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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6
votes
2answers
360 views

Are there any organized websites for seminar/conference videos?

These days, there are many conference centers and universities recording seminars and conference talks and make them available on the web. Some examples: http://www.fields.utoronto.ca/video-archive ...
100
votes
10answers
6k views

What non-categorical applications are there of homotopical algebra?

(To be honest, I actually mean something more general than 'homotopical algebra' - topos theory, $\infty$-categories, operads, anything that sounds like its natural home would be on the nLab.) More ...
3
votes
0answers
77 views

Choice of MIP (mixed integer programming) solver

I would start using MIP solver for the research on the tiling. I know (heard of) the open source solver jump: https://github.com/JuliaOpt/JuMP.jl and also the gold standard solver from IBM cplex. ...
76
votes
6answers
7k views

Mistakes in mathematics, false illusions about conjectures

Since long time ago I have been thinking in two problems that I have not been able to solve. It seems that one of them was recently solved. I have been thinking a lot about the motivation and its ...
10
votes
1answer
360 views

Sources to find industrial jobs for mathematicians with a Ph.D., or with advanced backgrounds? (preferably research positions but not necessarily)

Several companies (google, IBM etc.) are known to hire mathematicians with advanced degrees (Ph.D. and so) to work in different sectors; I mean mostly research oriented positions in industry but could ...
0
votes
2answers
443 views

Guidelines for writing proofs in math papers [closed]

In the light of the recent "proof wars" in symplectic geometry (in which some groups contend that proofs given by some other groups are wrong, see here, here and here) I thought it would be good to ...
5
votes
2answers
858 views

Why can't mathematics be formalised in terms of classes rather than sets? [closed]

I've always been curious about the seeming compulsion to found mathematics upon sets, be it ZF(C) or some other system. Of course, there are other approaches these days like category theory and type ...
8
votes
3answers
657 views

Correct spelling of names, Chebychev and Cholesky [closed]

I'm writing a paper on orthogonal polynomials and I have to cite results by Chebychev and Cholesky. I found several and different translitterations from Russian. I wonder if there is a standard and ...
15
votes
8answers
1k views

Should a theorem be numbered by where it is first stated or where it is proven?

Suppose I am writing a paper in which an important lemma has a proof which is either long and unenlightening or requires additional background of the reader (or both). Thus, to avoid disrupting the ...
21
votes
4answers
798 views

Which journals allow authors to retain copyright…?

I became motivated to ask this question after seeing the inspiring "© The Author(s) 2013 " in the header of this very interesting article, published in Compositio Mathematica. Apart from open access ...
11
votes
4answers
1k views

Does formalizing math require search and creativity, or is it near-mechanical?

I remember reading somewhere that it takes about a week to convert a page of math into something a proof-assistant like Isabelle or HOL Light would accept. Is this type of conversion something that ...
4
votes
1answer
661 views

What is the critical idea behind Hardy-Littlewood circle method?

I want to know what the critical idea behind Hardy-Littlewood circle method is. It seems that they divide the circle into major arcs and minor arcs to ignore the singularities of generating function ...
5
votes
1answer
262 views

Where can I find resources for creating a mathematics “bridge course”?

My department is in the very early stages of developing a "bridge course" or "introduction to proofs" course, motivated by our lower-level courses not currently doing a good job of preparing our ...
0
votes
1answer
211 views

Choosing Notation for Variable Substitution into Derivative Expressed with Differentials [closed]

Consider function $f(x)$. I've counted 4 possible notations to write a derivative of $f(x)$ at point $x = a$: $f'(a)$; $\frac{\operatorname{d}{f(a)}}{\operatorname{d}x}$; ...
8
votes
3answers
308 views

Punctuation and Other Rules for Variables and Their Verbal Definitions in Math Narrative [closed]

To better understand what I'm asking about, let's immediately define some examples. Imagine that you are writing some paper which involves a lot of math narrative. And you have a term, say, computing ...
6
votes
1answer
829 views

Is there a “big program” in mathematics at the moment? [closed]

I apologize in the event that you should find this question off topic. Please feel free to delete it if that is the case. Years ago, I studied undergrad mathematics at university. The understanding ...
11
votes
8answers
794 views

Interesting examples of generic behavior of mathematical objects being either unreasonably structured or simply unreasonable

My experience seems to be that quite often "generic" mathematical objects tend to be either extremely well behaved or structured, or at the opposite extreme are as unstructured as possible. For ...
6
votes
4answers
2k views

'Category-theory'-free areas of pure math, 'category-theory'-loaded areas of applied math

To put it short: In which active research areas of (pure) mathematics no (or only minimal) knowledge in category theory is required ? To put it long: I know almost nothing about category theory - but ...
1
vote
2answers
274 views

when will the surfficient large power of a rational matrix be a integer matrix?

$A$ is a $n\times n$ matrix whose elements are all non-negative rational numbers and $Det(A)$ is a non-zero integer.Under what condition the following is true?(0) There exist a positive integer $M$ ...
19
votes
1answer
1k views

Is two years without a referee report normal?

Firstly, the help page for Mathoverflow does not forbid asking such a question. Secondly I found a similar question on Mathoverflow and thirdly as far as I know, waiting for two years for a referee ...
6
votes
3answers
921 views

How to publish two interdependent papers

I have two finished articles (each about 25 pages long) but the second one uses results from the first one, none of which has been published yet. I would like to send them to some standard journal for ...
2
votes
0answers
122 views

characterization of all periodic tiling of a simple set of Wang Tile

Consider a set of Wang Tile such that all the edges are either 1 or 0.... there are 16 elements in such a set. Now, I wish to characterize all the periodic tilings of this set (better if they are ...
0
votes
0answers
234 views

Applied Math author order

In applied math it seems to be more common to list authors according to their contribution rather than alphabetically. This being the case, in the instance where there are more than 2 authors, I was ...
1
vote
1answer
94 views

simple cycle analog in 2D (with application in tiling)

We know that any closed cycle of a graph could be decomposed into sum of simple cycles. To translate this theorem into tiling of 1D (Wang tile). We know that any 1D periodic tiling could be ...
6
votes
3answers
755 views

Why isn't there more interest in “large powerset axioms”?

By a large powerset axiom, let us mean informally an axiom that says that for some cardinal numbers $\kappa$, we have that $2^\kappa$ is somehow "large" or "difficult to access from below." For ...
52
votes
8answers
5k views

Have you solved problems in your sleep? [closed]

I have hit upon major (for me—relative to my trivial accomplishments) insights in my research in various sleep-deprived altered states of consciousness, e.g., long solo car-drives extending ...
4
votes
0answers
157 views

Stable homotopy of spheres non-locally

Are there any results/conjectures about the stable homotopy groups of spheres that relate the picture at different primes? Something like Gauss's reciprocity law in number theory? I know about the ...
7
votes
5answers
1k views

Advice on choosing an area of specialization

I'm not sure if this is an appropriate question for MO, but I figured it couldn't hurt to ask. I'm a second year graduate student, currently gearing up to construct a committee and syllabus for my ...
2
votes
2answers
468 views

Have axioms / axiom schemata of this flavour been proposed or otherwise considered?

With the exception of a few miscellaneous cases, the axioms (and/or schemeta) of ZFC can roughly be divided into two kinds: Those that guarantee the existence of more complicated sets, given that ...
1
vote
0answers
224 views

Recreating the wheel [closed]

I recently finished my Phd in pure maths and I am looking for open problems in my research area, functional analysis. Without going into the details, I stumbled onto an interesting problem and I ...
4
votes
1answer
166 views

What is the early history of the concepts of probabilistic independence and conditional probability/expectation?

In the 1738 second edition of The Doctrine of Chances, de Moivre writes, Two Events are independent, when they have no connexion one with the other, and that the happening of one neither forwards ...
7
votes
4answers
1k views

Advice for number theory library

Hi I just got a faculty position and it comes with a generous start up funds for "office supplies", which I must use or lose. What does a pure mathematician need? I have good computers already. I ...
2
votes
2answers
353 views

Beautiful constructions in algebraic topology that facilitate one's understanding of homotopy theory [closed]

There is an army of interesting constructions in AT, and Understanding them are usually very helpful for appreciate the theory underneath. So I would like to invite you to share those examples that ...
3
votes
1answer
228 views

References for von Neumann Algebras

I have some -possibly- simple but broad questions: Where to begin the study of von Neumann Algebras? Which are the important questions in the field that guide current research? I'm interested in ...
12
votes
2answers
585 views

Applications of really large numbers

I have seen several questions here on MO regarding large numbers, (uparrow notation, etc.), and different way to construct and compare such numbers. I am curious what the applications are for the ...
1
vote
0answers
444 views

Is it possible to give a fair assessment of the influence of Bourbaki's “Eléments de mathématique”? [closed]

Well, I apologize if this "soft-question" (related to the "Arnold-Serre" debate) is considered as irrelevant for MO, and for possible misunderstandings in the two earlier versions of this post (which ...
42
votes
11answers
9k views

What areas of pure mathematics research are best for a post-PhD transition to industry?

I have a student who is looking to start a PhD in pure mathematics. She is talented and motivated, and will do quite well. She is still in a phase of her development where she is still open to the ...
3
votes
0answers
162 views

Looking for author of calculus quote

When I was a lowly calculus student many many years ago, my calculus teacher quoted some famous mathemtician: "Calculus is the last course in arithmetic and the first course in mathematics that one ...
0
votes
1answer
89 views

Inserting maple or macaulay script in a paper [closed]

I see many wonderful papers where the authors include some script written in Maple, Macaulay or other software that are needed for their proof. How do you insert that in your tex file?
6
votes
0answers
110 views

Duality between large and small scale structures

A rather immediate reaction to seeing the definition of a coarse structure, at least to me, is to be reminded of a uniform structure. The axioms for a coarse structure $\mathcal{C}$ (defined by a ...
14
votes
1answer
2k views

What have simplicial complexes ever done for graph theory?

(I am asking in a somewhat tongue-in-cheek fashion, of course, but nevertheless...) Are there examples of results in "classical" [*] graph theory that have been achieved by using simplicial ...
3
votes
4answers
464 views

Understanding reasons for best constants in inequalities

Why, in functional analysis, is so important to calculate best constant in an embedding inequality? Cross-posted from ...
0
votes
0answers
191 views

Game Theory - need references on analysis of particular game

My hobby AI research have led me to a thorethical game of particular design. As design is pretty simple, I was sure that such game has well-known name. But my question on math.stackexchange, where I ...
4
votes
4answers
458 views

Determine if a graph has a large clique

This question is quite specific and practical. I hope it is still relevant for MO and will not be removed. I have a collection $\mathcal{C}$ of graphs having from 5000-6000 vertices and edge density ...
6
votes
0answers
400 views

Is there a theory of abuse of notation? [closed]

Is there any theory about the different ways notation can be abused and which abuses are ineliminable without complicating the notation in some essential way? We can define "abuse of notation" as any ...
72
votes
9answers
8k views

Analogues of P vs. NP in the history of mathematics

Recently I wrote a blog post entitled "The Scientific Case for P≠NP". The argument I tried to articulate there is that there seems to be an "invisible electric fence" separating the problems in P ...
3
votes
0answers
469 views

Does Pure Mathematics glue Science together? [closed]

A little while ago, I was reading Cathy O'Neil's post Why is math research important (subtext: why does Pure Math deserve funding), where she discusses 3 possible answers. One of these is the usual ...
6
votes
1answer
413 views

Sources of Theorem drafts by the original author

When I look at first time to a theorem and I try to understand it or when I try to memorise a useful theorem I always have difficulties (I am not the only one. For example: I read a question: I always ...
22
votes
3answers
933 views

“Paradoxes” in $\mathbb{R}^n$

One may think of this question as a duplicate of this one. I see it more like an extension. The "inscribed sphere paradox" discussed in the aforementioned question states that if you inscribe a ...
24
votes
1answer
5k views

Who made the famous error in calculation that 'wasted' the final years of his life?

Sorry, I am merely a Middle School maths teacher at an Australian secondary school. I remember reading years ago about a famous mathematician (18th or 19th Century?) who calculated table upon table of ...