**3**

votes

**1**answer

384 views

### Use of infinitude of primes in the Green-Tao theorem [on hold]

In a video I watched last night on nuking mathematical mosquitos, Matt Parker gave the following proof of the infinitude of primes: suppose there are finitely many primes. The Green-Tao theorem says ...

**11**

votes

**0**answers

220 views

### Have Grothendieck's notes in Montpellier already been investigated?

Grothendieck, who passed away on November 13, 2014, left a huge amount (around 20.000 sheets) of personal notes in the University of Montpellier that he thought he was the only one to be able to ...

**-2**

votes

**0**answers

95 views

### Equilibria of 2d periodical structures [on hold]

(I've posted a similar question on Physics SE [optics] site some time ago ).
This is on finding special cases of 2d periodical structures. Central point is finding structures which correspond to the ...

**2**

votes

**0**answers

134 views

### Can we do better than zero padding of FFT?

My background is in signal processing, and never took any course related to functional analysis or even advanced algebra. But I have a strong conviction (may be wrong) that we may be do better then ...

**0**

votes

**0**answers

113 views

### Advice on dealing with the gap [on hold]

A young mathematician AA is writing a paper proving a property X for a certain model. There have been quite a few articles proving the property X for various models. One of the first ones, let's call ...

**1**

vote

**1**answer

659 views

### Hard maths on viXra? [closed]

A few years ago a nice paper surveyed the differences in quality between papers submitted to arXiv and those submitted to arXiv's rough cousin, viXra. However, that paper was about generic ...

**27**

votes

**5**answers

1k views

### Can one make high-level proofs about chess positions?

I realize this question is risky (as the title and the tags indicate), but hopefully I can make it acceptable. If not, and the question cannot be salvaged, I'm sorry and ready to delete it or accept ...

**4**

votes

**2**answers

551 views

### What is the mathematical significance of the IHES logo?

The logo of the IHES
http://www.ihes.fr/jsp/site/Portal.jsp
(upper left) is lovely, but what exactly does represent mathematically?
(There's a slightly larger version at
...

**4**

votes

**0**answers

57 views

### The metric gives the optimal element in a class

In geometry there is plenty of examples in which the following happens:
Some elements are considered equivalent, in some topological or algebraic sense
We take the quotient
The metric is usually not ...

**0**

votes

**0**answers

15 views

### “Can't” and “don't” in a mathematical paper [migrated]

I am refereeing a paper (a good one) for a mathematical journal. The author repeatedly writes like this: "we can't do", "we don't know" etc. He is not a native English speaker, and this paper is his ...

**16**

votes

**2**answers

963 views

### Why do people say DG-algebras behave badly in positive characteristic?

It seems to be a common wisdom in derived algebraic geometry that commutative DG-algebras are not, in general, a good model for derived rings, with the stated reason that they behave badly in positive ...

**-1**

votes

**1**answer

188 views

### Everyday, real-life applications of mathematical concepts, and human intuition vs mathematical analysis [closed]

I'm working on an educational project about the applications of reasonably 'lofty', high-ish-level mathematical concepts in the real world. I've already scoured these links (1) (2) (3) after ...

**-1**

votes

**0**answers

89 views

### Soft question: take complex analysis or cryptology? [migrated]

I am math major junior considering math grad school. I need to decide whether to take complex analysis or cryptology this semester. Complex analysis seems to be a recommended course for people ...

**3**

votes

**0**answers

114 views

### Pronunciation of ¡ (inverted exclamation mark, historically used for subfactorial)

For anyone who uses ¡ (inverted exclamation mark) in a mathematical context, how do you pronounce it?
Background: I have privately been using ¡ in a couple of notations for a while, and am ...

**25**

votes

**0**answers

601 views

### Greatly expanded new edition of a Bourbaki chapter on algebra?

Recently I discovered by accident that Bourbaki issued in 2012 a radically expanded version of their 1958 Chapter 8 Modules et anneaux semi-simples (like other chapters, initially in French) within ...

**1**

vote

**1**answer

841 views

### What is the modern consensus on the difficulty of infinitesimals?

At a related thread at MSE an expert in reverse mathematics noted that "As the modern consensus is that only nonstandard models have infinitesimals, it will be quite challenging to give a concrete ...

**4**

votes

**0**answers

103 views

### Geometric Characterization of Martingales

Recently I've read a paraphrasing from Ito saying that he sometimes thinks of martingales as Geodesics in a very large dimensional manifold.
My question is, is there any research studying this idea?
...

**12**

votes

**5**answers

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

**8**answers

5k 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

**1**answer

161 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

**1**answer

156 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:
...

**21**

votes

**4**answers

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

**0**answers

175 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

**1**answer

115 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

**3**answers

676 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

**3**answers

572 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

**0**answers

241 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 ...

**3**

votes

**1**answer

453 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

**1**answer

203 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

**1**answer

396 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

**2**answers

725 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

**0**answers

169 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 ...

**30**

votes

**4**answers

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

**1**answer

244 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

**0**answers

177 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

**0**answers

45 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

**30**answers

10k 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

**3**answers

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

**4**answers

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

**4**answers

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

**1**answer

305 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

**3**answers

683 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

**1**answer

220 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

**0**answers

172 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

**9**answers

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

**0**answers

347 views

### Examples of beautiful theories without applications [closed]

What are examples of beautiful theories, which have no known applications?

**1**

vote

**0**answers

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 $k$ ...

**45**

votes

**17**answers

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 ...

**34**

votes

**29**answers

7k 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

**2**answers

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 ...