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.

learn more… | top users | synonyms

3
votes
1answer
464 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
441 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
751 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
177 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
248 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
179 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 ...
21
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
315 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
705 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
222 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
398 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 $k$ ...
47
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 ...
35
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
142 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
198 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
115 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
194 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
357 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
249 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
152 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
120 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
84 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 ...
10
votes
1answer
455 views

Listing ORCiD in LaTeX papers

The ORCiD unique author identifier, run by a non-profit organisation, has been around for a number of years now. Its stated goal is to become a de facto standard for uniquely identifying authors, even ...
2
votes
1answer
109 views

Is there any parameter space of Cramér–Rao_bound

It is known that Cramér–Rao_bound is the lower bound of variance of a parameter. A useful link is https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93Rao_bound There is also a term called ...
4
votes
2answers
298 views

Categories of finite objects

In my experience, category theory is very successful at providing powerful machinery to reason about large objects or objects unrestricted in size, for example (logical) models (via accessible ...
5
votes
1answer
376 views

soft: Reference/ Suggested Read: Homological Algebraic techniques in PDEs

I was reading this article on wikipiedia and was interested by the apparent link between Homological Algebra and PDEs. What is an accessible reference which showcases the link between these topics? ...
3
votes
0answers
231 views

Why only Normed Linear Spaces? [closed]

It is well known that "Norm on a vector space can be used to obtain a metric on that space." I think easily we can generalize the notion of norms to groups and rings. My questions are, Why ...
10
votes
0answers
555 views

Which journals publish applied mathematics with mostly pure mathematics content?

In the spirit of Which journals publish expository work? please advise: What consistently high quality journals$^1$ today publish results that would otherwise go to a pure mathematics journal if ...
0
votes
0answers
29 views

Characterization of complete lattices with join-incomplete lattice endomorphisms

Let $L$ be an complete lattice. A lattice homomorphism $f: L\to L$ is said to be join-incomplete if there is an infinite set $S \subseteq L$ such that $f(\bigvee_L S) > \bigvee_L f(S).$ How can ...
34
votes
2answers
1k views

When to postpone a proof?

One possible practice in writing mathematics is to prove every theorem and lemma right after stating it. A long, technical proof — and sometimes even a short one — can interrupt the flow ...
2
votes
0answers
175 views

Newer list of open problems in model theory

In the book Model Theory by C. C. Chang and H. J. Keisler, there is a list of open problems in model theory. More exactly, this list is called "Open problems in classical model theory" (on page 597, ...
12
votes
1answer
468 views

Which nice/deep elaborations on the (operators <-> sheaves) / (endomorphisms <-> objects) theme are there?

A linear operator $T:V\to V$ on a (say) vector space over a field $k$ is just a $k[T]$-module, and may be viewed as the sheaf $\mathscr F_T$ over $\mathbb A^1_k$, with fibre over $\lambda\in k$ equal ...