# Questions tagged [soft-question]

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.

**18**

votes

**1**answer

532 views

### What to do if you notice a substantial improvement to a result in a paper whilst refereeing it?

What would you do/have you done in such a situation?
1) Hand out the improvement for free in your report
2) Wait until the result is published and then submit elsewhere
3) Inform the editor about ...

**-3**

votes

**0**answers

57 views

### Rounding to decimal places by using simple formula and basic math operations [on hold]

Is there way to round number to decimal places using just simple math operations in one formula?
No converting to text allowed.
No considerations (like "if point is..then") allowed.
No ...

**2**

votes

**0**answers

160 views

### Is there a theory behind these puzzles? (communicating by modifying data)

Consider the following puzzles:
Problem 1: Alice is given two data by Zora: a binary string $w$ of length $2^r$, and a position $p$ in the string (which we can view as an integer $0\leq p<2^r$). ...

**43**

votes

**11**answers

5k views

### What definitions were crucial to further understanding?

Often the most difficult part of venturing into a field as a researcher is to come up with an appropriate definition. Sometimes definitions suggest themselves very naturally, as when you solve a ...

**-3**

votes

**0**answers

189 views

### About article status of AMS Journals [closed]

I have recently submitted to one of the Journals of AMS. Soon after submission (within a few days) the status changed to "Article status : Reviewing" \n "Your paper is being handled by an Editor". I ...

**6**

votes

**0**answers

178 views

### Best software to do big number calculations quickly [on hold]

I am trying to do some work on some math conjecture. I am testing the conjecture numbers using very large math numbers (100+ digits ). I am currently using python to test these numbers.
In the ...

**28**

votes

**5**answers

3k views

### Should computer code be included within publications that present numerical results?

Many research papers include numerical results obtained through computation. Most of the time such computations are performed using software that is used by many mathematicians, i.e., Maple, ...

**8**

votes

**1**answer

263 views

### Polymath type websites for specialized areas

This question is inspired by the success and more importantly, the democratizing affect of the polymath projects and Mathoverflow. I put the idea in my NSF proposals a few times, but the panels don't ...

**6**

votes

**0**answers

84 views

### A generalization of matrix minors to non-integer values

I am interested to know if there exist a notion of $k$-minors of a real square matrix, for non-integer positive values of $k$
One approach I thought of was to use the fact that the $k$-minors are (...

**0**

votes

**5**answers

432 views

### Mathematical phantoms, specifically but not exclusively in applied mathematics [duplicate]

A while ago over at our sister site, there was an interesting question [not by me] with next to no answers which I feel is, fleshed out in a more precise fashion, appropriate for MathOverflow.
The ...

**36**

votes

**1**answer

2k views

### On proof-verification using Coq

So i recently learnt that there is now a certain software called ''Coq'' by which one can check the validity of mathematical proofs. My questions are:
Are there limitations on the kinds of proofs ...

**10**

votes

**2**answers

321 views

### What are the 'wonderful consequences' following from the existence of a minimal dense subspace?

In Peddechio & Tholens Categorical Foundations they quote PT Johnstone in their chapter on Frames & Locales:
...the single most important fact which distinguishes locales from spaces: the ...

**32**

votes

**3**answers

3k views

### Publishing a Simple Paper as an Undergraduate

First off I apologize if this question does not belong here, I would be happy to hear about any better locations to post this on.
I am a (first year) undergraduate mathematics student, and I recently ...

**-5**

votes

**1**answer

264 views

### Big list of “outstanding paper awards” [closed]

What are the prizes awarded for significant papers published in mathematical journals?
One of them is the SIAM Outstanding Paper Prize.
I'd be particularly interested in hearing about prizes ...

**2**

votes

**0**answers

55 views

### Reference on elliptic obstacle problem that covers the material in the lecture notes by Caffarelli

Can you recommend a modern, self-contained, readable reference that covers (approximately) the results on elliptic obstacle problem that are covered in the lecture notes by L. Caffarelli (Scuola ...

**5**

votes

**0**answers

263 views

### Theorems conditional on false conjectures

What is an example of a theorem that was conditional on a conjecture that later turned out to be false?

**5**

votes

**1**answer

234 views

### Progress towards a computational interpretation of the univalence axiom?

I will preface this by saying that I am not an expert on type theory. I am just a curious outsider slowly making my way through the HoTT book when I (rarely) have some spare time.
I am just curious ...

**26**

votes

**8**answers

5k views

### How to explain to an engineer what algebraic geometry is?

This question is similar to this one in that I'm asking about how to introduce a mathematical research topic or activity to a non-mathematician: in this case algebraic geometry, intended as the most ...

**5**

votes

**4**answers

509 views

### mixing theorem with definition (definition with proof)

I often find myself writing a definition which requires a proof. You are defining a term and, contextually, need to prove that the definition makes sense.
How can you express that? What about a ...

**3**

votes

**1**answer

203 views

### Generating function for 3 -core partitions: Part II

Let $\lambda$ be an integer partition: $\lambda=(\lambda_1\geq\lambda_2\geq\dots\geq0)$. Further, let $h_u$ denote the hook-length of the cell $u$.
We call $\lambda$ a $t$-core partition if none of ...

**5**

votes

**1**answer

119 views

### Generating function for $3$-core partitions

Let $\lambda$ be an integer partition: $\lambda=(\lambda_1\geq\lambda_2\geq\dots\geq0)$. Further, let $h_u$ denote the hook-length of the cell $u$.
We call $\lambda$ a $t$-core partition if none of ...

**15**

votes

**2**answers

644 views

### How to handle results from an unpublished paper?

I am writing a paper right now, and part of the paper makes use of a (trivial) generalization of a number of really nice theorems and constructions from a paper that was never made public. The author ...

**6**

votes

**1**answer

218 views

### How to visualize local complete intersection morphisms?

As the question title asks for, how do others visualize local complete intersection morphisms? My experiment in asking people in real life didn't pan out, so I'm consulting the MO algebraic geometry ...

**4**

votes

**1**answer

317 views

### Question on academic affiliation when submitting paper

I just finished grad school, earning a Phd in mathematics. Currently I do not know if I want to continue my academic career or not, but in the meantime I have written an article containing some of the ...

**21**

votes

**2**answers

2k views

### Should I inform the editor about a generalized result of a result in a paper under review?

Hoping that my question is appropriate for MO, I would like to ask the following question: I have sent one of the editors of a very good math journal a paper of mine which contains a main result, call ...

**4**

votes

**0**answers

96 views

### Is there a simple algebraic setup to accomodate fibres and cofibres at the same time?

If I understand it correctly, there are two mutually dual "leading principles" in homotopy theory:
never perform quotients, add structure instead;
never require subobjects, take fibres instead.
...

**10**

votes

**1**answer

649 views

### Research semester in math

Admittedly, this is a soft question.
My own experience in mathematical research has been of long periods of research, mostly characterized in long "blocks" and sporadic breakthrough.
How does this ...

**8**

votes

**2**answers

656 views

### How Much Flesh to the Bones does an Initial Online Publication need?

Background of my question is the following: I have found a solution for my question Smoothness Conditions for Planar “Mock-parametric” Spline Interpolation and while developing the solution, I ...

**3**

votes

**1**answer

517 views

### CMI at 20 conference [closed]

Just recently (September 24 - 26) there was a conference at Oxford dedicated to 20th anniversary of CMI. (https://www.claymath.org/events/cmi-20) The program looks interesting. Does anyone know if ...

**18**

votes

**2**answers

889 views

### Has Apéry's proof of the irrationality of $\zeta(3)$ ever been used to prove the irrationality of other constants?

Apéry's proof of the irrationality of $\zeta(3)$ astounded contemporary mathematicians for its wealth of new ideas and techniques in proving the irrationality of a known constant. It is often the case ...

**1**

vote

**0**answers

245 views

### Professionalism of using relevant but non-technical images in mathematics presentations to “soften” up some of the slides [closed]

Suppose someone is presenting at a mathematics conference. He or she wants to soften up some of the less-technical slides with relevant images from a site like Pexels. It seems to me that, at least in ...

**11**

votes

**5**answers

1k views

### Early examples of mathematicians publishing (from home) in a foreign language?

Today this is common, but how exactly did it start? I am looking for examples in various languages, and suggest:
Exclude Latin (as more “ancient” or “international” than “foreign”)
Exclude French ...

**2**

votes

**1**answer

113 views

### What is the Essential Difference Between Random Matrices and Random Graphs?

I have the impression, that random graphs and random matrices seem to be perceived and treated as separate areas of interest; I'm not an expert in either of the subjects, so maybe my impression is ...

**7**

votes

**2**answers

546 views

### Research in applied algebra

I am in my final year of my doctoral study in Mathematics, where my research topic is $p$-groups, specifically classification of $p$-groups by coclass. My work involves a great deal of computation in ...

**91**

votes

**10**answers

9k views

### Examples of notably long or difficult proofs that only improve upon existing results by a small amount

I was recently reading Bui, Conrey and Young's 2011 paper "More than 41% of the zeros of the zeta function are on the critical line", in which they improve the lower bound on the proportion of zeros ...

**1**

vote

**1**answer

507 views

### State-of-the-art geometry book? [closed]

For my best friend's birthday, I am looking for a geometry book. He's currently doing his math PhD and is really fond of geometry, especially hyperbolic or higher-dimensional ones, also interested in (...

**0**

votes

**0**answers

94 views

### Is there a precise relationship between ``Geometric Functional Analysis" and high-dimensional probability/information theory?

The 2009 course on GFA by Roman Vershynin (https://www.math.uci.edu/~rvershyn/papers/GFA-book.pdf) introduced the subject with this line on the course page, "...

**52**

votes

**16**answers

4k views

### What are examples of books which teach the practice of mathematics?

One may classify the types of mathematics books written for students into two groups: books which merely teach mathematics (i.e., they present theorems and proofs, ready-made, as it were) and those ...

**27**

votes

**2**answers

984 views

### Should I publish a paper if its results overlap significantly with an earlier paper?

I have a preprint X that is sitting in the ArXiv for which I am not sure if it is still worth publishing. It turns out the paper I wrote has considerable overlap with another preprint Y after one of ...

**14**

votes

**1**answer

906 views

### What happened to “Research in the Mathematical Sciences”?

The journal "Research in the Mathematical Sciences" was founded in 2014 and originally published by SpringerOpen, a division of Springer supporting Open Access journals. In the first article of the ...

**1**

vote

**1**answer

124 views

### Intuition for coercive functions

I have been working with $\Gamma$-convergence for some time now; it has lead me to wonder: What is the intuition behind coercive functions?

**69**

votes

**18**answers

19k views

### What programming language should a professional mathematician know? [closed]

More and more I am becoming convinced that one should know at least one programming language very well as a mathematician of this century. Is my conviction justified, or not applicable?
If I am right,...

**3**

votes

**1**answer

150 views

### Does the space of harmonic forms change continuously with the metric?

Let $(M,g_0)$ be a closed $n$-dimensional Riemannian manifold. Let $1<k<n$ be fixed, and let $\Delta_{g_0}:\Omega^k(M) \to \Omega^k(M)$ be the $g_0$-Laplacian. Let $H^k_{g_0}=\text{ker} \Delta_{...

**28**

votes

**3**answers

5k views

### Naming in math: from red herrings to very long names

The are some parts of math in which you encounter easily new structures,
obtained by modifying or generalizing existing ones. Recent examples
can be tropical geometry, or the theory around the field ...

**73**

votes

**5**answers

11k views

### Has incorrect notation ever led to a mistaken proof?

In mathematics we introduce many different kinds of notation, and sometimes even a single object or construction can be represented by many different notations. To take two very different examples, ...

**10**

votes

**2**answers

429 views

### What kind of computer tools topologists/geometrists use to visualize the objects they deal with?

I have recently started to read a bit about geometry and topology. Hopf fibration, Lense spaces, CW complexes, stuff that are discussed in Hatcher's Algebraic Topology and other things that require ...

**7**

votes

**0**answers

850 views

### Work of Caucher Birkar [closed]

I am asking this since the work of this Fields medallist was not covered in the related question on work of 2018 ICM plenary speakers below.
Work of plenary speakers at ICM 2018
Terry Tao has some ...

**35**

votes

**2**answers

3k views

### ICM 2018 lecture videos

Is there a place to watch ICM 2018 plenary lectures (and other lectures if possible)?
Here is the official Youtube channel of the ICM but they don't seem to be posting the lectures.
https://www....

**3**

votes

**2**answers

181 views

### Best notation for fibrant/cofibrant replacement

In Quillen's original text on model categories (homotopical algebra) he uses $Q$ and $R$ to denote cofibrant and fibrant replacement respectively.
This notation has been used by several other ...

**12**

votes

**3**answers

597 views

### General principles which lead to good questions in many concrete situations [closed]

I believe that in various fields of mathematics there are general principles which might lead to good questions and good results in many concrete situations. I would like to have a list of such ...