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Results tagged with soft-question
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user 18263
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
Good "casual" advanced math books
Elementary Applied Topology by Ghrist does a fantastic job surveying recent trends in the application of (co)homological methods to practical science and engineering. It goes all the way from Euler ch …
15
votes
Is it worthwhile to give off-topic talks?
Perhaps I should clarify this "answer" in light of the downvote as well as the OPs comment.
I don't intend to cause offense or make light of your situation. I went through a similar enough phase as …
3
votes
Where to break paragraphs in a proof?
I'm not sure what type of answer to give here, except don't be tasteless, and do what looks right. The obvious thing to do, if an idea is spanning multiple paragraphs, is to make it a separate proposi …
38
votes
What are some deep theorems, and why are they considered deep?
As a very concrete example of a deep theorem different from the ones you've already mentioned, I'd nominate the Atiyah-Singer Index theorem and its more general cousins for consideration in your talk. …
11
votes
Why Cohen-Macaulay rings have become important in commutative algebra?
I'm no expert on the evolution of Cohen-Macaulay rings, so I will leave that part of your question for those who actually know their history.
On a high level, Cohen-Macaulay rings are wonderful prec …
- 15.5k
15
votes
Accepted
Discrete Morse theory and chess
The quick answer to your question is no, discrete Morse theory has not been used to study chess moves yet (unless this has been done in some very obscure journal). I would like to highlight a few like …
- 15.5k
3
votes
Financial Mathematics Books
The standard reference for derivative pricing and the role of Ito calculus are still the books by Shreve called Stochastic Calculus I (discrete) and Stochastic Calculus II (continuous). The whole theo …
8
votes
3
answers
3k
views
Homology versus cohomology of Lie groups
A central advantage of cohomology theory over homology -- at least in terms of richness of structure and strength as an invariant -- is the additional ring structure from the cup product. Recall that …
- 15.5k
7
votes
Accepted
Raoul Bott's quote on Morse Theory cited by Bestvina and Kahle: where is it from?
Here is Mladen's response to my email asking this question:
I heard him say it in a colloquium talk in 2001 (I think).
Case closed, unless Bob MacPherson has a different answer.
- 15.5k
17
votes
1
answer
1k
views
Raoul Bott's quote on Morse Theory cited by Bestvina and Kahle: where is it from?
I wanted to properly cite the following awesome quote:
Every mathematician has a secret weapon. Mine is Morse theory. - Raoul Bott
Now this has been attributed to Bott in precisely two places th …
- 15.5k
22
votes
0
answers
3k
views
Origins of the Nerve Theorem
Recently, I've read two papers which have cited the Nerve Theorem, one crediting Borsuk with the result and another Leray. Here is the question:
Who was the first to prove the Nerve Theorem?
- 15.5k
55
votes
10
answers
6k
views
How often do people read the work that they cite?
I have the following question:
How likely it is that an author carefully read through a paper cited by him?
Not everyone reads through everything that they have cited. Sometimes, if one wants to …