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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-3
votes
0answers
77 views

John H. Conway's Mathematics: a Survey

Is there any (fairly) comprehensive survey of J.H. Conway's extensive research work? Additional Information: I know from having read some books and papers of his that he has worked and is ...
0
votes
0answers
25 views

How to write an equation for a fixed range scale [on hold]

I apologize if this question isn't professional grade. I'm writing a report and I need to use an equation to express a relationship in the Methodology section. It's a two-part equation but it's the ...
-2
votes
0answers
84 views

Mathematical Expositions on Motivation [on hold]

I wanted to ask this question, However I hope that it is not too soft for this site. What I want to ask is if writing an exposition on motivation for a topic of mathematics would be relevant? I.e., I ...
2
votes
2answers
322 views

Popular books written by great mathematicians [on hold]

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, ...
6
votes
1answer
448 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, ...
0
votes
0answers
148 views

For a mathematician that English is not the native language, does he/she think in english or graph or native language? [on hold]

For example, if you are a mathematician with Chinese the native language. During your research you find most of the books or papers are in English, of course when you read them, you probably will ...
2
votes
0answers
53 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
181 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 ...
0
votes
0answers
191 views

Can mathematics get from other sciences what it got from physics? [closed]

Throughout history, physics has been an unparalleled source of '' inspiration'' for discovering/inventing mathematical ideas, which is due to its ability to describe the physical world. But can this ...
3
votes
3answers
243 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
71 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
375 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 ...
2
votes
1answer
345 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 ...
12
votes
7answers
694 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
197 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
129 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
180 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
568 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
564 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 ...
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votes
2answers
288 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 ...
8
votes
0answers
192 views

How should one interpret a requirement that a proposal in pure math be “jargon-free?” [migrated]

I'm applying for a fellowship wherein they ask for a long proposal about what I'm working on (a PhD thesis in pure math). Then they advise me that some of those evaluating me will be from non-math ...
0
votes
1answer
100 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
552 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
637 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
207 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, ...
30
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
103 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
955 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
364 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
161 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
253 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 ...
2
votes
2answers
545 views

What's so special about $1$-categories?

I have been pretty thoroughly convinced for some time now that, when thinking about mathematics, one really should be thinking 'categorically', that is, one should always be thinking of the morphisms ...
23
votes
3answers
865 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
470 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
313 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
210 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
340 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
148 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
156 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
196 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 ...
16
votes
1answer
737 views

What makes the amenability of Thompsons group $F$ such a tricky problem?

An open problem that seems to get a lot of attention every once in a while is the amenability of Thompsons group $F$. The problem seems to generate both proofs and disproofs at a fairly high rate, ...
0
votes
0answers
92 views

Degree of Map between Pseudomanifold

There are two different ways to define a degree of map. Let $M$, $N$ be smooth, and $M$ is compact, $N$ is connected. If $f\in C(M,N)$, we define $\deg f$ by smooth approximation. [Milnor/Topology ...
0
votes
0answers
96 views

Proof of Faà di Bruno's formula with convolution identity

Faa di bruno's formula can be expressed as follows $$ \frac{d^n}{dx^n}[f(g(x))] = \sum_{k=1}^{n}f^{(k)}(g(x)) B_{n,k}(g'(x),....,g^{(n-k+1)}(x)) $$ On this Wikipedia page, there is a convolution ...
28
votes
6answers
2k views

Synthetic vs. classical differential geometry

To provide context, I'm a differential geometry grad student from a physics background. I know some category theory (at the level of Simmons) and differential and Riemannian geometry (at the level of ...
8
votes
0answers
357 views

How much algebraic geometry do I need to study complex geometry?

As one can deduce from the questions I have asked on MO, I'm interested in complex geometry. I am aware that there are many facets to the field, some of which I am more comfortable with than others. ...