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Questions tagged [research]

For questions on the process and the impact of mathematical research, its accessibility to (new) researchers and its applicability in various fields. Do not use this tag just because your question is related to research you are doing.

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can a career in mathematical research be combined with another job? [closed]

I'm currently an undergraduate student studying maths and philosophy. I am very interested in pursuing a career in mathematical research, but I would ideally like to combine it with my other interest; ...
Tinka's user avatar
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1 vote
0 answers
63 views

What makes a mathematical theorem research paper worthy? Is it purely subjective or are there objective criteria? [closed]

There are infinitely many theorems of mathematics, but only a tiny portion of them are interesting enough to be publishable in a research journal. Is the criterion for which theorems are interesting ...
user107952's user avatar
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2 votes
0 answers
92 views

Algebraic Topology and Robotics

How active is the current research scene on the application of algebraic and differential topology to robotics? I have spent a decent portion of time researching and reading introductory papers, but ...
Tom's user avatar
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3 votes
0 answers
82 views

How to learn necessary concepts for research and avoiding a fake impression of understanding?

As an undergraduate engaged in applied mathematics research, specifically within mathematical programming, my work has quite some intersection with areas like algebraic geometry for polynomial ...
wsz_fantasy's user avatar
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1 vote
1 answer
232 views

When I finish an introductory abstract algebra book, where will I be? [closed]

In a few months, I think I'll be done with self-studying Introduction to Abstract Algebra by Nicholson. This book covers things like basic group theory, polynomials, factorization in integral domains, ...
iwjueph94rgytbhr's user avatar
1 vote
0 answers
107 views

Most accessible field for undergraduate independent research [closed]

I am studying in Europe as a mathematics undergraduate and I would like to start my own independent research in pure mathematics. I do not expect to find a field in which I would be able to prove new ...
Anonimity's user avatar
3 votes
2 answers
360 views

When to give up on a problem (for maximal learning of a specific area)? [closed]

There are many things to admire about the so-called Moore method, in which all the theorems and aspects of a course (e.g. real analysis) become problems for you to solve on your own. But sometimes, ...
Chris Sanders's user avatar
4 votes
1 answer
217 views

Is there still active research in Euclidean geometry?

Is there still ongoing and active research in Euclidean geometry? I have heard somewhere that Euclidean geometry is a solved subject with no open problems. But perhaps I heard wrong. Is there still ...
user107952's user avatar
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4 votes
1 answer
158 views

Problems in $p$-adic numbers accessible to an early undergraduate

I am going for a research internship this summer in $p$-adic numbers. I am currently taking a number theory course, and have the essentials of a first year mathematics student, like multivariable ...
Mahdi El Zein's user avatar
4 votes
2 answers
240 views

How to efficiently find articles/theory/books on topics I want to learn more about

Thank you for taking the time to open this post. My question is as follows: how do I efficiently find papers/books/talks/any academic resources that have been published about topics that I find myself ...
Connorlindquist's user avatar
2 votes
0 answers
82 views

To what extent are visual proofs acceptable

In geometry, it seems that visual proofs are much more acceptable than in for example algebra (for good reason). My question is about when visual proofs are sufficient in the context of mathematics ...
Carlyle's user avatar
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60 views

Hypothesis about products of prime numbers [duplicate]

As an undergrad I had a hypothesis about the prime numbers that goes as follows: For the nth prime P(n) and the mth prime P(m) Then P(n) * P(m) > P(n+m) The base case for prime 2 is well known: 2 * ...
Brian's user avatar
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0 answers
52 views

Doing mathematical research alone.

Currently I am no researcher in mathematics, but in the future I might consider becoming one. Before that, I want to know, out of my curiosity, that whether anyone can perform mathematical research ...
Sillyasker's user avatar
0 votes
1 answer
222 views

What is the purpose of mathematical research? [closed]

This is a bit of a soft and philosophical question, but what is the purpose of mathematical research? It seems to me that there is no end goal of mathematical research, because everything can be ...
user107952's user avatar
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0 votes
1 answer
50 views

Reference Request: Louis B. Rall, George F. Corliss: An Introduction to Automatic Differentiation SIAM, 1996

Automatic Differentiation (AD) seems like the swiss army knife of quickly solving optimization problems (involving partial derivatives) on a computer. I was looking at the website dedicated to AD. It ...
Kedar Mhaswade's user avatar
6 votes
1 answer
245 views

How do mathematicians keep track of thoughts in a quick and reproducible manner [closed]

The way I work on homework questions, especially for analysis and topology, might be a little different (or maybe not). I would remember the questions and think of them when I run, take a shower, and ...
wsz_fantasy's user avatar
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2 votes
0 answers
135 views

Connections between graph theory and applied functional analysis for PDEs

I have a relatively strong background in the theory of numerical analysis of partial differential equations (PDEs) and functional analysis, particularly applied to the numerical analysis of PDEs using ...
Raúl Astete's user avatar
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0 answers
70 views

Where can I learn about the "geometry of the equivalence classes of rationals"?

I was reading about the formal construction of the rational numbers as pairs of integers on wikipedia and was interested in the diagram (see below) illustrating the equivalence classes geometrically ...
confusedscreaming's user avatar
4 votes
1 answer
121 views

What does the equation $x^2+y^2=r^2$ represent when $x, y, r$ are complex numbers?

I know this question is vague or maybe broad and subjective. But, I am interested in studying the equation $x^2+y^2=r^2$ when $x,y,r$ are complex numbers. What are a few directions that I can follow ...
QTDA's user avatar
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2 votes
0 answers
72 views

Papers on Applied Algebraic Topology

I am taking a course on applied algebraic topology and we are tasked with presenting a paper on the subject. We were given https://arxiv.org/search/math to look for potential papers, but I am having ...
Ethan's user avatar
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1 vote
0 answers
16 views

Statistical test used to compare outcomes of patients on 2 different wards

This audit's true numbers and details have been changed to abide by confidentiality standards. An audit of the patients in a hospital of a certain specialty is carried out to assess whether you are ...
Ben Hughes's user avatar
2 votes
1 answer
220 views

Euler's constant's role in the Prime numbers

I know that: $$\lim_{k\rightarrow\infty}\frac{1}{\log p_n}\prod_{i=1}^k\frac{p_i}{p_i-1}=e^\gamma$$Where $p_n$ is the $n$th prime and $\gamma$ is Euler's constant. But why does this make the number $\...
Kamal Saleh's user avatar
  • 6,549
2 votes
1 answer
134 views

Fields of math to learn to understand this paper

I was looking at the Davidson $2021$ fellows and decided to take a look at Apoorva's paper. What fields of math do I need to learn to understand her research paper? Currently I know most of Complex ...
Kamal Saleh's user avatar
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2 votes
0 answers
384 views

Research Topics for Advanced High School Students

I am currently a junior attending a small high school that requires a project called senior thesis. Each one of us will have to come up with a topic/question on our own, work on the project and do ...
William Wei's user avatar
3 votes
1 answer
64 views

Searching Erdős paper on the lower bound of the Ramsey number

In the wikipedia article on the probabilistic method mentions in the paragraph "First Example" a proof attributed to Erdős. It is attributed to him in a 1947 paper. There is no 1947 paper in ...
Asqiir's user avatar
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11 votes
3 answers
2k views

Current research areas of Group Theory

I'm finishing an undergraduate degree in mathematics and am really passionate about group theory. Currently, my research projects have been mostly in ring theory, however (since my university does not ...
Gauss's user avatar
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0 votes
0 answers
151 views

What are some popular stereotypes of mathematical research?

I know this is a soft question, but what are some of the popular stereotypes of mathematical research? I guess that one would be that mathematicians just do hard arithmetic or algebraic calculations ...
user107952's user avatar
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0 votes
0 answers
63 views

Love Analysis, Optimization and PDEs but i dont know where i should specialise? or what is the most active field of research?

I am a student in first year of masters degree in mathematics. My backround in analysis consists of Real and Complexe Analysis, Measure Theory, ODEs and stability,Optimization, Numerical Analysis, ...
Arselane HADJ SLIMANE's user avatar
3 votes
1 answer
106 views

Is most higher level math written in English? [closed]

There are many math journals published in English. Are there a lot of math journals written in Chinese, Russian, German, French, etc. they have no English translation? Are they only accessible to ...
user1035015's user avatar
1 vote
0 answers
44 views

Is there a sub-topic of graph theory that "attaches" a function to each node/edge?

I'm going through Graph Theory by Bondy, U. S. R. Murty and trying to get a grasp of basic graph theory, and am looking for literature (if it exists) that deals with graphs in which there is a " ...
Adam Shegan's user avatar
1 vote
0 answers
381 views

Most efficient way of getting a brief overview of the current active research areas in Algebraic Topology.

I'd be applying for a Ph.D. at various grad schools in the U.S. in the coming months and while I know I'd like to pursue research in the field of Algebraic Topology, I am not knowledgeable enough yet ...
ZSMJ's user avatar
  • 1,206
3 votes
1 answer
186 views

What should you do if you have a research idea outside your area of expertise?

Background Sometimes, I have ideas for research in mathematical subjects about which I don't know much. Let me describe an example to make it more concrete. In his 2009 article "The ...
Max Muller's user avatar
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0 votes
0 answers
39 views

Can we give a dual of a minimization problem in terms of a feasibility problem in a research paper?

For a given complex Hermitian matrices $A_1,A_2$ and $A_3$, I have the following problem: \begin{equation}\tag{1} \begin{array}{ll} \underset{k\geq1,X\in\mathbb{C^{n\times n}}}{\text{minimize}} & ...
Lee's user avatar
  • 1,910
5 votes
1 answer
140 views

Research Collaboration Outside Academia

I am trying to brainstorm ways for folks interested in studying or researching math as a hobby to connect with each other. The pleasures of doing math in a social setting is something I have missed ...
Ari Herman's user avatar
0 votes
1 answer
119 views

Analytic works versus synthetic works in mathematical research

With the purpose to clarify my ideas about terminology I would like to ask in Mathematics Stack Exchange what is the difference of two verbal expressions: when a professional mathematician understands ...
user759001's user avatar
0 votes
0 answers
28 views

Process after solving a problem

I think I may be on the verge of solving a previously unsolved problem. It is not a hugely interesting or revolutionary problem. However, I was wondering if there would be something I should do after ...
mscj's user avatar
  • 69
2 votes
1 answer
64 views

Difficulty with Complex Computation in Proof on Ford Spheres

I am reading a paper on arXiv taking the idea of Ford circles and putting it into three dimensions, but am having difficulty with the following lemma, at a very basic level. Most of the details aren't ...
Thomas Anton's user avatar
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-1 votes
1 answer
62 views

Publishing Research Papers on Mathematical Software Packages

I have written some LaTeX package for Mathematics. It involves substantial work. In general only a person having good knowledge of Mathematics and TeX could develop such things. There are other ...
user61681's user avatar
  • 420
6 votes
2 answers
262 views

What topics in mathematics have no or very little research done about them, so far? [closed]

This is a bit of a soft and subjective question, but can someone give me some examples of mathematical topics or areas which have no or very little research done about them? I love reading math texts ...
user107952's user avatar
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2 votes
0 answers
38 views

Helix with mixed handedness

I'm currently interested in the mathematics and the mechanism of chirality inversion that could take place in (regular/irregular) helices, for which it possesses both left- and right-handed sections. ...
aqvadef's user avatar
  • 51
0 votes
0 answers
46 views

Has there been any mathematical research on redundancy in axiom sets?

This is a bit of a soft question, but has there been any significant research on redundancy in axiom sets? Let me explain what I mean. I know that a few papers deal with proving that a particular ...
user107952's user avatar
  • 21.4k
4 votes
1 answer
123 views

How do you know when trying to find a proof/counterexample isn't worth it?

This is quite a general question... apologies if it is too general; I'm just wondering if anyone has any useful tips or advice. As part my final year university project I've made an algebriac/...
M. McIlree's user avatar
1 vote
0 answers
60 views

Closed form of $\sum\limits_{m=0}^\infty \frac{(a)_m\text B_p(b+m,c-b)z^m}{m!}$ with the Incomplete Beta function.

This question comes from related “sum of incomplete gamma function” problems. Also,there are many research papers trying to make the Hypergeometric Incomplete. Here is one confluent example from ...
Тyma Gaidash's user avatar
0 votes
0 answers
277 views

Suggestion of topics in General Topology for PhD interview

I got shortlisted for PhD admission .I've to prepare a presentation as a part of my interview.My research interest is General Topology. I've studied Munkre's topology upto Chapter 8. Please suggest me ...
PrimeNumber's user avatar
-2 votes
1 answer
264 views

Is mathematics a deductive science?

As it was discussed, for instance, in answers to this MSE question, formal mathematical proofs are deductive in nature. The question I am interested in is: What is the nature of mathematics at the ...
iwab's user avatar
  • 203
0 votes
1 answer
265 views

Axiomatic combinatorics

I'm curious about combinatorial analysis. I have some questions about this topic because when I think of combinatorics I recall some technics to solve problems but that's all. I'm curious at a ...
Bayesian guy's user avatar
2 votes
0 answers
62 views

New/up-and-coming/lesser known mathematical topics [closed]

Having spent a lot of time with popular science, I am generally exposed to topics that are either very well-developed (like calculus) or have a very rich history (like geometry). Authors tend to avoid ...
Tham's user avatar
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0 votes
0 answers
31 views

Is there is any name of the adjacence matrix constructed in such way?

I have constructed an adjacence matrix for a non-conjugate graph of a generalized quaternion group.In this matrix if two elements which are conjugate to each other are operated gives "0" ...
Mathematics's user avatar
5 votes
2 answers
460 views

How are contributions to mathematics reviewed/published? [closed]

Let's say you're a hobbyist who's seemingly found a novel identity/solution/method or other general contribution to some field of mathematics. What you don't know however is: If you're actually the ...
Bailen Huggins's user avatar
0 votes
0 answers
62 views

Help with writing research proposal about topological divisor of zero

I have completed my M.Sc. and I want to do Ph.D. I am very much interested in Banach Algebras and the topic that has got my attention is Topological divisors of zero. I would like to study properties ...
Shreya Chauhan's user avatar

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