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        Questions tagged [soft-question]

        Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. In other words, questions that can be answered without making computations or applying theorems and axioms.

        3
        votes
        1answer
        136 views

        Reference request: Gauge theory

        What are some good introductory texts to gauge theory? I have some basic differential geometry knowledge, but I don’t know any algebraic geometry. Also, as a side question, what intuitively is a ...
        20
        votes
        1answer
        370 views

        Videos of Gian-Carlo Rota Lectures

        I apologize if this is off topic. I think most of his listeners would agree with me that Gian-Carlo Rota had a wonderful style of lecture delivery. I have heard him lecture, both as an undergraduate ...
        7
        votes
        0answers
        232 views

        Visualization and new geometry in higher stacks (soft question)

        I am trying to develop a geometrical intuition for "higher spaces", i.e. both in the sense of higher dimensional spaces (more than three dimensions) and in the sense of abstractions beyond manifolds ...
        2
        votes
        0answers
        48 views

        Why control a continuous approximation of stochastic gradient descent instead of just the SGD?

        In "Stochastic modified equations and adaptive stochastic gradient algorithms" (Li et. al 2015) the authors approximate stochastic gradient descent, as in $$x_{k+1} = x_k - \eta u_k \nabla f_{\...
        92
        votes
        13answers
        26k 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 ...
        6
        votes
        1answer
        726 views

        Which branches of mathematics can be done just in terms of morphisms and composition?

        Consider the first-order language $L_{\omega\omega}$ of the signature $L:=\{\mathrm{dom}, \mathrm{cod}, \mathrm{comp}\}$, where $\mathrm{dom}$ and $\mathrm{cod}$ are unary function symbols and $\...
        19
        votes
        4answers
        971 views

        Can anything deep be said uniformly about conjectures like Goldbach's?

        This is a soft question sparked by my curiosity about the intrinsic depth of Goldbach-like conjectures as perceived by current experts in number theory. The incompleteness theorem implies that, if our ...
        46
        votes
        4answers
        4k views

        Consequences of lack of rigour [closed]

        The standards of rigour in mathematics have increased several times during history. In the process some statements, previously considered correct where refuted. I wonder if these wrong statements ...
        3
        votes
        1answer
        136 views

        History of the Taxonomy of Quadrilaterals

        Question: how did the classification of quadrilaterals come into being? Was there a single major contributor who coined terms like "rectangle", "square", "trapez/ium/oid", "kite", "deltoid", ...
        0
        votes
        2answers
        111 views

        On the 2018 paper “On the discretization of Laine equations” by K. Zheltukhin, et al [closed]

        I desperately need to read this paper, before meeting a would-be supervisor but with limited undergraduate knowledge that I have like Aluffi's Algebra and Churchill's Complex Analysis, Rudin's ...
        3
        votes
        0answers
        57 views

        Pohozaev identity and related non-existence result for a nonlinear problem

        Is it possible to prove a Pohozaev identity and the related non-existence result for non-trivial critical points of the functional $$\int_\Omega \left(A(x,u,\nabla u) -\frac{\lambda}{2} |u|^{2} - \...
        4
        votes
        1answer
        246 views

        How are the fields of dynamical systems, stochastic processes and additive combinatorics, inter-related?

        Currently I’m interested in a couple of fields, namely dynamical systems, stochastic processes, and additive combinatorics. I was wondering if it’s feasible to keep pursuing all 3, and whether I can ...
        8
        votes
        4answers
        1k views

        Is there any physical or computational justification for non-constructive axioms such as AC or excluded middle?

        I became interested in mathematics after studying physics because I wanted to better understand the mathematical foundations of various physical theories I had studied such as quantum mechanics, ...
        3
        votes
        2answers
        239 views

        Applications of flat submanifolds to other fields of mathematics

        Developable surfaces in $\mathbb{R}^{3}$ have lots of applications outside geometry (e.g., cartography, architecture, manufacturing). I am a curious about potential or actual applications to other ...
        1
        vote
        1answer
        182 views

        On the 2002 paper “Dynamics of polynomial automorphisms of $\mathbb{C}^k$” by Guedj and Sibony

        I desperately need to read the paper [1] before meeting a would-be supervisor, but with limited undergraduate knowledge that I have like Aluffi's Algebra and Churchill's Complex Analysis, not even one ...

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        山西福彩快乐十分钟
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