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        Questions tagged [big-list]

        Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.

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        1answer
        201 views

        Topological Invariants for Group

        Let $\mathbf{Grp}$ be the category of groups and $\mathbf{Top}$ be the category of topological spaces. To each group $(G, \circ_G)$, we can associate a topological space $(G,\tau_G)$ the basis for ...
        15
        votes
        2answers
        588 views

        Examples of problems where considering “discrete analogues” has provided insight or led to a solution of the original problem

        The Kakeya conjecture posits that any Kakeya set in $\mathbb{R}^n$ has dimension $n$. A discrete (finitized?) version of this problem is the Finite Field Kakeya conjecture, which was proved by Dvir ...
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        votes
        2answers
        249 views

        Big list of comonads

        The concept of a monad is very well established, and there are very many examples of monads pertaining almost all areas of mathematics. The dual concept, a comonad, is less popular. What are ...
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        votes
        0answers
        113 views

        Has the external knit product been used to construct a previously unknown group?

        In the Wikipedia article Zappa–Szép product , the knit product (a.k.a. Zappa–Szép product, Zappa–Rédei-Szép product, general product, exact factorization) is defined, and its basic properties are laid ...
        14
        votes
        8answers
        1k views

        Applications of the idea of deformation in algebraic geometry and other areas?

        The idea of proving something by deforming the general case to some special cases is very powerful. For example, one can prove certain equalities by regarding both sides as functions/sheaves, and show ...
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        votes
        1answer
        285 views

        Open problems concerning all the finite groups

        What are the open problems concerning all the finite groups? The references will be appreciated. Here are two examples: Aschbacher-Guralnick conjecture (AG1984 p.447): the number of conjugacy ...
        101
        votes
        13answers
        28k views

        What are some noteworthy “mic-drop” moments in math?

        Oftentimes in math the manner in which a solution to a problem is announced becomes a significant chapter/part of the lore associated with the problem, almost being remembered more than the manner in ...
        2
        votes
        1answer
        143 views

        Practical applications of Sobolev spaces

        What are the examples of practical applications of Sobolev spaces? The framework of Sobolev spaces is very useful in the theoretical analysis of PDEs and variational problems: the questions of ...
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        votes
        2answers
        332 views

        When was the generalization easier to prove than the specific case? [duplicate]

        I distinctly remember from my long-ago undergraduate math that there were some interesting cases where a solution (proof) was sought for some specific thing but it wasn't easy to find - and in a few ...
        103
        votes
        18answers
        13k views

        Good “casual” advanced math books

        I'm curious if there are any good math books out there that take a "casual approach" to higher level topics. I'm very interested in advanced math, but have lost the time as of late to study textbooks ...
        84
        votes
        24answers
        13k views

        Noteworthy, but not so famous conjectures resolved recent years

        Conjectures play important role in development of mathematics. Mathoverflow gives an interaction platform for mathematicians from various fields, while in general it is not always easy to get in ...
        49
        votes
        9answers
        4k views

        Your professional $\LaTeX$ experiences that saves your time in typesetting

        In $\LaTeX$ typesetting, when we repeat a long and complex formula in long documents, it is appropriate to create a new command that just by calling this new command we get the desired output. For ...
        120
        votes
        45answers
        14k views

        Old books you would like to have reprinted with high-quality typesetting

        There are some questions on mathoverflow such as What out-of-print books would you like to see re-printed? Old books still used with answers that tell us things such as: Mathematicians prefer to ...
        3
        votes
        1answer
        360 views

        Improvements to one's own theorems

        What are some notable (famous?) instances where the following has occurred. A particular author proves: Every P which satisfies Q has property Z. A few years later (roughly speaking) the same ...
        7
        votes
        0answers
        215 views

        List of modern points of view simplifying or clarifying classical topics

        There are many modern mathematical achievements which greatly clarify or (and) simplify classical important topics. I believe a list of such achievements, among other benefits, would be a big help for ...

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        山西福彩快乐十分钟
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