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Results tagged with soft-question
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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.
5
votes
How do you become a good listener?
This is perhaps not a particularly useful or practical suggestion, but here goes: Ask questions. Interrupt the lecturer every time you get lost. Of course, if you really do this, you'll get a lot more …
5
votes
Examples of "miraculous" proofs
Gromov's theorem on groups with polynomial growth has, I think, an amazing proof. It's where he introduced Gromov-Hausdorff distance and showed, using the solution to Hilbert's fifth problem, that a …
10
votes
Examples of "miraculous" proofs
It's not really a theorem and maybe not miraculous, but I think the way Gromov, in his book Partial Differential Relations solves an underdetermined system of PDEs (fewer equations than unknown functi …
24
votes
What are good non-English languages for mathematicians to know?
My impression is that the vast majority of mathematical articles written in the last 20 years are in English and that even foreign mathematicians try to write their better papers in English. It is, fo …
3
votes
Quantitatively speaking, which subject area in mathematics is currently the most research ac...
I'm skeptical that this question can be asked and answered in a meaningful manner. Do we really want to know which area of mathematics produces, say, the most papers? Or even the most citations? What …
9
votes
Memorizing theorems
I agree with Gowers 100%. I would only that my goal is always to find my own easy and obvious proof and avoid all trickery and sophistication as much as possible. When I run into an obstacle that I ca …
7
votes
Examples of "miraculous" proofs
My favorite example is Gunther’s radically simpler proof of the Nash isometric embedding theorem, which came out of nowhere.
13
votes
How Do You Go About Learning Mathematics?
I doubt there is a universal formula for this, but here's my view (expressed before on MathOverflow):
As much as possible, learn things together with others. A working seminar is a wonderful way to …
- 27.5k
98
votes
What's a great christmas present for someone with a PhD in Mathematics?
I'm surprised no one has yet suggested a lifetime supply of Hagoromo chalk.
63
votes
How has "what every mathematician should know" changed?
I advise against using MathOverflow as a guide to what most young mathematicians do or ought or learn. The last time I saw such a strong bias towards "abstract nonsense" was when I was a graduate stud …
11
votes
Research statement in PhD applications--how much is too much?
Some random thoughts:
1) I recommend that you discuss this with a professor who knows you well and show him drafts of your statement.
2) There is no reason why you need to submit the same research s …
7
votes
Accepted
Mathematical difference between entropy and energy
First, note that entropy is well-defined only if $u$ is positive. Using integration by parts, it is in fact true on the flat torus or $\mathbb{R}^n$ (if $u$ is nonnegative and decays in space fast eno …
- 27.5k
9
votes
How do professional mathematicians learn new things?
It seems to me that the most important thing to learn when you're a graduate student is how to learn more mathematics. Everything else is detail. So you do what you learned to do as a graduate student …
5
votes
What are the most overloaded words in mathematics?
"Let" (which does not meet the 15 character minimum)
0
votes
Famous mathematicians with background in arts/humanities/law etc
Frank Ryan isn't really a famous mathematician, but he was at one point famous and he did manage to get a Ph.D. in Mathematics. See Sports Illustrated article on Frank Ryan