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Results tagged with soft-question
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user 6871
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.
37
votes
Do names given to math concepts have a role in common mistakes by students?
My favourite is this: some books use "completely reducible" for semi-simple and "irreducible" for simple. As a result, every irreducible module is completely reducible.
17
votes
10
answers
11k
views
Should one use "above" and "below" in mathematical writing?
I started thinking about this question because of this discussion:
http://sbseminar.wordpress.com/2010/08/10/negative-value-added-by-journals/
about how journals often change a paper (for the worse) …
31
votes
Most intricate and most beautiful structures in mathematics
One of the most beautiful structures, in my mind, is the classical Hopf fibration, which allows you to visualize the $3$-sphere $S^3$ as a smooth circle bundle over the $2$-sphere. When you view $S^3$ …
22
votes
Examples of great mathematical writing
Every differential geometer should read at least the first two volumes of Spivak's A Comprehensive Introduction to Differential Geometry. In particular, volume 2 is an absolute gem. Not only does it r …
8
votes
Resubmitting a paper
Since you are so early in your career, in my opinion you are much better off leaving the paper where it is and hopefully it will be published soon. It's possible that you could have initially aimed hi …
23
votes
2
answers
6k
views
Why are they called isothermal coordinates?
On a Riemannian manifold, a coordinate system is called "isothermal" if the Riemannian metric in those coordinates is conformal to the Euclidean metric:
$$g_{ij} = e^{f} \delta_{ij}$$
My question is …
- 3,540
2
votes
Video lectures of mathematics courses available online for free
There are lots of links to various pages filled with online video lectures here.
Go to "Links" on the left hand side.
Some of the links are broken or out of date, but there's still a ton of good stuff …
19
votes
Open questions in Riemannian geometry
There is also "Review of Geometry and Analysis" by S.-T. Yau (Asian Journal of Mathematics, vol. 4, no. 1, pp. 235-278, March 2000), where he discusses many big open problems in Riemannian geometry, s …
11
votes
Most memorable titles
I like Cliff Taubes's simple titles: "Gr -> SW", "SW -> Gr", and "SW = Gr". (Okay, they each also have a subtitle, but the first part is enough to tell the reader exactly what the paper is about.)