## Lacking creativity...

I love Maths very much. However, most of the time I can't find new questions to answer nor know what to do with an unfamiliar problem. I really think this is going to be my disadvantage in my maths career. Does any have this problem and any advice?

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 Think, think and think.
 Well, there are millions of Math textbooks and I am certain that you haven't worked through EVERY one of them...

## Lacking creativity...

solving problem is not a problem. The problem is that I can't create problem for myself.

 Well, this maybe a long shot, but you can always look at Hilbert's problems or Clay institute millenium problems... Maybe you won't solve any of those (maybe you will ;) ) but they may present you with a direction to take in your thoughts or open the door to an interesting field... Kolmogorov was also famous for posing questions and I remember seeing one book collecting them, but I can't remember the title. Best luck, and report here if you find a good answer to your question :)

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 Quote by leon1127 I love Maths very much. However, most of the time I can't find new questions to answer nor know what to do with an unfamiliar problem. I really think this is going to be my disadvantage in my maths career. Does any have this problem and any advice?
If you're no professional mathematician yet, that shouldn't bother you, since you've got a lot more to learn. Otherwise, the answers are already given - work hard and you shall be rewarded.

 leon1127, where are you at in your studies? What was the last math class you have taken? This question could mean a lot of different things depending on where you are at. If you still in the basics, calc 1 - 4, diff eq, lin alg, I might be able to help, assuming I understand your question correctly. If you are into your higher level math classes, mathwonks advice would be more beneficial then anything I could hope to send you.

 Quote by kdinser leon1127, where are you at in your studies? What was the last math class you have taken? This question could mean a lot of different things depending on where you are at. If you still in the basics, calc 1 - 4, diff eq, lin alg, I might be able to help, assuming I understand your question correctly. If you are into your higher level math classes, mathwonks advice would be more beneficial then anything I could hope to send you.
I am senior. I have done topology, analysis and so. I am about to start some studies in Clifford Algebra later. I have tried to put some effort on numerical solution of Euler differential equation, but I couldn't find the question that has not been answered and suitable for my knowledge at the same time. I have also put a lot of effort on calculus of variations, and manifold theory. This is the stage I am at in my education.

I am still trying to digest the answer that Mathwonk has given me.

Recognitions:
 Quote by mathwonk it took me my whole life to notice it, but there is a standard theory of finitely generated classification of modules over pid's, but not more general rings, as far as i knew. on the other hand, i knew that a dedekind domain is basically q ring that is locally a pid. thus there should be some weakker classification theorem for finitekly generated modules over a dedekind domain. guess what? there is, and it appears at the end of books like dummitt and foote. b
Just in case anyone wants a more complete citation: see section 19.5 of Eisenbud, Commutative Algebra with a View Towards Algebraic Geometry for an series of exercises on the classification of modules over a Dedekind domain. But I guess Eisenbud also sinned, since he failed to stress that this generalizes the classification over PIDs...

 Recognitions: Homework Help Science Advisor this "sin" of eisenbud's book, is in not showing where the idea for the result came from. presumably that was not his goal. but this is the reason i emphasize trying to solve problems yourself, or prove theorems yourself, as opposed tor eading them only in books. many people here still believe that learning should come first, and of course there is much to elarn. my point however is that one of the thigns you want to learn, namely how to find problems and their solutions, cannot be elarned by merely reading and retaining more and more proofs in books. i have tried to demonstrate here over several years, that one can generate proofs of many statements merely by getting that statement clear in the first place, then analyzing it for its resemblance to other basic ideas and tools. let me congratulate you on this question, as I do not immediately recall another question concerning the all important topic of creativity in the years i have been posting here. the only secret i myself have for doing research is "analogy". I learn as much good math as possible, really learn it down deep in my pores, and then when I listen to another problem I try to compare it to something else I know in some way, to see if there is a leson from the old case to apply to the new one. hopefully that provides the "inspiration". the other 99% is all hard work. it helps to appreciate your own inspirations too. once iwas loistening to a talk, and the speaker ahd a mysterious result he could not imnterpret geometrically. When I heard hima sk the puzzle the night before, I had no idea either, but after listening to him speak for an hour, and all the juices were flowing, I saw a way to comopare it to anoither situation which ompletely explained the mystery. everyone just sat with their mouths open,a nd afterwards he askede me what eh shiould do with the result. i said well it was inspired by hi talk, and it was his problem so take it. he published it afterward with no specific credit to me, and the reviewer for the paper singled out that one resukt as the mosts triking and origina in the paper. years later other smart peopel also rediscovered and opublished this result. so perhaps i would have benefited professionally from requesting credit. but at least i have the pleasure of remembering my insight. the practical side is that over the years it ahs not ahppoened all that often.
 Recognitions: Homework Help Science Advisor here is a copy of hadamard's delightful and unique book: The Psychology of Invention in the Mathematical Field Jacques Hadamard [30 Day Returns Policy] Bookseller: thriftbooks.com (Seattle, WA, U.S.A.) Book Price: US$1.78 notice again the principle that really good books are often very cheap.  Recognitions: Homework Help Science Advisor here is a copy of polyas book: How to Solve it G. Polya Bookseller: Usedbooks123 (Sumas, WA, U.S.A.) Price: US$ 3.48 [Convert Currency] Quantity: 1 Shipping within U.S.A.: US\$ 3.88