Questions tagged [open-problems]

If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"

MathOverflow is not the right place to ask an open problem--i.e., a question that a number of serious mathematicians have already considered and have been unable to answer. You should post questions you think have some reasonable chance of being answered here. If you're thinking about a well-known open problem, provide some background and ask about something specific related to the problem, like "Such and such is a well-known open problem. So-and-so proposed this and that approach in the 80s. Does anybody know if this aspect of their proposal can be made to work under these circumstances?" If you want to contribute to (or view) a list of open problems, visit the Open Problem Garden.

If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added, and the question is converted to community wiki. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?" That way, the MO thread for the problem becomes a repository of resources related to the problem. Perhaps the answers could be organized by approach, with an outline of the basic approach, followed by a horizontal rule and a summary of what is promising about the approach and why it doesn't give a complete solution.

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Open problems with monetary rewards

Since the old days, many mathematicians have been attaching monetary rewards to problems they admit are difficult. Their reasons could be to draw other mathematicians' attention, to express their belief in the magnitude of the difficulty of the…
Unknown
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Is there an associative metric on the non-negative reals?

Recall that a function $f\colon X\times X \to \mathbb{R}_{\ge 0}$ is a metric if it satisfies: definiteness: $f(x,y) = 0$ iff $x=y$, symmetry: $f(x,y)=f(y,x)$, and the triangle inequality: $f(x,y) \le f(x,z) + f(z,y)$. A function $f\colon X\times…
aorq
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Open Problems for Undergraduates

Suppose: I am a 'problem-solver' rather than a 'theory-builder' I am an undergraduate student I have a passion for solving mathematical problems The homework I get is not satisfying (in the sense that the problems are computing-problems rather than…
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Are there any open sourced or crowd source math research projects?

I’m looking for open source math research projects as I know computer science students can easily have access to material they can contribute to but this is not the case with math as far as I’m aware. But I am looking for a possible answer with open…
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Profound but not popular mathematical topics and notions

The algebraic Theory of Invariants used to be a hot topic until David Hilbert proved his two theorems about invariants. Then for tens of years, the popularity of the topic went down a long time before it picked up again. Question What are today's…
Wlod AA
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Important (interesting) unsolved problems

I think it would be interesting to have a list of important unsolved problems in mathematics. What are the important (interesting) problems in your field of work? It would be especially nice, to have a list of "non-mainstream-problems" in the…
Spinorbundle
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