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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17
votes
6answers
1k views

How to cite authors from any country correctly?

It has always seemed to me that the Mathematical Community gives a high importance to the act of properly citing an author (Do not write Erdos! It's Erdős. Cauchy must be read as in French, not as in ...
29
votes
8answers
6k views

What are some important but still unsolved problems in mathematical logic?

In the past, First order logic and its completeness and whether arithmetic is complete was a major unsolved issues in logic . All of these problems were solved by Godel. Later on, independence of ...
1
vote
1answer
171 views

Is there a reason for different nomenclature on Calculus of Variations?

While sightseeing aspects of Calculus of Variations, the following fact elludes me: there is a plethora of new definitions which seem redundant to me. This phenomenom happens, of course, with other ...
-4
votes
1answer
173 views

When do Theorems (or Algorithms or Methods) Become Celebrated? [closed]

I recently noticed that certain theorems (e.g. Tutte's 1-factor theorem or, Edmond's Blossom algorithm) are attributed celebrated. A quick search on the internet yields further examples: ...
23
votes
5answers
1k views

What are the advantages of the more abstract approaches to nonstandard analysis?

This question does not concern the comparative merits of standard (SA) and nonstandard (NSA) analysis but rather a comparison of different approaches to NSA. What are the concrete advantages of the ...
9
votes
0answers
191 views

Algebraic K-theory of a ring.

I started to learn some algebraic $K$-theory and its relation to geometric topology problems. My question is : What is the list of rings such that all their algebraic $K$-theory groups are known ? I ...
5
votes
1answer
130 views

Historical refererences for Castelnuovo-Mumford regularity

Does anyone know a good reference to understand the historical background of Castelnuovo-Mumford regularity? I know the backgound for the modern commutative-algebra approach (using free graded ...
11
votes
3answers
683 views

Bibliographic request concerning an article by Bernstein and Robinson

Concerning the article "Bernstein, Allen R.; Robinson, Abraham. Solution of an invariant subspace problem of K. T. Smith and P. R. Halmos. Pacific J. Math. 16 1966 421-431" I am interested in finding ...
4
votes
3answers
600 views

About presenting hard proofs in seminar [closed]

I am in a study seminar with my advisor. By the nature of the seminar, sometimes we have to go into details of hard proofs instead of waving our hands like in an ordinary seminar. My question is: How ...
7
votes
0answers
250 views

Pedagogical question on Lie groups vs. matrix Lie groups

There are two common approaches taken in introductory texts on Lie groups: studying all Lie groups, or focusing only on matrix Lie groups. The main advantage of the latter approach is that one can ...
2
votes
1answer
466 views

How does your productivity change after receiving prizes? [closed]

Okay the question is really soft. But I am wondering about the relationship between one's productivity (namely quality of papers, number of papers published) and prizes received. So here is my ...
5
votes
1answer
210 views

Definition of a normed ring

A normed ring "should" be a monoid object in the monoidal category of normed abelian groups. There are (at least) two choices of morphisms of normed groups, namely bounded or short homomorphisms, ...
16
votes
1answer
448 views

Okounkov-Vershik approach to representation theory of $S_n$

This is a rather soft question. I was wondering if someone could explain on a fundamental and intuitive level, what the Okounkov-Vershik approach to representation theory of $S_n$ is all about. It's ...
6
votes
2answers
760 views

A new result on the Diophantine equation $x^3 + y^3 +z^3 = 3$ [closed]

The above Diophantine equation is unknown to have any further integer solutions other than $(x, y, z) = (1, 1, 1)$ and $(4, 4, -5)$. I am a prospective undergraduate mathematics student in Zimbabwe ...
3
votes
0answers
179 views

Does the reference letter writer know which school his/her letter is sent to? [closed]

I am using AMS Mathjob. I am wondering: If a reference letter writer could write different letters for different schools. To do that, He/She needs to know which school his/her letter is sent to. Can ...
31
votes
4answers
1k views

When is an erratum necessary?

A typo, a spelling error etc., in a published article, is definitely not enough for issuing an erratum. If a mistake destroys a main result, then an erratum is definitely necessary, and the proof ...
8
votes
1answer
249 views

Base schemes and Bayesian priors

One of Grothendieck's dicta about algebraic geometry is to consider "the relative situation", where one doesn't consider the category of schemes but of schemes over a fixed base scheme. In Bayesian ...
6
votes
0answers
180 views

Authorship and the exact wording of a quote about mathematics

This has been troubling me for a few days now and I just can't seem to bring Google to reveal the truth. Which brings me here despite the risk of this question being closed as off-topic. A few years ...
1
vote
0answers
51 views

Mathematical difference between broad and narrow band Spectral estimation [closed]

Is there different mathematical formulation behind spectral estimation of narrow band and wide band? By spectral estimation I mean estimating the frequencies in a given signal. Fourier transform is ...
70
votes
30answers
11k views

What are some very important papers published in non-top journals?

There has already been a question about important papers that were initially rejected. Many of the answers were very interesting. The question is here. My concern in this question is slightly ...
53
votes
3answers
4k views

What was Hilbert's view of Gödel's Incompleteness Theorems?

According to Solomon Feferman, in his slide presentation "Three Problems for Mathematics", Hilbert wrote (in regards to Gödel's second incompleteness theorem): ...the end goal [is] to establish as ...
20
votes
4answers
2k views

Publication rates in Mathematics

Have there been any studies of publication rates in Mathematics? We are trying to construct a workload model for the Faculty of Science and Engineering at my institution. Part of this involves ...
35
votes
4answers
2k views

Hilbert's (cancelled) 24th problem

Hilbert's 23 problems, ten of which were presented at the 1900 ICM in Paris, are too famous for any mathematician to not know. If one reads the descriptions of the problems in Hilbert's paper, one ...
11
votes
1answer
321 views

'Updated' book in the same spirit as Dieudonné's Panorama des mathématiques pures

Today a colleague of mine asked me if I knew of any "more modern version" of J. Dieudonné's Panorama des mathématiques pures. Le choix bourbachique. The very first thing that instantly came to my ...
6
votes
3answers
707 views

What are the usual deadlines in paper submission procedure?

I've submitted a paper to a journal 10 days ago, and I did not yet get any news from the handling editor. Of course, 10 days is quite short, but I hope I will not wait one year without any news for ...
2
votes
1answer
223 views

Where does the name $NE(X)$ come from?

Why do we call the cone of curves(effective one cycles) on a variety $X$ as $NE(X)$, what does $NE$ stand for?
2
votes
0answers
175 views

Originality of an idea [closed]

How can I verify (ensure myself) that a research question in mathematics was not already treated ? or at least see where a particular paper was cited ? thank you. PS : I hope i am posting in the ...
40
votes
9answers
6k views

How does a mathematician choose on which problem to work?

Main question: How does a mathematician choose on which problem to work? An example approach to framing one's answer: What is a mathematical problem - big or small - that you solved or are ...
3
votes
0answers
406 views

Examples of beautiful theories without applications [closed]

What are examples of beautiful theories, which have no known applications?
1
vote
0answers
92 views

Curve meeting an open subset

I would like a reference for the following (easy/classical?) result: Let $X$ be a quasi-projective irreducible algebraic variety of dimension $\ge 1$, defined over an algebraically closed field $k$ ...
46
votes
17answers
5k views

Essays and thoughts on mathematics

Many distinguished mathematicians, at some point of their career, collected their thoughts on mathematics (its aesthetic, purposes, methods, etc.) and on the work of a mathematician in written ...
36
votes
29answers
8k views

Most intriguing mathematical epigraphs

Good epigraphs may attract more readers. Sometimes it is necessary. Usually epigraphs are interesting but not intriguing. To pick up an epigraph is some kind of nearly mathematical problem: it ...
22
votes
2answers
2k views

Amount of math research published in other languages?

I'm curious what languages contribute the largest fraction of published research mathematics. That is, for a given language the percent of new research being published in that language. I'm especially ...
2
votes
0answers
143 views

What should I read to prepare for research in Number Theoretic Cryptography? [closed]

I am not sure if this is the correct place to ask this, and if it is not the correct place, I would appreciate if you could direct me to where I could get this problem answered. I have just begun my ...
2
votes
2answers
202 views

type theory that does not treat the terms of $\mathrm{Prop}$ as types

In type theory there is a type $\mathrm{Prop}$ that contains every proposition, so $p\colon\mathrm{Prop}$ (in words, "$p$ is of type $\mathrm{Prop}$") where $p$ is a proposition. In all type theories ...
1
vote
2answers
117 views

classical typed higher order logic natural deduction

Has somebody worked out a typed higher order logic? I mean something like type theory but not with this intuitionistic touch. Is there a natural deduction system for this logic?
11
votes
1answer
2k views

Mathematical writing : using an “out-of-date” notation

When I wrote my master's thesis, a professor who read it said that I should not use the phrase "A function of class $k$." but instead "A function of class $C^k$". I am not an expert about mathematical ...
3
votes
1answer
213 views

Lecture notes on Invariant theory of finite groups [closed]

I am looking for a book or lecture notes on invariant theory of finite groups. I am a beginner in this subject. Any basic references or lecture notes will be very helpful.
0
votes
1answer
195 views

A question regarding models of $ZF+I_0$ [Revised]

In his answer to user42090's mathoverflow question"Minimal Generalized Contnuum Hypothesis & Axiom of Choice", Prof. Hamkins writes: "...one can build the analogue of the symmetric models for ...
14
votes
3answers
1k views

Current Research in Numeric Mathematics

To me, as an non-expert in the field, it seems as if numeric mathematics should have lost its importance because nowadays symbolic calculations or calculations with unlimited precision are generally ...
21
votes
2answers
2k views

Derived algebraic geometry: how to reach research level math?

I know the question "how to study math" has been asked dozens of times before in many variations, but (I hope) this one is different. My goal is to study derived algebraic geometry, where derived ...
-3
votes
1answer
142 views

Encyclopedia of Mathematics?(non-Alphabetical) [closed]

Do you know any Encyclopedia of Mathematics which is in non-alphabetical order, like it starts from basic mathematics and then goes up to very advanced level. And what's the difference between say, ...
13
votes
0answers
369 views

Research situation in the field of Information Geometry

I am now doing an article survey on the field of information geometry started by S.Amari and Barndorff-Nielson. I want to know some research situation in this field. I have read (4) and parts of (3). ...
10
votes
1answer
250 views

Finding combinatorial models / statistics

In many cases in combinatorics and especially algebraic combinatorics with some representation theory, the main problem is about finding the correct statistic on a mathematical object. For example, ...
28
votes
5answers
2k views

Why should we care about “higher infinities” outside of set theory?

Let's say you are a prospective mathematician with some addled ideas about cardinality. If you assumed that the natural numbers were finite, you'd quickly vanish in a puff of logic. :) If you ...
3
votes
0answers
68 views

Can Mumford-Shah functional be adapted to lower $L^1$ space?

The well know Mumford-Shah functional functional $$ F(u)=\int_\Omega|\nabla u|^2+\mathcal H^{N-1}(S_u) \tag 1 $$ where $u\in SBV(\Omega)$ and $\nabla u$ is the absolutely continuous part of ...
1
vote
0answers
158 views

Importance and intuition of global sections in sheaf cohomology

I am trying to understand why global sections of a sheaf are "important" or interesting objects of study. Perhaps I have too weak of a background to appreciate it (and that is certainly an acceptable ...
3
votes
0answers
67 views

Families of trigonal curves with hyperelliptic limit

Suppose I have a family of trigonal curves $C\to D$ over a closed disk $D$ where the central fiber $C_0$ is hyperelliptic (this is of course possible since the hyperelliptic locus is in the closure of ...
0
votes
1answer
122 views

Is there relation between vector valued RKHS and interpolation space?

Vector valued RKHS which is covered extensively in the book "Pick Interpolation and Hilbert function spaces" . In a different context interpolation space is defined in the wikipedia link: ...
1
vote
0answers
85 views

Can we have extension of Mercer theorem to interpolation? [closed]

This question is related to Mercer theorem, Reproducible kernel Hilbert space(RKHS) and interpolation. The wikipedia links are https://en.wikipedia.org/wiki/Mercer%27s_theorem and ...