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Results tagged with soft-question
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user 78
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.
31
votes
A single paper everyone should read?
One paper that I want to share with any of my colleagues, although it is not in my field, is Doyle and Conway, Division by Three, math/0605779v1.
To emphasize why this paper is so great, let me quote …
- 4,713
35
votes
Examples of great mathematical writing
Proofs from the Book, Martin Aigner, Günter M. Ziegler, 2000.
Anyone in [mathematics] who hasn't read this [book] has led an impoverished existence.
- 4,713
2
votes
Should the "L" in the term latin/Latin square be capitalized?
A close mathematician friend of mine used to try to stick to the rule of capitalizing any word that derives from a person's name: Noetherian (not "noetherian") ring, Abelian (not "abelian") group, etc …
- 54.6k
8
votes
Which nice/deep elaborations on the (operators <-> sheaves) / (endomorphisms <-> objects) th...
What you describe in the opening of your question is most naturally an equivalence of categories, not some dimension-shifting thing between endomorphisms and objects as you suggest. Indeed, let $\mat …
- 54.6k
18
votes
Favorite popular math book
Title: The Symmetries of Things
Authors: John Horton Conway, Heidi Burgiel, and Chaim Goodman-Strauss
Description: The authors begin by introducing the general concept of geometric symmetry / regu …
- 775
37
votes
Intuition behind the definition of quantum groups
Here is an answer to question (1). I recommend that you split of question (2) as a separate question.
Define the quantum plane to be the "spectrum" of the noncommutative ring $\mathbb K\langle x,y\r …
- 54.6k
138
votes
Accepted
What is Quantization ?
As I'm sure you'll see from the many answers you'll get, there are lots of notions of "quantization". Here's another perspective.
Recall the primary motivation of, say, algebraic geometry: a geometr …
- 6,308
13
votes
Accepted
On mentioning recommenders' names in cover letter for postdoctoral applications
I have made my answer CW, because I believe the question should be.
My answer should carry very little weight, because I have never served on a postdoc committee: I am in my final months as a graduat …
- 54.6k
11
votes
Discovering and selecting conferences
Preamble: I am a graduate student at a large program, about to start a postdoc, so I can speak about what has worked for me at the (hopefully) beginning of my career.
One thing I do occasionally is t …
- 54.6k
9
votes
Impact of LHC on math ?
I am not an expert on the following aspect of LHC, so I'll bring it up but hope others will elaborate (feel free to use the community wiki features!):
One of the major contributions of LHC has been t …
- 54.6k
17
votes
Accepted
Convenient definition of "category of Riemannian manifolds"?
I'm sure the answer to your question is "it depends on the application". Here are three categories that come to (my idiosyncratic) mind.
Perhaps the most general category in the direction you're loo …
- 54.6k
21
votes
Examples of seemingly elementary problems that are hard to solve?
I will list two very hard problems in linear algebra, that are in fact closely related.
Recall that the cross product of vectors in $\mathbb R^3$ is not associative, and so if I write $v_1 \times v_ …
- 54.6k
0
votes
Jordan Curve Theorem for Manifolds
Alexander's horned sphere (Wikipedia) shows that even when the first part of your conjecture (1) holds, you cannot expect the second part to. The horned sphere is a continuous embedding $\mathbb S^2 …
- 54.6k
2
votes
2-morphisms in structured 2-categories
Let me focus in on your third example, but I'll also wave at your other two. Here's everything in full:
A symmetric strong monoidal category consists of:
0-morphisms: a category $C$.
1-morphisms: …
- 54.6k
16
votes
Are there any good websites for hosting discussions of mathematical papers?
I'm pretty sure the answer to the question as asked is "No". At present there does not seem to exist a unique web location dedicated to discussing each individual mathematical article.
It would be t …
- 54.6k