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.

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33
votes
62answers
19k views

What's your favorite equation, formula, identity or inequality? [closed]

Certain formulas I really enjoy looking at like the Euler-Maclaurin formula or the Leibniz integral rule. What's your favorite equation, formula, identity or inequality?
13
votes
15answers
1k views

Most helpful heuristic?

What's the most useful piece of mathematical "folk wisdom" you've encountered? I'm talking here about things that aren't theorems, or even conjectures, or even shadows of conjectures -- just broad ...
26
votes
6answers
2k views

Errata database?

Some authors do a really great job by collecting errors and comments to their books and putting a list on their websites. I wonder if there is some (perhaps wiki-style) website where errata are ...
5
votes
5answers
708 views

Examples of well-displayed mathematics on the internet [closed]

I'm interested in hearing of examples of mathematical (or, at a pinch, scientific) websites with serious content where the design of the website actually makes it easy to read and absorb the material. ...
39
votes
19answers
8k views

Great mathematical figures and/or diagrams?

Most math papers have few figures, if any, although sometimes a well-chosen figure can be a tremendous help in understanding mathematical concepts. Does anyone have any examples of notable uses of ...
11
votes
10answers
1k views

Algorithmic Combinatorics resources?

Some branches of combinatorics lend themselves naturally to algorithms; graph theory is a natural example. However, straight-up enumerative combinatorics relies much more on analytic and algebraic ...
58
votes
10answers
4k views

Why are characters so well-behaved?

Last year I attended a first course in the representation theory of finite groups, where everything was over C. I was struck, and somewhat puzzled, by the inexplicable perfection of characters as a ...
24
votes
8answers
5k views

What is the “right” definition of a ring?

This is somewhat related to Greg's question about groups and abelian groups. Suppose you met someone who was well-acquainted with groups, but who was unwilling to accept rings as a meaningful object ...
12
votes
3answers
3k views

Are there any recordings of Grothendieck online?

Illusie mentions tape recordings of Grothendieck explaining his trace formula and more. Are they or similar recordings online? I guess, even if (what I doubt) everything he thought about that is ...
46
votes
12answers
21k views

Homological Algebra texts

I would like to hear the communities' ideas on good Homological Algebra textbooks / references. The standard example is of course Weibel (which I'll leave for someone else to describe). As usual, ...
31
votes
13answers
26k views

Mathematical podcasts/audio

Just to ask if anyone is aware of any interesting math podcasts? I am particularly interested in podcasts describing mathematics in the wider world; but interesting academic podcasts would also be ...
6
votes
3answers
777 views

“Plateaus” to watch out for [closed]

I'm a lot earlier in my math education that most of the people on this site. Currently I'm studying computer science, and I'm interested in looking into statistical and optimization applications, as ...
154
votes
36answers
35k views

Most harmful heuristic?

What's the most harmful heuristic (towards proper mathematics education), you've seen taught/accidentally taught/were taught? When did handwaving inhibit proper learning?
41
votes
77answers
10k views

What is the first interesting theorem in (insert subject here)? [closed]

In most students' introduction to rigorous proof-based mathematics, many of the initial exercises and theorems are just a test of a student's understanding of how to work with the axioms and unpack ...
9
votes
5answers
1k views

Visual representation of mathematical research interrelationships

I remember seeing a visualization in the form of a 2d (nodal) graph of all areas of academia, with math, physics and engineering over in one section, connecting in an arc to the central area of ...
30
votes
15answers
8k views

Learning LaTeX properly [closed]

I have never learned how to use Latex properly. Whenever writing a paper, I use hacks to override behavior of the underlying template. What would be an intermediate to advanced book on learning how to ...
110
votes
71answers
18k views

Most helpful math resources on the web

What are really helpful math resources out there on the web? Please don't only post a link but a short description of what it does and why it is helpful. Please only one resource per answer and let ...
234
votes
41answers
86k views

A single paper everyone should read? [closed]

Different people like different things in math, but sometimes you stand in awe before a beautiful and simple, but not universally known, result that you want to share with any of your colleagues. Do ...
49
votes
48answers
12k views

Describe a topic in one sentence. [closed]

When you study a topic for the first time, it can be difficult to pick up the motivations and to understand where everything is going. Once you have some experience, however, you get that good high-...
19
votes
9answers
4k views

Learning new mathematics

While many of us have had the experience of learning mathematics informally by osmosis or more formally in classes, there are times when we have to sit down and systematically learn, without the ...
111
votes
16answers
31k views

How do you keep your research notes organized? [closed]

One of the things I struggle with most in doing research is keeping my notes organized. Since research tends to do a lot of branching, keeping notes in a linear fashion seems useless to me. On the ...
162
votes
76answers
60k views

Best online mathematics videos?

I know of two good mathematics videos available online, namely: Sphere inside out (part I and part II) Moebius transformation revealed Do you know of any other good math videos? Share.
26
votes
9answers
6k views

How to write math well?

Let's learn about writing good mathematical texts. For some people it could be especially interesting to answer about writing texts on Math Overflow, though I personally feel like I've already ...
193
votes
42answers
71k views

Most interesting mathematics mistake?

Some mistakes in mathematics made by extremely smart and famous people can eventually lead to interesting developments and theorems, e.g. Poincaré's 3d sphere characterization or the search to prove ...
26
votes
7answers
12k views

Advice on doing mathematical research [closed]

Please share any general tips or advice you have on doing mathematical research. How do you identify good problems to work on or to think about? What do you do when you get stuck on a problem? Etc.
171
votes
88answers
42k views

Examples of great mathematical writing

This question is basically from Ravi Vakil's web page, but modified for Math Overflow. How do I write mathematics well? Learning by example is more helpful than being told what to do, so let's try to ...
86
votes
8answers
79k views

Which are the best mathematics journals, and what are the differences between them? [closed]

Suppose you have a draft paper that you think is pretty good, and people tell you that you should submit it to a top journal. How do you work out where to send it to? Coming up with a shortlist isn't ...

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