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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
1answer
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
0answers
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
0answers
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
11answers
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
0answers
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
0answers
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
5answers
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
1answer
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
0answers
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
5answers
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
1answer
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
2answers
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
3answers
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
1answer
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
0answers
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
0answers
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
1answer
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
8answers
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
4answers
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
1answer
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
1answer
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
2answers
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
1answer
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
1answer
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
2answers
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
0answers
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
1answer
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
2answers
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
1answer
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
2answers
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
0answers
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
5answers
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
1answer
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
2answers
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
10answers
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
1answer
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
0answers
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
16answers
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
2answers
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
1answer
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
1answer
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
18answers
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
1answer
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
3answers
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
5answers
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
2answers
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
0answers
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
2answers
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
2answers
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
3answers
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 ...