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Results tagged with soft-question
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user 4790
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.
6
votes
Making an intuition precise
You think about it and try to clarify your ideas, till you can write them up precisely. If there is another way, I am not aware of it.
8
votes
Accepted
Jordan Curve Theorem for Manifolds
As pointed out by Francesco, part (1) is false in general; however, it is true when the first Betti number of $M$ is 0. Part (2) is correct. All this follows easily from Alexander duality, stating tha …
- 27k
27
votes
Major mathematical advances past age fifty
Zariski proved what might be arguably his greatest result, the theorem on formal functions, just after turning fifty. He also initiated a whole field of enquiry, the theory of equisingularity, in his …
28
votes
When and how is it appropriate for an undergraduate to email a professor out of the blue?
Dylan, this is a very good question, and you got really excellent advice. I have received emails from (Italian) undergraduates and graduate students asking me how to solve random exercises; furthermor …
68
votes
Accepted
Mathematically mature way to think about Mayer–Vietoris
The Mayer-Vietoris sequence is an upshot of the relationship between sheaf cohomology and presheaf cohomology (a.k.a. Cech cohomology).
Let $X$ be a topological space (or any topos), $\mathcal U$ a c …
- 27k
21
votes
Varieties as an introduction to algebraic geometry / How do professional algebraic geometers...
When you are truly fluent in scheme theory, you don't know whether you are "thinking schemes" or "thinking varieties", the intuitions are merged together.
As to learning, for most people starting wit …
40
votes
A book you would like to write
What I would really like to write is the new Da Vinci code, that is, a book that's an absolute piece of trash but sells 80 million copies. Purely for the sake of my bank account, of course.
Oh, but p …
47
votes
How to refer to a “theorem” that you have shown to be wrong
I once saw a mathematician giving a talk about a theorem that he thought he had proved, for which a counterexample had later been found. He stated the "result" as follows:
Theorem (1983–1987): Let $A …
7
votes
What is "Data" involved in a mathematical construction?
"Data" is the plural form of the Latin word "datum", which means, among other things, "thing that is given". Viewed this way, it makes perfect sense, doesn't it?
- 27k