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Results tagged with soft-question
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user 750
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.
34
votes
Accepted
What is sheaf cohomology intuitively?
One way to think about $H^1(A)$ is to use the long exact sequence not as a property of cohomology, but outright as a definition. That is, given an exact sequence of sheaves,
$$ 0\rightarrow A\rightar …
- 26.3k
366
votes
What are some examples of colorful language in serious mathematics papers?
I don't even know if this is intentional or not. In his book Teichmuller theory, John Hubbard frequently references the category of Banach Analytic Manifolds. He adheres to the convention that a cat …
- 44.4k
15
votes
Lecture notes on representations of finite groups
I enjoyed Pavel Etingof's lecture notes for his representation theory class, which can be found here:
http://www-math.mit.edu/~etingof/replect.pdf
(there is a link to it on his website)
They move fast …
- 13k
17
votes
Accepted
Why is algebraic geometry so over-represented on this site?
I agree that the founder effect is a significant factor, but I also have another (more crackpot-ish) theory. I think some disciplines, like algebraic geometry, are harder to pick up in a traditional …
- 13k
2
votes
Cocktail party math
I have a go-to math fact to bring out at parties when people want to hear one. The cute part is that they can do it themselves.
Take a pen and paper and draw a
quadrilateral. There are no
re …
- 41.1k
18
votes
What is the "right" definition of a ring?
Much like abelian groups and groups, commutative rings and non-commutative rings have different motivations in my mind.
As people have said, non-commutative rings are naturally endomorphisms of abeli …
- 13k
55
votes
Describe a topic in one sentence.
Homological algebra - In an abelian category, the difference between what you wish was true and what IS true is measured by a homology group.
- 13k