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. Do not use this tag for easy or supposedly easy mathematical questions.

Filter by
Sorted by
Tagged with
6 votes
0 answers
576 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
8k views

Research topics restricted to students at top universities?

Hello everybody. I am a Ph.D student in North America looking for advice about my prospective research area. My supervisor works in a research area, let's say area A, so as soon as I was accepted as ...
6 votes
0 answers
291 views

Best software to do big number calculations quickly [closed]

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 ...
34 votes
5 answers
4k 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, ...
7 votes
1 answer
481 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 ...
7 votes
0 answers
138 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 (...
31 votes
3 answers
6k 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 ...
114 votes
30 answers
16k views

New grand projects in contemporary math

When I was a graduate student in math (mid-late eighties and early nineties) the arena was dominated by a few grand projects: for instance, Misha Gromov's hyperbolic groups, which spread into many ...
157 votes
28 answers
29k views

How To Present Mathematics To Non-Mathematicians?

(Added an epilogue) I started a job as a TA, and it requires me to take a five sessions workshop about better teaching in which we have to present a 10 minutes lecture (micro-teaching). In the last ...
6 votes
4 answers
603 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 ...
59 votes
7 answers
7k views

Status of PL topology

I posted this question on math stackexchange but received no answers. Since I know there are more people knowledgeable in geometric and piecewise-linear (PL) topology here, I'm reposting the question. ...
2 votes
0 answers
87 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
359 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?
249 votes
29 answers
163k views

Intuitive crutches for higher dimensional thinking

I once heard a joke (not a great one I'll admit...) about higher dimensional thinking that went as follows- An engineer, a physicist, and a mathematician are discussing how to visualise four ...
3 votes
1 answer
321 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 ...
15 votes
2 answers
899 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 ...
7 votes
1 answer
1k 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 ...
23 votes
2 answers
3k 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
108 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. ...
3 votes
1 answer
577 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 ...
7 votes
2 answers
743 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 ...
68 votes
20 answers
18k views

Fun applications of representations of finite groups

Are there some fun applications of the theory of representations of finite groups? I would like to have some examples that could be explained to a student who knows what is a finite group but does not ...
34 votes
2 answers
4k 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....
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 ...
19 votes
2 answers
2k views

The geometric median of a triangle

Let $\Omega\subset \mathbb R^n$ be a compact domain of dimension $n$. Define the geometric median on $\Omega$ as the point $m_{\Omega}\in \mathbb R^n$ such that the integral $\int_{\Omega}|x-m_{\Omega}...
7 votes
2 answers
830 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 ...
5 votes
1 answer
558 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 ...
1 vote
1 answer
689 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 (...
13 votes
7 answers
4k views

Suggestions for mathematics encyclopedia

On daily basis I need to check (and re-check and re-check...) some definitions and main theorems that are not in my research area. Usually I accomplish this by a Google-search and/or a visit to our ...
5 votes
3 answers
4k views

Physicist trying to understand modern mathematics

I'm a physicist trying to gain a deep understanding of mathematics that is required for my work.I intend to specialize in string theory which is a very math intensive branch of theoretical physics ...
11 votes
1 answer
288 views

Duality between large and small scale structures

A rather immediate reaction to seeing the definition of a coarse structure, at least to me, is to be reminded of a uniform structure. The axioms for a coarse structure $\mathcal{C}$ (defined by a ...
9 votes
3 answers
3k views

What is soliton

I am new to this word.. This is not research level problem and it is soft question in nature. Just for curiosity, i am asking.. In literature, i am finding following words:(Wikipedia+ others). ...
1 vote
0 answers
251 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, "...
31 votes
5 answers
3k views

What is the status of the Hilbert 6th problem?

As you know, the Hilbert sixth problem was to axiomatize physics. According to the Wikipedia article, there is some partial succes in this field. For example, Classical mechanics, I believe, can be ...
32 votes
2 answers
2k 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 ...
3 votes
1 answer
175 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_{...
2 votes
1 answer
1k 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?
7 votes
2 answers
1k views

Yet another graph invariant: the similarity matrix

Preliminaries Let $n \in \mathbb{N}$ and $v$ be a vertex of a graph $G$. Let the $n$-neighbourhood of $v$, $N_n(v)$, be the induced subgraph of $G$ containing $v$ and all vertices at most $n$ edges ...
6 votes
0 answers
1k 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 ...
29 votes
6 answers
37k views

Reading materials for mathematical logic [closed]

Hi everyone, the summer break is coming and I am thinking of reading something about mathematical logic. Could anyone please give me some reading materials on this subject?
34 votes
18 answers
6k views

Non-rigorous reasoning in rigorous mathematics

I was wondering what role non-rigorous, heuristic type arguments play in rigorous math. Are there examples of rigorous, formal proofs in which a non-rigorous reasoning still plays a central part? ...
24 votes
9 answers
13k views

Graduate ODE textbook

Suppose that a hypothetical math grad student was pretty comfortable with first-year real variables and algebra, and had even studied some other things (algebraic geometry, Riemannian geometry, ...
9 votes
7 answers
7k views

Review papers in mathematics

Are there review papers, literature reviews in mathematics that describe the recent developments in various fields for a newcomer? Or is the prerequisite knowledge always provided in research ...
15 votes
2 answers
1k 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 ...
56 votes
3 answers
11k views

Work of plenary speakers at ICM 2018

The next International Congress of Mathematicians (ICM) will be next year in Rio de Janeiro, Brazil. The present question is the 2018 version of similar questions from 2014 and 2010. Can you, please, ...
3 votes
2 answers
411 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
644 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 ...
39 votes
13 answers
4k views

Examples of "miraculous" proofs [closed]

Concerning the proof that $\zeta(3)$ is irrational, Van der Poorten famously noted that "Apéry's incredible proof appears to be a mixture of miracles and mysteries". Indeed, many ideas introduced in ...
41 votes
15 answers
12k views

What's so great about blackboards? [closed]

Many mathematicians seem to think that the only way to give a mathematics talk is by using chalk on a blackboard. To some, even using a whiteboard is heresy. And we Don't Talk About Computers. I'd ...
15 votes
1 answer
1k views

Math journal publishing work related to combinatorics, probability, counting problems etc.?

I'm a high school student. My peer and I have done some work on the Ballot Theorem counting problem and Catalan Numbers. We have come up with a new proof to the Ballot Theorem and we demonstrate the ...

1
20 21
22
23 24
45