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.
6
votes
2answers
648 views
Publication in proceedings
Why and how publishing a paper in proceedings?
What are the difference with a "classical" journal?
What's the list of the main proceedings in which one can publish?
Do proceedings papers (never, ...
8
votes
3answers
213 views
How do small central extensions drop the dimension of a faithful representation?
Apologies in advance that this is a very soft question. I might be talking complete nonsense. But I hope I am talking about something that has even been studied...
I am interested in the phenomenon ...
22
votes
2answers
567 views
Different styles of writing/reading articles
Recently, I discovered a rather unexpected thing. We are writing an article in collaboration and we permanently have some discussions about how to write, in which order, how to organize material etc.
...
1
vote
0answers
166 views
Intuitive Approach to Sheaf and Cech Cohomology [closed]
Sheaf and Cech cohomology $H^*(X,\mathcal{F})$ (which give the same result when applied to good enough topological spaces) are a useful generalisation of the concepts of de Rham and Dolbeault ...
5
votes
2answers
311 views
Applications of cohomology to probability and statistics
Are there interesting/useful applications of cohomology (and homological algebra in general) to probability and statistics, or information theory?
By "interesting/useful", I mean "not merely ...
4
votes
3answers
295 views
Need examples of homotopy orbit and fixed points
I am no expert in equivariant homotopy theory. Let's say, I am planing to give a talk on homotopy fixed points and orbits. My audience will be graduate students who are doing algebraic topology or ...
1
vote
1answer
239 views
How to decide whether the journal is pure or applied?
I am a beginner in research and have draft ready for my first article. I have a little confusion about the pure and applied journal in Mathematics. My work belongs to pure mathematics(I think). And ...
8
votes
0answers
524 views
How to approach the stigma of not having a math degree? [closed]
I am a faculty member in a department that is not mathematics, but is highly-ranked in my field. I greatly enjoy working with mathematicians, and have had a number of successful collaborations.
...
3
votes
1answer
394 views
Mathematics of Computer science and AI [closed]
Computer science and Artificial Intelligence have been fertile grounds for research for decades, not only for Engineers but particularly for Mathematicians. What kinds of Mathematics have emerged ...
3
votes
3answers
311 views
Reference request: a guide through quantum probability
Could you point out a comprehensive reference book (or more than one, if it is the case) on Quantum Probability that introduces the subject and then gradually builds up to the edges of contemporary ...
2
votes
2answers
232 views
Heuristics for 2-morphisms of (algebraic) stacks
For topological spaces and simplicial sets one can consider each pair of parallel morphisms $f,g:X\rightrightarrows Y$ as equipped with a set of 2-morphisms given by homotopies $H:f\simeq g$ (let's ...
5
votes
2answers
852 views
Physicist trying to understand modern mathematics
I'm a physicist trying to gain a deep understanding of mathematics that is required for my work.I intend to specialize in string theory which is a very math intensive branch of theoretical physics ...
2
votes
2answers
395 views
Popular books written by great mathematicians [closed]
I read:
H. Poincare. Value of science
F. Klein. Development of Mathematics in the 19th Century
J.E. Littlewood. A Mathematicians Miscellany
G.H. Hardy. A Mathematician’s Apology
R. Courant, ...
7
votes
2answers
802 views
Surveys of the items of Erdős' “toolbox”
Could you point out some survey papers and monographs that highlight the kernel of tricks, techniques, and tools that Paul Erdős employed the most in his research work (in particular in graph theory, ...
3
votes
1answer
92 views
Reference for exercises with solutions for affine Lie algebras
I am doing self-study of affine Lie algebras, and while I have all recommended reference material, I find it hard to prepare for the exam.
It was quite easy to study finite-dimensional simple Lie ...
7
votes
2answers
204 views
Recent trends in effective analysis
The references listed at http://en.wikipedia.org/wiki/Computable_analysis have all been published 30-15 years ago. Are the approaches which these references expose still up-to-date and relevant to the ...
3
votes
3answers
262 views
Survey papers of results (relevant to mathematics) produced during research on the relationship between mathematics and music theory
It is well-known that there is a relationship between music and mathematics, and there are many references that explore this topic (for example, Benson's book).
However, I would like to ask if there ...
1
vote
0answers
82 views
Why are they called 'pernicious' numbers?
The definition of a pernicious number:
In number theory, a pernicious number is a positive integer where the Hamming weight (or digit sum) of its binary representation is prime.
The meaning of ...
8
votes
1answer
409 views
Open access journals in number theory
I'm a phd student in number theory, and I'm required (by the funding council) to publish any article I write in open access journals. The problem is that all journals I can find are either out of my ...
3
votes
1answer
376 views
Do hom-sets really live in the category Set?
This isn't really a research-level question (sorry!), but I asked on
math.se (link), and though the question was upvoted a few times, I didn't
get any answers. So since there may well be more ...
13
votes
7answers
763 views
Examples of categorical adjunctions in analysis, Lie theory, and differential geometry?
In introductory texts on category theory, it seems like the majority of examples come from algebraic topology, algebra, and logic. Are there any good examples of adjunctions in analysis, Lie theory, ...
1
vote
1answer
219 views
What would undergraduate research consist of? [closed]
For undergraduate mathematics students looking to go to grad school, what kind of opportunities are open for research? I would assume undergrads would not be under any pressure or obligations to write ...
2
votes
1answer
142 views
Survey on functional equations and inequalities
Where can I find a comprehensive survey monograph on functional equations and inequalities from sketch to current research trends with some focus on applications (both inside and outside mathematics)?
...
-3
votes
1answer
198 views
How many of Ramanujan's discoveries have had a practical application? [closed]
I was reading about the Indian mathematician Srinivasa Ramanujan who, before dying at the age of 32, independently compiled nearly 3900 results (this is from Wikipedia). So based on this he seems to ...
21
votes
1answer
599 views
Which properties of a variety are detected by its derived category of coherent sheaves?
Context: I'm giving an informal seminar/reading group collection of talks on derived categories, following on from earlier talks giving the abstract definition. I am starting to talk about ...
11
votes
2answers
589 views
What is the longest recorded gap between “proof” of a “theorem” and discovery that the result is false [duplicate]
I hope this question is not a duplicate. I am motivated by wondering when widely accepted results may be considered have a secure place in the mathematical literature. The question is intended to ...
-5
votes
2answers
304 views
Are there any with Erdös number 1 on mathoverflow? [closed]
I learned today that one of my professors wrote a paper with Erdös and Sós back in 1985, thus granting him the honor of having his Erdös number equal 1.
I was wondering - did any of the ...
0
votes
1answer
108 views
Heat Equation on LCA Group
I am reading The Laplacian on A Riemannian Manifold. In the book, author defines the heat equation on manifold. In the situation $\mathbb R$ and $\mathbb S$, people often use Fourier transformation ...
9
votes
3answers
583 views
How to refer to plural of mathematical symbols - with or without an apostrophe [closed]
Which one is correct, $x_i$s or $x_i$'s?
Example sentence:
The $x_i$s form a sequence.
The $x_i$'s form a sequence.
7
votes
1answer
669 views
Research and exposition: how does writing “basic” books affect your “serious” research work?
I can see the benefit of writing a mathematical monograph: you revise and organize your own work and recollect the key ideas of your own research. But this applies only to books aimed at researchers ...
49
votes
4answers
4k views
Are there any serious investigations of whether “mathematicians do their best work when they're young”?
There is no shortage of anecdotes and conjectures on both sides of this widespread belief, but good supporting data either way is harder to find. Can anyone provide any references for serious ...
1
vote
0answers
223 views
On the remainder term in Taylor's formula [closed]
(1) What are the main differences, in terms of "usefulness" while solving problems (even at research level), among Cauchy, Lagrange, and Schlömilch's forms of the remainder in Taylor's formula? Could ...
12
votes
2answers
1k views
New research and re-discovering classic results in “basic” real analysis
Sometimes, it happens that researchers publish a new proof of an old well-known result in "basic real analysis" (I'm referring to what some American people may call "honors calculus"). For instance, ...
31
votes
7answers
3k views
Companion to theoretical physics for working mathematicians
In the Princeton Companion to Mathematics one reads that even pure mathematicians should know some theoretical physics and applied mathematics. What are some well-organized comprehensive companions to ...
2
votes
0answers
120 views
Comprehensive survey on mathematical modelling of neural networks: from the basic ideas to contemporary research topics [closed]
I am looking for a comprehensive survey (paper(s) or book(s)) on mathematical modelling of neural networks (both artificial and biological).
It should start from the very basic concepts of modelling ...
21
votes
5answers
1k views
Collaboration or acknowledgment?
This post is a sequel of: When should a supervisor be a co-author?
A general answer may be a proper adoption of the American patent law rejection (of a coautorship): the alleged research ...
18
votes
5answers
1k views
Collection of conjectures and open problems in graph theory
Is there something similar to the Kourovka Notebook for graph theory (or anyway an organized, possibly commented, collection of conjectures and open problems)?
6
votes
2answers
377 views
Generalization of Sylvester-Gallai theorem
The Sylvester-Gallai theorem states that it is not possible to arrange a finite number
of points so that a line through every two of them passes through a
third unless they are all on a single ...
5
votes
1answer
169 views
Survey paper on isoperimetry
I am searching for a comprehensive survey article (or more different articles) on the subject of isoperimetric problems from ancient Greece to modern mathematical physics. Could you point out some ...
6
votes
1answer
265 views
Is there a “good” reason that the universal central extension of $SL(2,\mathbb Z)$ is $Br_3$?
Let
$$ Br_3 := \langle \tau_1,\tau_2\ :\ \tau_1 \tau_2 \tau_1 = \tau_2 \tau_1 \tau_2 \rangle $$
be the braid group on three strands, and consider the surjection
$$\phi : Br_3 \twoheadrightarrow ...
23
votes
3answers
891 views
Graduate program applications that require questionnaires and other non-letter material
In the December 2014 AMS Notices, a letter to the editor (http://www.ams.org/notices/201411/rnoti-p1311.pdf) by Deconinck and Medlock addresses the problem of (math) graduate programs requiring letter ...
3
votes
2answers
472 views
Is a particular type of question about certain infinite sets still being asked?
I apologize in advance if this question is thought to be too soft or otherwise inappropriate for mathoverflow.net. Let M be the infinite set of all homeomorphism types of finite dimensional ...
11
votes
1answer
319 views
What are the current views on consistency of Reinhardt cardinals without AC?
It's well known that Reinhardt cardinals are inconsistent, provided that we have access to axiom of choice, but, as far as I know, we are clueless about this when we don't assume choice. For me, the ...
4
votes
1answer
216 views
Decidability of Frankl's union-closed sets conjecture
Is it conceivable that Frankl's union closed sets conjecture is undecidable in $\mathsf{ZFC}$, or is this quite implausible, perhaps due to the "finitistic" nature of the statement, or for some other ...
3
votes
0answers
350 views
Well-known or prolific mathematicians that have never written a sole-author article? [closed]
Dear mathoverflow community,
I have a junior colleague who will be coming up for tenure and who has written many articles, but all of them as a co-author. I don't see this as a problem (after all, ...
4
votes
1answer
149 views
What can be said about graphs if there are homomorphisms in both directions?
Let $G,H$ be simple undirected graphs without loops such that there are graph homomorphisms $f_1:G\to H$ and $f_2: H\to G$.
An easy argument shows that we have $\chi(G) = \chi(H)$, even for graphs ...
7
votes
3answers
1k views
The resolution of which conjecture/problem would advance Mathematics the most? [closed]
This is an impossibly broad question, and makes the unwarranted assumption that Mathematics is a uniform field. It might make more sense to ask the same question restricted to, say, Mathematical ...
22
votes
7answers
2k views
What problem would you base your mathcoin on?
Recently, a variant of electronic currency, based on prime sextuplets,
broke the record in generating the largest known set of six primes, packed as closely as possible, that is, a sextuple ...
2
votes
1answer
163 views
Axiomatization of Degree Theory
I am reading Ruiz's Mapping Degree Theory, and find an axiomatization of degree theory of $\mathbb R^n$ in P38. It says that there exists a unique map $d(f,D,y)\in\mathbb Z$ satisfies
Normality
...
4
votes
0answers
212 views
Etale Slice Theorem
I found the Luna's Slice Theorem very Technical. It will be helpful if someone illustrates the geometry involved in the theorem. Also why this theorem so useful?
This is Luna's Slice theorem from a ...
