# 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

**1**answer

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

**1**answer

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

**0**answers

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

**0**answers

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

**13**answers

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

**1**answer

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

**4**answers

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

**4**answers

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

**1**answer

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

**2**answers

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

**0**answers

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

**1**answer

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

**4**answers

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

**2**answers

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

**1**answer

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 ...