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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.

      8
      votes
      0answers
      70 views

      Is there a “formula” for the point in $\text{SO}(n)$ which is closest to a given matrix?

      $\newcommand{\Sig}{\Sigma}$ $\newcommand{\dist}{\operatorname{dist}}$ $\newcommand{\distSO}[1]{\dist(#1,\SO)}$ $\newcommand{\distO}[1]{\text{dist}(#1,\On)}$ $\newcommand{\tildistSO}[1]{\operatorname{...
      4
      votes
      1answer
      198 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 ...
      6
      votes
      2answers
      506 views

      Books on the History of math research at European universities

      Are there good books that cover the history of math and mathematical science (ex. physics, chemistry, computer science) PhD programs in the Occident? My primary motivation is to figure out how the PhD ...
      13
      votes
      1answer
      665 views

      Journal losing indexing services

      I recently had a paper accepted by a journal. When I looked it up on the AMS’ Mathematical Reviews, I noticed that it was previously indexed by the service but, at present, is it not. The journal is ...
      2
      votes
      1answer
      157 views

      Reference request: Gauge theory [on hold]

      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
      386 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 ...
      8
      votes
      0answers
      343 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 ...
      3
      votes
      0answers
      64 views
      +50

      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
      730 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
      977 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
      113 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} - \...

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