Mathematics Stack Exchange
Mathematics Stack Exchange

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.

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.

315 questions
207
votes
9 answers

"Advice to young mathematicians"

I have been suggested to read the Advice to a Young Mathematician section of the Princeton Companion to Mathematics, the short paper Ten Lessons I wish I had been Taught by Gian-Carlo Rota, and the Career Advice section of Terence Tao's blog, and I…
Dal
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162
votes
18 answers

How do you describe your mathematical research in layman's terms?

"You do research in mathematics! Can you explain your research to me?" If you're a research mathematician, and you have any contact with people outside of the mathematics community, I'm sure you've been asked this question many times. For years…
Jared
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90
votes
9 answers

Why do mathematicians sometimes assume famous conjectures in their research?

I will use a specific example, but I mean in general. I went to a number theory conference and I saw one thing that surprised me: Nearly half the talks began with "Assuming the generalized Riemann Hypothesis..." Almost always, the crux of their…
Joseph DiNatale
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67
votes
4 answers

Is it normal to treat Math Theorems as "Black Boxes"

It seems to me that as one goes higher up in mathematics, the proof of theorems get more involved and convoluted, that at some point one must postpone (or even give up?) understanding all prior theorems, and take them as "Black Boxes" instead? Is…
yoyostein
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53
votes
6 answers

What to answer when people ask what I do in mathematics

This is not really a math question, but I think that every mathematician and student in math (specially pure) struggles with this at some point. Inevitably at some point when we're talking with family, friends, etc... which are not in academia,…
Bob
  • 539
47
votes
5 answers

Big list: books where we "...start from a mathematically amorphous problem and combine ideas from sources to produce new mathematics..."

What books are there like like Radin's Miles of Tiles , which share these particular features: Theme: "In this book, we try to display the value (and joy!) of starting from a mathematically amorphous problem and combining ideas from diverse sources…
bzm3r
  • 2,812
38
votes
1 answer

Research in differential geometry

Background: I am a 3rd-year undergraduate student interested in mathematics and theoretical physics. I have been reading some classical differential geometry books and I want to pursue this subject further. Questions: I have three questions: What…
Andrew Miller
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28
votes
6 answers

How can a high schooler get more involved in mathematics?

For a high school student interested in majoring in math and learning more about math, what kinds of mathematical research can a student in high school get involved in? How can a high school student get involved? If a high school student does…
okarin
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5 answers

Can a chemical engineer become a self-taught mathematician?

My background covers calculus, analytical geometry, linear algebra, ODEs, numerical methods, statistics. Not to mention all the physics, chemistry and typical chemical engineering subjects. I am finishing my degree but I really like math. I would…
Luan Ildefonso
  • 337
21
votes
0 answers

Compute $\lim\limits_{n\to\infty}(x_{n+1}-x_n)$ if $x_n =\sum\limits_{k=1}^{n-1}f(\frac kn)$ and $f$ continuous (but not continuously differentiable)

The following question from Furdui's book (Exercise 1.32. page 6) is an "open problem" : Let $f: [0,1] \to \mathbb{R}$ be a continuous (and not a continuously differentiable) function and let $$x_n = f\left(\dfrac{1}{n}\right) +…
Emma
  • 535
20
votes
0 answers

Need advice or assistance for son who is in prison. His interest is scattering theory.

My name is Dan Cunningham and the letter below is written by my son. I have been sending him text books and looking for answers on the internet to keep his interest up. He has progressed so far on his own and now he needs direction and assistance…
Dan Cunningham
  • 309
19
votes
1 answer

Errors in math research papers

Have there been cases of errors in math papers, that were undetected for so long, that they caused subsequent errors in research, citing those papers. ie: errors getting propagated along. My impression is that this type of thing is extremely…
Ameet Sharma
  • 2,997
18
votes
4 answers

Visual research problems in geometry

I am considering doing research in mathematics to be my career (and my life) someday. I'm a visually oriented person in general; for example, I prefer chess over cards because when I play chess, I do all my thinking by looking at the board and…
Akram Hassan
  • 1,097
18
votes
1 answer

Is Algebraic Number Theory still an active research field?

I've took an introductory course on Algebraic Number Theory during my Master's, which I really enjoyed. Now that I'm beginning to think about my PhD area, I wonder if I shouldn't go for something in that direction. However, as in practically all…
rmdmc89
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14
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3 answers

Are there any big controversies in contemporary mathematical research?

Are there any big controversies in contemporary mathematical research? Other domains contain big controversial research topics (for example string theory in physics). The specific nature of mathematics however, makes me suspect that there isn't much…
smurf
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