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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6
votes
1answer
111 views

Construction of the Lie functor: left vs. right invariant vector fields on Lie groups and Lie groupoids

When constructing the Lie algebra $L(G)$ of a Lie group $G$, one usually uses the identification of the tangent space $T_1 G$ with left invariant vector fields $\mathcal{V}^l(G)$ to construct the Lie ...
15
votes
7answers
914 views

Continuous relations?

What might it mean for a relation $R\subset X\times Y$ to be continuous? In topology, category theory or in analysis? Is it possible, canonical, useful? I have a vague idea of the possibility of ...
49
votes
12answers
14k views

Top specialized journals

In geometry/topology, there are (at least) three specialized journals that end up publishing a large fraction of the best papers in the subject -- Geometry and Topology, JDG, and GAFA. What journals ...
2
votes
0answers
88 views

reference on aperiodicity and cluster [on hold]

From this image: I believe there is a message relating those clusters drawn in picture and aperiodic tiling. Does anyone have some reference on this? Thank you :)
2
votes
2answers
105 views

Software producing complex trees

Does anyone know any kind of graph software that could produce graphs like this for publication? Those links and crosses and numbers actually needs to be presented…. Thank you:) One small update, ...
48
votes
11answers
3k views

Why is Set, and not Rel, so ubiquitous in mathematics?

The concept of relation in the history of mathematics, either consciously or not, has always been important: think of order relations or equivalence relations. Why was there the necessity of singling ...
-4
votes
0answers
178 views

Can there ever be symbolic formalism (of importance) without intuitive heuristics? [closed]

Problem solving consists of using generic or ad hoc methods, in an orderly manner, for finding solutions to problems. Some of the problem-solving techniques developed and used in artificial ...
88
votes
19answers
20k views

Examples of unexpected mathematical images

I try to generate a lot of examples in my research to get a better feel for what I am doing. Sometimes, I generate a plot, or a figure, that really surprises me, and makes my research take an ...
58
votes
11answers
4k views

Are there any good websites for hosting discussions of mathematical papers?

I was wondering if there are any websites out there which systematically provide space for the discussion of mathematics articles (particularly those on the arXiv, though not necessarily just ...
2
votes
0answers
317 views

Help with my research topic [closed]

I have a masters degree in mathematics and I'm currently a PHD student. Since the beginning of my studies (2 years ago) I haven't progressed and still don't have a research topic. I was a very good ...
1
vote
0answers
234 views

Which are the constructs utilizing certain morphisms? [closed]

It seems to be a fact that most mathematical constructs have canonical morphisms. In some cases, nevertheless, there is a choice between several different classes of morphisms. I found my way to ...
4
votes
2answers
3k views

Something like mathoverflow in other sciences [closed]

Are the sites similar to mathoverflow in other sciences related to mathematics? statistics, computer science, physics, economics, etc? Let me explain what I mean by "similar": those are sites devoted ...
54
votes
16answers
7k views

Are there examples of non-orientable manifolds in nature?

Whilst browsing through Marcel Berger's book "A Panoramic View of Riemannian Geometry" and thinking about the Klein bottle, I came across the sentence: "The unorientable surfaces are never discussed ...
13
votes
7answers
653 views

Where to find (personal) motivation [closed]

I think it would be appropriate to make this question CW... It is likely that this question will not survive here on MO for long, but I do hope that the community gives it a chance. I also hope to ...
37
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?
-3
votes
1answer
381 views

Publishing problem [closed]

First, I want appreciate your work on this platform, as I have been getting very helpful advice even though I am not a member. My problem is that I have been working on-off on a famous math problem ...
8
votes
6answers
3k views

why haven't certain well-researched classes of mathematical object been framed by category theory?

Category theory is doing/has done a stellar job on Set, FinSet, Grp, Cob, Vect, cartesian closed categories provide a setting for $\lambda$-calculus, and Baez wrote a paper (Physics, Topology, Logic ...
196
votes
22answers
22k views

Thinking and Explaining

How big a gap is there between how you think about mathematics and what you say to others? Do you say what you're thinking? Please give either personal examples of how your thoughts and words ...
4
votes
1answer
240 views

Lower bound on the irrationality measure of $\pi$

There seems to be a lot of work on the upper bound for the irrationality measure of $\pi$, but I could not find anything on a lower bound except the general $\mu(\pi)\geq2$. Looks like it is the best ...
4
votes
2answers
407 views

Why considering schemes over discrete valuation rings?

For many times, I find people working on schemes over DVRs, and prove theorems on such setting. For example, my latest experience is the "semi-stable reduction theorem" by Kempf, Knudsen, Mumford and ...
40
votes
13answers
5k views

Contest problems with connections to deeper mathematics.

Hi, I already posted this on math.stackexchange, but I'm also posting it here because I think that it might get more and better answers here! Hope this is okay. We all know that problems from, for ...
0
votes
0answers
111 views

Looking for rapidly converging series for the reciprocal gamma and/or gamma function

There are rapidly converging infinite series for Pi and the such but it is difficult to locate those for either the gamma or reciprocal gamma function. I am searching for rapidly converging series ...
3
votes
1answer
120 views

Countable model theory for $\omega$-stable theories?

This is a bit of a fishing expedition, because I'm not sure what I'm looking for. Very vaguely stated, here's the driving question: What conditions on an $\omega$-stable theory make the class of ...
4
votes
2answers
616 views

Salvaging Leibnizian formalism?

Can one justify Leibniz's formalism in a suitable algebraic or topological context? We have published some papers recently where we argue that Leibniz's formalism for the calculus wasn't ...
11
votes
1answer
1k views

ICM 2014 streaming video

Is there a possibility to watch ICM 2014 opening ceremony and the big talks online? I hope there is since it was possible for the previous meeting.
44
votes
25answers
7k views

Cocktail party math [closed]

Ok, hotshots. You're at a party, and you're chatting with some non-mathematicians. You tell them that you're a mathematician, and then they ask you to elaborate a bit on what you study, or they ask ...
12
votes
4answers
684 views

Examples of research on how people perceive mathematical objects

What examples are there on research related to human perception and mathematical objects? For example, the shape of a beer glass influences drinking habits, since people are bad at integrating. ...
29
votes
1answer
3k views

A topologist is not a mathematician - a small question

Years ago I read about a topologist who was to enter the states as an immigrant and was asked a question about his profession. He indicated he was a topologist, but as this was not included on the ...
7
votes
5answers
1k views

Where can I find the text of Weyl's Fields Medal speech for Serre?

I thought about asking this question a while ago, but decided against it. But now I see a question about Eichler's "modular forms" quote, so while I guess it's probably still, um, questionable, what ...
20
votes
10answers
2k views

What math institutes offer research in pairs/research in teams?

Some math institutes offer programs in which a small number of researchers are enabled to meet at the institute for a week or more. A list seemed as if it could be useful.
3
votes
0answers
64 views

Almost everywhere in a rectangle [duplicate]

I would like to ask a question about the product (Lebesgue) measure on rectangle. I tried to solve the problem but I couldn't. Let $S$ be a subset of a region, say $R$ which is enclosed by a ...
30
votes
6answers
2k views

Negative impact of wrong or non-rigorous proofs

The recent talks of Voevodsky (for example, http://www.math.ias.edu/~vladimir/Site3/Univalent_Foundations_files/2014_IAS.pdf), which describe subtle errors in proofs by him as well as others, as well ...
8
votes
0answers
130 views

Literature that helps explain what the theory of numerosities contributes with

Since 2003 a group of Italian mathematicians (Benci, Di Nasso and Forti) has developed a new measure for infinite sets that satisfies the Euclidian principle: The whole is greater than the part. The ...
42
votes
33answers
3k views

Dimension Leaps

Many mathematical areas have a notion of "dimension", either rigorously or naively, and different dimensions can exhibit wildly different behaviour. Often, the behaviour is similar for "nearby" ...
24
votes
8answers
3k views

Why differential forms are important?

Importance of differential forms is obvious to any geometer and some analysts dealing with manifolds, partly because so many results in modern geometry and related areas cannot even be formulated ...
23
votes
15answers
4k views

Examples of famous 'workhorse' theorems

I use the term 'workhorse' to describe a theorem which is technically challenging to prove, perhaps very deep, but the statement is either uninteresting at first glance or too imposing to be ...
73
votes
45answers
30k views

Interesting mathematical documentaries

I am looking for mathematical documentaries, both technical and non-technical. They should be "interesting" in that they present either actual mathematics, mathematicians or history of mathematics. I ...
7
votes
3answers
2k views

How to find/guess a polynomial sequence?

My question is motivated by the recent question and more recent appearance of its author Bruce Westbury. Most of you know that the best way to find a sequence of integers is looking for it on The ...
49
votes
13answers
4k views

What makes four dimensions special?

Do you know properties which distinguish four-dimensional spaces among the others? What makes four-dimensional topological manifolds special? What makes four-dimensional differentiable manifolds ...
0
votes
1answer
252 views

a book comparable to Development of mathematics in the 19th century by F.Klein? [closed]

This book is apparently very interesting according to Vladimir Arnold. I couldn't get my hand on a copy yet, therefore I would to ask you for any reference similar to it, and also can you post ...
2
votes
4answers
338 views

Should all equations which appear in a thesis be numbered?

I was just wondering if there is any sort of consensus on the topic of when to number math expressions. For example different lines in a proof, these should be tagged or not tagged?
24
votes
5answers
5k views

What is the etymology of the term “perverse sheaf”?

Grothendieck famously objected to the term "perverse sheaf" in Récoltes et Semailles, writing "What an idea to give such a name to a mathematical thing! Or to any other thing or living being, except ...
12
votes
19answers
7k views

Textbook recommendations for undergraduate proof-writing class

I am teaching the proof-writing class (for the 3rd time) in the Fall and plan to buck the party line and use a different text than the default Bond and Keane. My parameters are as follows: Logic, ...
39
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 ...
74
votes
16answers
6k views

How does one justify funding for mathematics research?

G. H. Hardy's A Mathematician's Apology provides an answer as to why one would do mathematics, but I'm unable to find an answer as to why mathematics deserves public funding. Mathematics can be ...
3
votes
4answers
244 views

Which fields could be applied to neurosciences?

I have a friend who wants to study something applied to neurosciences. He is going to begin his grad studies in mathematics. He asked me which areas of mathematics could be applied to neurosciences. ...
39
votes
11answers
6k 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 ...
38
votes
19answers
6k views

Mathematicians whose works were criticized by contemporaries but became widely accepted later

Gauss famously discarded Abel's proof that an algebraic equation of degree five or more cannot have a general solution (Abel himself had rejected divergent series as the work of the devil). Cantor's ...
9
votes
3answers
780 views

Proof correctness problem

I was watching this talk by Vladimir Voevodsky which was given at the Institute of Advanced Study in 2006. In his talk the first slide he shows has the following written on it: ...
5
votes
0answers
320 views

Refereeing a paper containing strong statements about other papers

The title says it all. Suppose you are refereeing a paper where the author A makes strong statements about other papers by a different author B, like: the proof of Theorem 1 in paper [B] is wrong and ...