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.

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4
votes
1answer
185 views

An intutive reason why a “distance” metric may be a poor one for a procedure where we attempt to modify a string (mutating 0 OR 1 bits)

If I'm attempting to mutate one arbitrarily chosen binary string $s_a$, to another arbitrarily chosen binary string $s_b$, in the smallest number of steps (i.e. with the smallest number of mutations) ...
-5
votes
1answer
505 views

First PhD in pure math and the second PhD in applied math [closed]

Assume that someone has PhD in mathematics, and the dissertation was in Pure Mathematics. Is he eligible to apply to PhD program in Applied Mathematics? There are universities where the department of ...
6
votes
1answer
415 views

Origin of the term “weight” in representation theory

In representation theory, there are the related concepts of weights and roots. Since both are kinds of generalised eigenvalues, and eigenvalues are roots of e.g. the characteristic polynomial, the ...
18
votes
2answers
2k views

Where are Georg Cantor's Original Manuscripts?

Georg Cantor is famous for introducing transfinite numbers and set theory. A main part of his mathematical point of view about this new type of "numbers" and this new "realm of mathematics" cannot be ...
2
votes
2answers
539 views

Authorship, and order of authors [duplicate]

Currently I am writing a paper with several collaborators; although I am the primary author to this (I have done a large (>85%) majority of the work and have actually written the paper) my last name ...
2
votes
1answer
192 views

On non-unital ring and algebraic geometry

When I learned abstract algebra many years ago,I noticed the author deals with commutative ring say,$A$ has the proposition:$A^2=A$(without assuming it has identity).It seems that many proposition of ...
2
votes
2answers
604 views

L-functions and algebraic geometry

Robert Langlands commented in a letter to Deligne that perhaps some of the deepest problems of algebraic geometry lie in L-functions. I want to understand the general philosophy and the connection ...
40
votes
4answers
3k views

The Arnold – Serre debate

I have read (but I cannot now find where) that Arnold & Serre had a public debate on the value of Bourbaki. Does anyone have more details, or remember or know what was said?
5
votes
1answer
590 views

Submission of papers to ArXiv or similar [closed]

This is an extension of this question and this question on MathStackExchange. I have developed a formula for almost primes which is far more accurate asymptotically than Landau's well known ...
1
vote
1answer
209 views

Submitting lecture purposal to conferences. (lecture about a thesis) [closed]

I wish to consult with you about something: I have recently given a lecture about my master's Thesis in a local conference organized by my advisor. The subject had a lot to do with algebraic geometry ...
-6
votes
1answer
722 views

V.I. Arnold's high school problem [closed]

According to his interview to the Notices of the AMS, when Vladimir I. Arnold was 12 years old (in 1949) his teacher I.V. Morozkin, gave to his classroom (apparently 6th grade of a soviet primary ...
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
246 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 ...
25
votes
5answers
8k 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
214 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
459 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 ...
41
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
146 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
519 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
154 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
338 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
292 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
452 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
429 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
665 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
508 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 ...
44
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
333 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.‎ ‎ ...
8
votes
2answers
206 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
834 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
304 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
3k 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
569 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
245 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
788 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
329 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
218 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, ...
41
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
493 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
793 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
485 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
496 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 ...
38
votes
18answers
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 ...