Questions that ask about some aspect of mathematical research or study which doesn't involve the actual mathematics. In general, soft questions can be answered without using mathematical reasoning.

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0
votes
0answers
164 views

Examples of 'bad' notations and definitions [duplicate]

I am trying to compile a list of notations and definitions that has become ingrained in mathematical folklore, yet are still on some objective scale unsatisfactory. I offer two starting examples. For ...
4
votes
0answers
196 views

Design slides for presentation (conference talk) [closed]

Question: What are approved guidelines for design good slides for a conference talk, especially with focus on mathematics? I'm aware of the following, general best practices for holding a ...
23
votes
5answers
5k views

Advice for pure-math Phd students [closed]

Pursuing a Phd in pure math can be a daunting task. A number of students who begin a Phd in pure math don't complete it, and there are high-quality dissertations and those which are not so high ...
2
votes
0answers
208 views

Request for good research mailing list in Dynamical System & Chaos for notification of recent research results, conference, announcements [closed]

Are there some good research-level mathematics mailing list to be recommended in order to be notified of recent research results, news, announcements, conference, etc, particularly in Dynamical System ...
5
votes
2answers
428 views

Mazur's torsion theorem on elliptic curves and its generalisations

I want to study Mazur's torsion theorem for elliptic curves over $Q$ and its generalizations for number fields, i.e., papers by Kamienny, Kenku & Momose, Filip Najman. So please suggest to me what ...
40
votes
18answers
5k views

How can an extremely mathematically talented young person be helped to fulfill his/her potential?

Obviously, this question is not a research level mathematics question at all. But, I've just met an extremely mathematically talented 11 years old student and I don't know how I can help him. For ...
2
votes
1answer
145 views

English translation of Gauss' “Principia generalia theoriae figurae fluidorum in statu aequilibri”

I have been unable to locate an English translation of Gauss' work, "Principia generalia theoriae figurae fluidorum in statu aequilibri". A German translation exists (PDF), but my German is not quite ...
30
votes
7answers
3k views

Is it worthwhile to give off-topic talks?

I am a graduate student. Occasionally for some reason I am asked to give a talk on my research at a conference whose stated purpose is almost completely unrelated to my research. To preserve my ...
4
votes
1answer
475 views

a conjecture in sum-free sets

Let $ A $ be a set of non-zero integers. Then $A$ contains a sum-free subset $B$ of size $ |B|> \frac{|A|}{3} $ (a result of Erdős). It is conjectured that RHS can be improved to $\frac{|A|}{3} ...
2
votes
1answer
147 views

Name of the concept “Topological boundary of A intersected with A”

In closure spaces (thus, also in topological spaces), one may define the boundary of a set A as the closure of A minus the interior of A. This set is partitioned into "the closure of A minus A" and "A ...
5
votes
1answer
328 views

What does it mean for a Deligne-Mumford stack to have trivial generic stabilizers?

I have stumbled upon some literature on Deligne-Mumford stacks, and it seems to me, at least superficially, that there is a strong link between DM-stacks which have "trivial generic stabilizers" and ...
10
votes
2answers
1k views

How difficult will it be for me to switch fields (details below) after my Ph.D. in pure mathematics?

I'm a first year postdoctoral researcher, working in pure areas of Riemann surfaces and differential geometry, after just finishing my Ph.D. in 2013. Recently I've also started taking interest in ...
2
votes
1answer
287 views

Examples of Quot schemes

I'm studying Quot schemes, that I denote with $Quot_{N,X,P}$, with $N \in \mathbb{Z}$, $X \subset \mathbb{P}^d$ and $P \in \mathbb{Q}[t]$. So, I'm looking for explicit examples of Quot schemes. Could ...
9
votes
2answers
403 views

Model structure for cooperads and for coalgebras

I am studying the homotopy theory of (algebraic) operads and I came up with several questions I am unable to answer to. I would like to stress that I don't have applications in mind, I just would like ...
5
votes
1answer
412 views

Is Logic/Set Theory necessary for studying Topos Theory?

I have just completed a postgraduate course, in which I studied Category Theory, without having a background in Set Theory and Logic - this probably already sounds absurd to many. This did not seem to ...
10
votes
5answers
646 views

Accessible proofs of contemporary results in mathematics

Are there strong results in contemporary mathematical research (last 20 years) which have a proof which every mathematician (holding a PhD) can completely understand within a few days? -- If yes, ...
3
votes
1answer
413 views

Equal signs with fancy marks

Some people use $\stackrel{\mathrm{def}}{=}$, $:=$ or $\stackrel{\Delta}{=}$ for definitions. In more informal contexts, I have also seen $\stackrel{?}{=}$, for "I wish to prove this equality, which ...
43
votes
9answers
3k views

What is entropy, really?

I first saw the term "entropy" in a chemistry course while studying thermodynamics. During my graduate studies I encountered the term in many different areas of mathematics. Can anyone explain why ...
1
vote
0answers
331 views

On Mathematicians Who Did Their Masterworks After ‎40 Years Old [duplicate]

Remark: ‎‎The ‎idea ‎of ‎this soft ‎question ‎is ‎adopted ‎from ‎the following interesting ‎book‎. ‎ ‎ Timothy Gowers, Mathematics: A Very Short Introduction, Oxford University Press, 2002.‎ ‎ ...
7
votes
2answers
197 views

Natural $\Pi^1_2$ (or worse) classes of structures?

(To clarify, my interest is mainly lightface, that is, $\Pi^1_2$ instead of $\bf \Pi^1_2$, although it doesn't particularly matter.) This is just an idle curiosity. In logic, I find myself frequently ...
3
votes
1answer
282 views

Is “ultracompact” taken?

Almost-huge cardinals are characterizable in terms of coherent towers of supercompactness measures, with a certain property of the direct limit model (see Kanamori's book). A useful large cardinal ...
18
votes
1answer
772 views

Why is there a connection between enumerative geometry and nonlinear waves?

I'm not 100% sure that this question is appropriate for this site. If it's not, please tell me and I'll delete it. Recently I encountered in a class the fact that there is a generating function of ...
1
vote
0answers
290 views

about an ISI journal [closed]

I have a question that I don't know where I can ask it and so I prefer to ask it here. I submitted one of my paper in an ISI journal in september 2011 for possible accepting and publishing there. ...
8
votes
1answer
2k views

What is the source of this E̶r̶d̶ő̶s̶ quote?

Namely, the following one "All problems appeared once in the [American Mathematical] Monthly." I remember reading it several years ago... When I first posed the question, I believed that I had ...
21
votes
1answer
2k views

What does a theoretical mathematician do? [closed]

I'm 12, and really like mathematics and physics. I was just wondering what does a 'theoretical mathematician' do?
5
votes
3answers
390 views

New trends in Applied Graph Theory [closed]

What are current trends in Applied Graph Theory? I am interested mainly in non-algorithmical problems. Maybe even in applications of graphs to other mathematical disciplines. For example, abstract ...
1
vote
1answer
190 views

Quadratic variation for discrete Martingale

Is there any analogue of continuous martingale quadratic variation for the discrete case? If so, are there any theorems which characterize simple random walk using quadratic variation - similar to ...
12
votes
3answers
736 views

Writing Mathematics : Linking words

I'm trying to write mathematics in English and I'm clearly missing something : linking words. I'm writing "so, we get", "Observe that" too many times and I'm afraid to use some expressions : "it ...
78
votes
10answers
11k views

Work of plenary speakers at ICM 2014

The next International Congress of Mathematicians (ICM) will take place in 2014 in Seoul, Korea. The present question is meant to gather brief overviews of the work of the plenary speakers for the ICM ...
6
votes
6answers
326 views

Physical Disturbances to Computations [closed]

In this paper, page 7 (160 of the Journal), Fig 3, there is a particularly amusing (not to the authors!) caption: "... On April 1 of year 2 in the $S_0$ experiment, the computer was hit by a cosmic ...
25
votes
6answers
1k views

Does seeing beyond the course you teach matter? The case of linear algebra and matrices

This question is indeed very important for me. Thus I hope you bear with my subjective explanations for a few minutes. I am an "excellent" lecturer, at least according to course evaluation forms ...
0
votes
0answers
189 views

English version of “Quasi-Hopf Algebras”

I was wondering where I can find a pdf of Drinfeld's paper "Quasi-Hopf Algebras," which formulated the Grothendieck-Teichmuller group. The Russian version is in Algebra i Analiz, 1:6 (1989), 114–148, ...
38
votes
7answers
5k views

How do you not forget old math?

I am trying to not forget my old math. I finished my PhD in real algebraic geometry a few years ago and then switched to the industry for financial reasons. Now I get the feeling that I want to do a ...
5
votes
2answers
459 views

Is there a 3d equivalent of this picture?

This question arises apropos of an earlier question I asked that was (VERY!!!) helpfully answered by Anton Petrunin: Fitting a mesh to a density function The picture below is the image of a regular ...
17
votes
3answers
779 views

Where to break paragraphs in a proof?

I have some rules of thumb about writing research papers that I can actually articulate. For example, leave all definitions as late as possible (but not later!), so the reader won't fear "Do I need to ...
2
votes
2answers
440 views

Industry jobs involving mathematics, machine learning and biology [closed]

I have a MSc in Mathematics and a PhD in Bioinformatics (in two different European countries); during the PhD I was developing computational methods to analyse DNA sequence data, mainly using a ...
18
votes
2answers
1k views

Papers better than books?

Not so long ago I took a class called "Discrete analysis". I remember that I couldn't find any "novice" level material on Mobius functions in combinatorics. So then I went to the roots and read Rota's ...
2
votes
1answer
462 views

Hilbert style axiomatic proof or sequent Calculus?

I am puzzling with the question which of the two proof systems (Hilbert style axiomatic proofs or substructural Sequent Calculi) is the most discriminatory? With discriminatory I mean is which proof ...
36
votes
17answers
5k views

What are some deep theorems, and why are they considered deep?

All mathematicians are used to thinking that certain theorems are deep, and we would probably all point to examples such as Dirichlet's theorem on primes in arithmetic progressions, the prime number ...
5
votes
1answer
448 views

Naive question on adelic groups

The ever-reliable Wikipedia says: ... an adelic algebraic group is a semitopological group defined by... No more details are given, and I was wondering if the multiplication only being ...
18
votes
5answers
650 views

Online high quality colloquium talks

In my department we're thinking about showing online lectures one day per week at lunch, as sort of a virtual colloquium appropriate to mathematics undergraduates as well as faculty. To start with ...
23
votes
3answers
2k views

Contemporary mathematical themes

The presence of fruitful mathematical themes suggests the unity of mathematics. What I mean by a mathematical theme here is a basic idea or guiding principle that motivates or directs the central ...
2
votes
5answers
253 views

Equivalence relations not associated with a group

This is a vague question; so vague that I wonder if anyone will get it. Many, perhaps most, equivalence relations that are regularly used in mathematics correspond to the orbits of some group action ...
6
votes
1answer
627 views

What are current trends/questions in algebraic logic?

What are current trends/questions in algebraic logic? I mean the research developed by Paul Halmos. Could anyone give some references for the overview of its history? Any overview of its application ...
5
votes
1answer
405 views

What are good ways to present proofs of theorems requiring auxiliary lemmas? [closed]

I am writing an academic paper for submission to a journal. One of my co-authors wrote the following: Theorem Statement of the theorem Proof of theorem We first show the following result ...
9
votes
2answers
763 views

Rigid analytic spaces vs Berkovich spaces vs Formal schemes

I wonder if someone could explain briefly what is the relation between these 3 formal models, of a Berkovich space, a rigid analytic space and a formal scheme? I have been working with formal schemes ...
26
votes
4answers
1k views

Why Cohen-Macaulay rings have become important in commutative algebra?

I want to know the historic reasons behind singling out Cohen-Macaulay rings as interesting algebraic objects. I'm reviewing my previous lecture notes about Cohen-Macaulay rings because now I'm ...
15
votes
10answers
2k views

An example of a proof that is explanatory but not beautiful? (or vice versa)

This question has a philosophical bent, but hopefully it will evoke straightforward, mathematical answers that would be appropriate for this list (like my earlier question about beautiful proofs ...
5
votes
1answer
257 views

Origins of Axiomatic Reasoning

Is there any evidence that axiomatic reasoning has been used prior to Thales of Milet (624-547BC), who is generally credited for the "invention" of axioms. In this context I understand axioms in the ...
39
votes
15answers
4k views

How does the work of a pure mathematician impact society? [closed]

First, I will explain my situation. In my University most of the careers are doing videos to explain what we do and try to attract more people to our careers. I am in a really bad position, because ...