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Results tagged with soft-question
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user 9652
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.
117
votes
What are your favorite instructional counterexamples?
I like the double sequence $a_{nm} = \frac{n}{n+m}$ to show that $\lim_{n\to\infty}\lim_{m\to\infty} a_{nm}\neq \lim_{m\to\infty}\lim_{n\to\infty} a_{nm}$ .
99
votes
Mathematical games interesting to both you and a 5+-year-old child
The game "Set" seems to fit the bill. It's a card came where there are cards that show images which have four different features, each of which comes in three possibilities:
number (1, 2, or 3 objec …
53
votes
What do you do when you're stuck?
Here is an answer which may be math-specific: If you are stuck in some proof of some claim that you believe is true:
Add the missing piece as assumption and continue as planned.
50
votes
Changes forced by the pandemic
Online seminars
Research (and other) seminars have gone virtual. The obvious advantage is, that anyone can attend from basically all over the world. The page https://researchseminars.org/ compiles a h …
39
votes
Which way for reading the proofs?
My two cents on "proof-reading": It depends what you want to do with the proof.
Do you want to understand why the result is true? Then don't read to proof but try to find counterexamples and notice …
35
votes
Modeling in pure math
This one is pretty basic: linearization, e.g. replacing a nonlinear dynamic with a linear one allows to study stability and such.
Also, linearization is behind Newton's method and Taylor polynomials …
35
votes
19
votes
Examples of famous 'workhorse' theorems
Two workhorses of geometric measure theory are the covering theorems by Vitali and Besicovitch. When I first encoutered them they both seemed quite involved to state and their use was not obvious. Als …
16
votes
What's a great christmas present for someone with a PhD in Mathematics?
You may adopt a polyhedron in their name!
14
votes
Refereeing a Paper
I am not sure if this point has already be raised: If your report criticize something or votes for a revision, then give hint what the authors can do. Comments of a referee which are particularly usel …
14
votes
"Paradoxes" in $\mathbb{R}^n$
For the $n$-simplex
$$\Delta_n = \{x\in\mathbb{R}^{n+1}\ :\ x_i\geq 0, \sum x_i = 1\},$$
its "midpoint" $m = [1,\dots, 1]/(n+1)$, and its corners $e_k$ it holds that
$$\|m - e_k\|\to \infty$$
while …
- 12.7k
13
votes
Math videos containing real time rough thinking
When I taught a beginners course in analysis a few years ago I wanted to give the students an impression of how one can work on exam problems. I asked somebody to prepare a test exam (I had my exam pr …
11
votes
New grand projects in contemporary math
In numerical mathematics there is a recent new grand theme called randomized numerical linear algebra (RandNLA). One example (probably even a paradigm) is the "randomized range finder" from the paper …
10
votes
Which math paper maximizes the ratio (importance)/(length)?
Pretty late to the party here but Kantorovich's "On the translocation of masses" from 1942 is two pages. It gave a radically new look on the Monge problem of optimal transportation and can be seen as …
9
votes
Books that teach other subjects, written for a mathematician
Well, it's not exactly science, but
The Mathematics of Juggling by Burkhard Polster is written by mathematician and is for mathematicians. I may add that you can enjoy the book, even you can't juggle. …