the number of really significant new ideas produced whilst on drugs would be fairly minimal, with a few notable exceptions (e.g. the writings of Samuel Taylor Coleridge spring to mind).

Yes but if you learn too much, you can become ingrained in the methods of the field you have chosen making it different to formulate a different approach. Origin ideas come from a way to explain a phenomena which makes sense to you. Sometimes it is original sometimes it is not. Relativity was a great original idea, as it was a new way of looking at the world, Quantum filed theory although truely remarkable, was semi-inevitable as it combined to great theories, relativity and quantum mechanics into one, but essentially no new ground breaking ideas (although Feynmanns formulation was on par with Einstein's formulation of GR.)

Sorry about the typo: "mathjematics." Hehe. I proofread the post before I sent it but I guess I missed that one. I was thinking I had to learn everything I had to about the subject but as it was pointed out, I would get myself stuck in established methods. One thing I find interesting is that every once in a while I get ideas but later find out they have already been explored, if not still being explored. For expample, I discovered Euler's Constant, approximently 0.577. One thing I did do differently was derive a formula to approximate the summation of 1/x from x=1 to n. For anyone curious, the formula is ln[sqrt(n^2 + n)] + C where is Euler's Constant. It is accurate to one decimal place for n > 6 and n is an integer (duh). I made a program once to simulate the computer playing itself in the card game War. I found that some games, if played by a certain scrambling rule, were not completable (never could finish the game). However, if played by different scrambling rules, the player with the higher average of cards (average of the value of hand) had an average of a 57% chance of winning. I did other things, but I cannot think of them. Anyway, I do get ideas sometimes just by reading about things and then having questions. Maybe that is how I do it, learn something then ask questions? Maybe good quality :m: will do it ;-) However, I am very interested in getting the idea like Prof. Nash. His idea just seem to come out of nowhere. I am looking for that type of idea. I do not think many people have those ideas but I am sure if I looked hard enough I might. Or, I can just stop like it was pointed out ealier. Since creativity happens. Please Register or Log in to view the hidden image! James Sibley

One important point- it is easiest to come up with "original ideas" when you know absolutely nothing about a field. Of course, they are bound to be wrong ideas! (internet forums are excellent examples of both statements!) If you want to come up with GOOD original ideas, learn as much as you can about the field. You note that Nash had a Ph.D. When Wiles proved Fermat's Last Theorem, he had not only been working in the specific field of number theory (and even more specifically elliptic functions) for many years, he worked on FLT to the exclusion of everything else for six years. Edison's dictum is still true: "Genius is 1% inspiration, 99% perspiration". I don't know of any way to guarentee inspiration so I recommend you concentrate on the perspiration!

MY advice is to study Maths up to a PhD level than you will have to come up with an orginal idea for your thesis.

It doesn't matter that you're coming up with ideas that someone else already thought of. You can't have digested all the research and literature in your discipline yet at your age. The fact that they turned out to be really great ideas the first time around says a lot for your own intellect. Just keep learning and your next generation of ideas will build upon those that came before, instead of reproducing them. Be patient and do some relaxation techniques.

<i>One thing I did do differently was derive a formula to approximate the summation of 1/x from x=1 to n. For anyone curious, the formula is ln[sqrt(n^2 + n)] + C where is Euler's Constant.</i> I'm interested. Can you post the derivation, please?

When I was in high school I first learned about infinity, and didn't like some of what I read. I tried to figure out how to fix it then. Predictably, I failed. Now, 25 years and several degrees later I've actually made my way back to the issues that worried me then. I think I'm well on my way to solving them this time, but it took a lot of learning in between. Mind you, none of this is on the scale of Nash. But if you keep your mind open, and spend a lot of time studying, you actually can still contrubute new ideas to the world.

Hello, James. I will let you know how I derived it when I get all my work together. I must warn you it is not super math or anything but it works suprising well Please Register or Log in to view the hidden image! It converges faster than ln(x) + C to estimate the summation formula. James Sibley

The thing with original ideas is that they usually come from an alternate way of looking at a problem, arising due to the feeling of incompletedness or incorrectness of a current theory. I'll tell you about an experience I had lately. I was working my way through some statistical mechanics, you know boltzmann's theory, entropy and the like, and I had been mulling over it for a couple of weeks. I as trying to understand how a system would drive itself towards equilibrium, where say a random distribution of velocities would take on a Maxwell Boltzmann distribution. Then I had this idea, this way to represent this new quantity in a way that had not been done before. So I worked out a theory for this thing, came up with an entire algebra that it satisfied, a way it evolved in time etc, I would dream about it, see if it failed in any way and try to fix up any inconsistancies. I wrote up a draft and presentted it to a few people in the physics department where I am at. Turns out that it is wrong, I gave a quantity a property it simply does not had, and it all fell in a heap. The thing is though that the time I spent formualting this theory was exciting for me, and even though it was incorrect, I found that I learnt a hell of a lot more than I would have by sitting in any lecture theatre. Also, I was not looking for an original idea, it just came. I don't think you can try to have an original idea. It's like when you sit around with your amtes when your bored trying to think of things to do, you can never think of anything, but if you just chill out, shit happens.